universalcurriculum

Learn
About
Log in

Learning paths

Learning paths

Views

graph_3 Full curriculumExplore every unit

Log in to create personal paths

Learning path

Full curriculum

Full curriculum

close

Back to next steps

View entire curriculum

search

Absolute-temperature relations for gases Abstract interpretation Acceleration Acceptance sampling and lot-disposition risk Access-control policies, roles and permissions Accessible and inclusive interaction Accuracy, precision and measurement resolution Acid and base ionization constants $K_a$, $K_b$, $pK_a$ and $pK_b$ Acid-base behavior of salts in water Acid-base indicators and titration endpoints Acid-base neutralization and the equivalence point Acid-base titration curves AC power and power factor Actin filaments and myosin-based contractility Action and the Euler-Lagrange equations Action-potential propagation along axons Action potentials, threshold and refractory periods Active queue management and explicit congestion notification Adaptation as environment-dependent fit produced by natural selection Adaptive step-size control for ODE solvers Addition of quantum angular momenta Additive-increase multiplicative-decrease congestion control Additive-manufacturing anisotropy, defects and postprocessing Additive-manufacturing process families Additive white Gaussian noise channels Adhesive bonding, surface preparation and joint loading Ad hoc polymorphism and type-class constraints Aerodynamic force and pitching moment of a two-dimensional section Aerodynamic lift, angle of attack and stall Affine transformations and translation Affordances, signifiers, mappings and constraints Algebraic expressions Algorithm correctness Algorithms and programs Aliasing from undersampling Allele and genotype frequencies in diploid populations Allele-frequency change under viability and reproductive selection Allopatric speciation through geographic isolation and divergence Alpha, beta and gamma decay Alpha channels and compositing Alternative RNA splicing and transcript isoforms Amdahl's and Gustafson's scaling laws Amino acid protonation, zwitterions and isoelectric point Amino acid structure, chirality and side-chain chemistry Amorphous and semicrystalline polymer morphology Amortized analysis Amount of substance, the mole and molar quantities Ampère–Maxwell law Ampère's circuital law Amphipathic molecules and self-assembly in water Amplitude modulation and sidebands Amplitude quantization and quantization error Anaerobic respiration and alternative terminal electron acceptors Analog-to-digital conversion An end-to-end supervised machine-learning workflow Angles and radians Angular acceleration Angular impulse and change in angular momentum Angular momentum and torque for particle systems Angular momentum balance for a control volume Angular momentum conservation in pivoted impacts Angular momentum decomposition about the center of mass Angular momentum in fixed-axis rotation Angular position and angular velocity Anomaly detection Antiderivatives Apparent weight and weightlessness Application binary interfaces and platform compatibility Application configuration and deployment environments Application layers and separation of concerns Application metrics and dimensional telemetry Application packaging and installation Arc welding: current, voltage and shielding Area moment of inertia Arithmetic intensity and memory-bandwidth limits ARP and IPv6 Neighbor Discovery Array of structures and structure of arrays Arrays and contiguous storage Arrhenius analysis of chemical rate constants Assembly-line balancing under precedence constraints Assembly precedence, accessibility and sequence planning Asymptotic equivalences Asymptotic time and space complexity Atomic diffusion mechanisms in solids Atomic operations and hardware synchronization Atomic spectra and quantum transitions Atomic structure and chemical elements ATP-driven actin–myosin cross-bridge cycle in skeletal muscle ATP hydrolysis, phosphoryl transfer and energetic coupling ATP synthase and chemiosmotic ATP formation Attack surfaces and exposed interfaces Attention and self-attention Authenticated encryption Authentication, authorization and principals Automated software testing Automatic memory management and object reachability Autonomous differential equations and phase lines Autonomous systems and interdomain routing Autotrophy and heterotrophy as carbon-acquisition strategies Average value of a function Average velocity and speed Avogadro's law for gas volume and amount Axial deformation of bars Backpressure in network services Backpropagation and computational graphs Backtracking search Backward-compatible interface evolution Bagging and bootstrap aggregation Balanced three-phase systems Balancing chemical equations Band filling in metals, insulators and semiconductors Bare-metal reset and runtime startup Barometric pressure in an isothermal ideal-gas atmosphere Barrier synchronization and phased parallel algorithms Barycentric coordinates and interpolation on triangles Baseband and passband signals Baseband pulse shaping and intersymbol interference Base excision repair of damaged nucleotides Baseline predictors and meaningful model comparisons Basis and dimension Bayes' theorem Beam deflection by superposition and moment-area methods Beam deflection equation and double integration Bearer credentials, expiry and revocation Bell inequalities and local hidden-variable models Bellman-Ford shortest paths and negative cycles Bending stress in beams Bernoulli and binomial distributions Bernoulli function from Euler's equation Bernoulli's equation Beta reduction and normal forms Bézier curves and control points BGP path-vector routing and policy Bias-variance decomposition for squared prediction error Bifurcations in nonlinear dynamical systems Big-step operational semantics Bilinear forms and second-order tensors Binary heaps Binary linear block codes and parity-check matrices Binary representation Binary search Binary search trees and balanced search trees Bindings, free variables and alpha-equivalence Binomial coefficients and the binomial theorem Biological nitrogen fixation and assimilation Biot-Savart induced velocity of a vortex filament Biot–Savart law Bipartite graphs and matchings Bipolar junction transistor operation Bisection method for root finding Bit and symbol error probabilities Bits, bytes and integer encodings Bitwise operations and bit masks Bivariate data and association BJT operating regions and circuit model BJTs as electronic switches Blackbody radiation and emissivity Blasius laminar boundary layer over a flat plate Bloch's theorem and electrons in periodic potentials Block diagrams and interconnected systems Blocking, sleeping and wakeups Bode magnitude and phase plots Bolt preload and clamped joints Boltzmann factors and the canonical ensemble Bond enthalpies and estimating reaction enthalpy Bonding and broad property trends across material classes Boolean values and logic Boosting and additive ensembles Bootloaders and firmware updates Bootstrap resampling Bose-Einstein and Fermi-Dirac statistics Bottlenecks, capacity and utilization in production systems Boundary layers and flow separation Boundary-value problems for ordinary differential equations Bounded memory use in embedded software Bounding volumes and bounding-volume hierarchies Boyle's law for gas pressure and volume BPSK and QPSK modulation BPSK detection and bit error probability in AWGN Bragg diffraction from crystals Branch prediction and speculative execution Brazing and soldering by capillary filler flow Breadth-first search Brittle material failure criteria Broadcast domains and VLANs Brønsted-Lowry proton transfer and conjugate acid-base pairs Browser JavaScript and the DOM B-trees and storage-oriented search trees Buffer range and capacity Buffer solutions and resistance to pH change Build systems and build dependencies Bulk forming, volume constancy and true strain Bulk modulus and volumetric elasticity Buoyant force and Archimedes' principle Cache coherence in shared-memory multiprocessors Cahn-Ingold-Prelog priority rules for substituents Calcium control of skeletal-muscle contraction through troponin and tropomyosin Calcium-triggered synaptic vesicle release Calculating derivatives Calculating determinants Calculating eigenvalues and eigenvectors Calculating equilibrium composition from initial conditions Calculating inverse matrices Calibration curves and reference standards Calorimetry and thermal energy balance Calvin-cycle reduction and regeneration of RuBP Camber and zero-lift angle in thin-airfoil theory Camera and view transformations cAMP signaling through adenylyl cyclase and protein kinase A Capacitance Capacitors in AC circuits Capacitors in series and parallel Capacity of a discrete memoryless channel Capture-avoiding substitution Carbon cycling among atmosphere, organisms, oceans and geological reservoirs Carbon, electron-carrier and ATP accounting in aerobic glucose respiration Carbon skeletons and skeletal structural formulas Cardinality and comparing set sizes Cartesian coordinates and graphs Categorical features and one-hot encoding Causal consistency Causality, memory and BIBO stability Cell-cycle phases and the ordering of growth, DNA replication and division Cells as membrane-bounded chemical systems Cell-surface and intracellular receptors Cellular responses to signaling: protein regulation and gene-expression change Center of gravity and the line of action of weight Center of mass and center-of-mass motion Center of mass of continuous mass distributions Center-of-mass reference frame Center of pressure and aerodynamic center of an airfoil section Central-force motion and reduction to one body Central limit theorem Ceramic bonding, structure and property trends Certificates and public-key infrastructure Change of basis Channel capacity as a reliable-rate limit Charging conductors by electrostatic induction Chemical equations and conservation of atoms Chemical formulas and composition notation Chemical potential and the thermodynamic driving force for matter transfer Chemical reaction rates and stoichiometric rate relations Chemical reactions, activation barriers and catalysis Chemical synapses and presynaptic-postsynaptic organization Chip formation in metal cutting Chirality, enantiomers and diastereomers Chi-square diagnostics for experimental fits Chloroplast thylakoid and stroma compartmentation Choosing between dynamic arrays and linked lists Chromatin and nucleosome packaging of eukaryotic DNA Chromatin remodeling and epigenetic regulation of gene accessibility Chromosome structural variants: deletions, duplications, inversions and translocations CIDR prefixes and subnetting Circular orbits under Newtonian gravity Circulating potential flow around a circular cylinder Circulation and its relation to vorticity Circulation and the Kutta-Joukowski lift relation Citric-acid cycle as cyclic oxidation of acetyl groups Classical relative velocity and Galilean velocity addition Classical scattering in a central potential Class imbalance, thresholds, and asymmetric costs Client-server systems Clipping and viewport mapping Clocked processor datapaths and control Clocks and edge-triggered flip-flops Closed-loop op-amp voltage amplifiers Closed-loop transfer functions and the characteristic equation CNC machine axes, work coordinates and interpolation CNC part programs, tool changes and machining cycles Code generation and compiler optimization Coding-sequence consequences of base substitutions Coding-sequence consequences of insertions and deletions Coenzyme A and activated acyl-group transfer Coherent and envelope demodulation of AM Collaborative development and code review Collections and basic data structures Collective communication in parallel programs Color encoding and linear-light computation Column slenderness and inelastic buckling Combinational logic circuits Combinatorial proofs and double counting Combined gas-steam power cycles Common ancestry, lineage divergence and phylogeny Common-cause and special-cause process variation Common-emitter BJT amplification Common-ion effect on solubility Common mechanical forces Common-source MOSFET amplification Communication systems and channel impairments Comparison sorting and ordering properties Complementary DNA base pairing Complete dominance and recessiveness in heterozygous genotypes Complete ionic equations and spectator ions Complex Fourier series for periodic signals Complex impedance Complex inner products and conjugate transpose Complex numbers Complex sinusoids and frequency components Compose for multi-container applications Composite and covering database indexes Composite materials Composite quantum systems and tensor-product states Composition fractions and percentage concentrations Compressibility factor and real-gas behavior Compressors Computer hardware and input/output devices Computer networks Concentration near the boundary in high dimensions Concurrency, interleavings and race conditions Condensation and hydrolysis of biomolecular covalent linkages Conditional control flow Conditional entropy Conditional probability Conditioning and sensitivity of numerical problems Condition variables and waiting for predicates Conductivity, resistivity, and microscopic Ohm's law Conductors in electrostatic equilibrium Confidence intervals Conflict detection and resolution in replicated data Confusion matrices, precision, recall, and F1 Conservation of linear momentum Conservation of mass in fluid flow Conservation of mechanical energy Conservative forces and potential energy Conservative vector fields and scalar potentials Consistency and solution sets Consistent hashing for partition placement Constant-acceleration motion Constitutional isomerism and molecular connectivity Continuations and continuation-passing style Continuity Continuous- and discrete-time signals Continuous delivery and release pipelines Continuous integration Continuous random variables and probability density functions Continuous-time convolution Continuous-time impulse response of LTI systems Continuous-time poles, natural modes and stability Continuous-time step and Dirac impulse signals Continuous-time transfer functions Control charts for monitoring process stability Control-flow graphs and dataflow analysis Controllability of linear state-space systems Controls, reversals and null tests in experiments Convective heat transfer Convergence and order of numerical methods Convergence of series Convex optimization and global optimality Convex sets and convex functions Convolutional neural networks Cooperative superloops and event-driven firmware Coordinate measuring machines and geometric inspection Coordinates in a basis Coordinate spaces and transformation chains in graphics Correlation Corrosion-control strategies Coulomb's law and electrostatic force Countable infinite sets Counting experiments and background subtraction Counting principles Counting semaphores and permits Coupling, cohesion and dependency direction Covalent bonds and electronegativity Covariance Covariant derivatives, connections and geodesics Covectors and dual spaces C programming CPU cache hierarchy and cache lines Cramer's rule Creep deformation and creep curves Creep mechanisms and deformation-mechanism maps Cross-compilation and target toolchains Cross-entropy Cross-language linking and foreign-function interfaces Crossover interference and coefficient of coincidence Cross product Cross product through determinants and duality Cross-site request forgery Cross-site scripting and contextual output encoding Cross-validation Cryptographic hash functions Cryptographic randomness, nonces and replay Crystallographic directions, planes and Miller indices Crystal structure and atomic order in materials CSS Curl Curl-free fields and existence of scalar potentials Current density and drift velocity Curry-Howard correspondence Curved-arrow notation for electron-pair movement Cutting forces, power and specific cutting energy Cutting speed, feed, depth of cut and material removal rate Cutting temperature, lubrication and cutting fluids Cutting-tool wear and Taylor tool life Cycle time, lead time and takt time Cyclic photosynthetic electron flow and ATP-to-NADPH balancing Cyclin-CDK control and checkpoints of cell-cycle progression Cytokinesis as physical separation of daughter cells D'Alembert's paradox and the limits of inviscid potential flow Dalton's law of partial pressures Darcy-Weisbach pipe-friction loss and friction factor Database-backed web applications Database constraints and normalization Database indexes Database query plans and index selection Database schema migrations Database transactions Data-entry forms and validation feedback Data latches and race conditions Data layout, alignment and padding Data leakage in machine learning Data-oriented design Data parallelism and parallel loops Data partitioning and sharding Data replication and replica lag Dataset bias and subgroup evaluation in machine learning Data types Datums and geometric tolerances DC generator operation DC machine construction and commutation DC machine electromechanical relations DC motor operation DC operating points in nonlinear circuits Decibels and logarithmic power ratios Decimal and fixed-point arithmetic Decimal notation and place value Decision trees for prediction Deep drawing of sheet metal Defense in depth Denotational semantics Density-based clustering with DBSCAN Density-dependent and density-independent population regulation Density of states Density, porosity and relative density of materials Dependent types Depth buffering and hidden-surface visibility Depth-first search Derivative control and damping Deriving and testing rate laws from reaction mechanisms Descriptive statistics Designed experiments: factors, responses, randomization and replication Design for additive manufacturing Design for assembly and part-count reduction Design for manufacturability and process-aware product design Determinants Determining reaction orders by the method of initial rates Deterministic chaos and Lyapunov exponents Deterministic linear state-space models Detritus, decomposers and mineralization of organic matter Device controllers and memory-mapped I/O DHCP and automatic host configuration Diagonalization Dielectrics and polarization Differentiability of multivariable functions Differential criteria for convexity Differential form of Maxwell's equations Differential rate laws and reaction orders Diffraction gratings and spectral orders Diffraction-limited angular resolution and the Rayleigh criterion Diffraction of light Diffusion from random molecular motion and concentration gradients Diffusion models and iterative denoising Diffusive flux and Fick's first law Digital color channels and RGB Digital data acquisition in experiments Digital registers Digital signatures Digital symbols, bit rate and symbol rate Digital-to-analog conversion Dijkstra's shortest-path algorithm Dilution and stock solutions Dimensional metrology with calipers, micrometers and comparators Dimensioning and size tolerances Dimensions and dimensional consistency Diode clipping and clamping circuits Diode current-voltage behavior and circuit models Diode rectification and smoothing Directed graphs and directed acyclic graphs Directional derivatives Directional, stabilizing and disruptive selection on quantitative traits Direct memory access Direct proof and counterexamples Discrete memoryless channels Discrete random variables and probability mass functions Discrete-time convolution Discrete-time Fourier transform Discrete-time impulse response of LTI systems Discrete-time Markov chains Discrete-time poles, natural modes and stability Discrete-time step and impulse signals Discrete-time transfer functions Discretizing fluid equations Disjoint-set union Dislocations, slip and plastic deformation in crystals Displacement thickness, momentum thickness, and boundary-layer shape factor Distance-vector routing Distributed consensus Distributed-memory parallelism and message passing Distributed systems and partial failure Distributed transactions and two-phase commit Distribution shift and out-of-distribution generalization Divergence Divergence-free fields and vector potentials Divergence theorem (Gauss's theorem) Divide-and-conquer algorithms Divide-and-conquer recurrence analysis Divisibility and prime numbers Django DNA damage and mutations as distinct genome changes DNA double-strand breaks and the problem of restoring chromosome continuity DNA ligase and sealing of phosphodiester-backbone nicks DNA replication fidelity and polymerase proofreading DNA sequence substitutions, insertions and deletions DNA strand structure and double-helical organization Docker Domain decomposition and halo exchange Domain Name System Doppler effect Dot product Double integrals Drilling and hole-making operations Driven damped harmonic oscillator Ductile material failure criteria Dynamic dispatch and method lookup Dynamic memory allocation in C Dynamic programming Dynamic RAM and memory refresh Dynamic routing and convergence Dynamics of rolling without slipping Ecological disturbance and succession Ecological niches as multidimensional resource use and environmental requirements Ecological organization from organisms to populations, communities and ecosystems Ecological pyramids of energy, biomass and abundance Eddy currents, magnetic braking and induction heating Effective potential in central-force motion Effect systems Eigenvalues and eigenvectors Elastic column buckling Elastic, inelastic, and perfectly inelastic collisions Elastic strain energy and strain-energy density Elastic wave speed from stiffness and density Electrical breakdown and impact ionization Electrical machine losses and efficiency Electrical power and energy transfer in circuit elements Electrical synapses and gap-junction coupling Electric charge Electric current Electric dipole moment and torque in an electric field Electric-dipole radiation Electric-dipole transitions and selection rules Electric field Electric flux Electric potential Electrochemical cells and electrode potentials Electrochemical corrosion of metals Electrochemical gradients across membranes Electrolytes and ionic species in aqueous solution Electromagnetic momentum and radiation pressure Electromagnetic radiation from accelerating charges Electromagnetic spectrum Electromagnetic torque in rotating machines Electromagnetic waves Electromechanical energy conversion Electromotive force and internal resistance of a source Electron shells and the quantum origin of atomic structure Electron shells, valence and ions Electrostatic boundary-value problems Electrostatic fields and potential functions Electrostatic multipole expansion Electrostatic potential energy of charge configurations Elementary charge and charge quantization Elementary functions Elementary multivariable functions Elementary reactions, molecularity and reaction intermediates Element stiffness and finite element assembly Elliptic wing loading and the finite-wing lift-curve slope Embedded memory maps and linker scripts Embedded testing and hardware-in-the-loop Embedding language runtimes and native extensions Endocytosis, exocytosis and vesicular membrane transport Energy balance for a fixed control volume Energy bands and charge carriers in solids Energy flow versus matter cycling in ecosystems Energy in simple harmonic motion Energy per bit and $E_b/N_0$ Energy stored in a capacitor and in the electric field Energy, transfer and conservation Engineering drawings and orthographic projection Enthalpy and constant-pressure energy changes Entropy and the second law of thermodynamics Entropy balances and entropy generation Entropy changes of a system, surroundings and universe Entropy changes of ideal gases Environments and stores in language semantics Enzymes and biochemical catalysis Epsilon-delta definition of limits Equality-constrained optimization and Lagrange multipliers Equalization of linear communication channels Equations of state Equilibrium constants from standard Gibbs free energy Equilibrium expressions and the equilibrium constant Equilibrium pH calculations for weak acids and bases Equilibrium response to concentration and volume changes Equivalence principle and gravity as spacetime geometry Equivalence relations and partitions Equivalent conditions for invertibility Equivalent resultant force and moment of a distributed load Error budgets and reliability trade-offs Error prevention, recovery and undo Error-proofing assembly and manufacturing operations Errors, testing and debugging Ethernet and local frame delivery Ethernet switching and MAC learning Euclidean duality Euclidean geometry in higher dimensions Eukaryotic organelles and intracellular compartmentalization Eukaryotic pre-mRNA processing into mature mRNA Eukaryotic transcriptional regulation by cis elements and transcription factors Euler angles and gimbal lock Euler equations for rigid-body rotation Euler momentum equation for inviscid fluid flow Euler's method for initial-value problems Euler turbomachinery equation for rotor work Eutrophication, algal blooms and oxygen depletion Evaluating clustering without labels Evaluation contexts Evaluation strategies Eventual consistency Evolutionary fitness as relative contribution to future generations Evolution as change in heritable population composition across generations Exceptions to the octet model Exchange interactions and spin models Executable loading and dynamic libraries Execution tracing, spans and trace context Exergy and the dead state Exergy destruction and second-law efficiency Existence and uniqueness proofs Expand-and-contract database changes Expectation-maximization for latent-variable models Expected value Exponential distribution Exponential functions Exponential population growth from a constant per-capita rate Exponent laws Expressions and operators Extrusion and drawing through dies Facilitated diffusion through membrane proteins Factorial experiments and interaction effects Factoring polynomials False sharing and cache-line contention Faraday's law of induction Fatigue crack growth and the Paris law Fatigue failure and S-N curves Fatigue in bolted joints Fatty acids, saturation and triacylglycerols Feature engineering and basis expansion Feature flags and separating deployment from release Features, targets, and the design matrix Feedback and visibility of system status Feedback loops and closed-loop regulation Fermentation as regeneration of oxidized electron carriers Feynman diagrams as perturbative interaction bookkeeping Feynman's sum over paths Fiber-reinforced composites and anisotropy Fick's second law and transient diffusion Files and filesystems Finite-difference discretization of differential equations Finite element degrees of freedom and shape functions Finite element discretization and meshes Finite element solution, post-processing and mesh convergence Finite-wing planform geometry, taper, and aspect ratio FIR and IIR digital filters First-order exponential decay and half-life First-order linear differential equations First-order LTI systems and time constants First-order terms and unification Fixed-point combinators and recursion in lambda calculus Fixed-point iteration Fixed points of functions FlatMap, bind and monadic composition Floating-point representation Floating, sinking, and neutral buoyancy Flow stress and plastic work in metal forming Fluid drag Fluid flow, streamlines and flow rate Fluid-mosaic organization of biological membranes Fluid pressure variation and hydrostatics Fluid properties and the continuum model Flux Force Force and equilibrium from potential energy Forced second-order linear ODEs and undetermined coefficients Forced vibration as a frequency-response problem Force–velocity relationship of skeletal muscle Forging and die-controlled material flow Formal charge in Lewis structures Formal syntax and metavariables Founder effects and population bottlenecks as episodes of strong genetic drift Fourier transform Four-momentum and invariant mass Fractions, ratios and proportions Fracture toughness, crack-tip plasticity and toughening Framebuffers, refresh and double buffering Free-body diagrams Free fall near Earth's surface Frequency and phase modulation Frequency response of LTI systems Frequency-selective filtering From molecular motion to continuum fluid fields Fully developed laminar flow in a circular pipe Functional groups in organic molecules Function call stacks and stack frames Functions and parameters Functions as mappings between sets Fundamental interactions and mediator fields Fundamental theorem of calculus Fusion welding and weld-pool solidification Gain margin and phase margin Galvanic corrosion and area effects Gametes, fertilization and restoration of diploid chromosome sets Gas density and molar mass from the ideal-gas law Gauge freedom in electromagnetic potentials Gaussian elimination Gaussian mixture models Gaussian quadrature Gauss's law for electricity Gauss's law for magnetism Gene expression as production of functional RNA and protein Gene flow as movement of alleles between populations Gene loci, alleles, genotype and phenotype General-purpose digital input and output Generated EMF and back EMF Generative and discriminative classification Generative models and probability distributions over data Genes, genomes and chromosomes as levels of genetic organization Genetic drift as random allele-frequency change in finite populations Genetic map distance and centimorgans Geometric stereoisomerism from restricted rotation Geometric twist, aerodynamic twist, washout, and washin Gibbs free energy and spontaneity at constant temperature and pressure Git Glasses and amorphous inorganic networks Glass transition and melting in polymers Glass transition and structural relaxation in amorphous materials Glycolysis from glucose to pyruvate Glycosidic bonds and polysaccharide architecture Go programming G-protein-coupled receptors and heterotrimeric G-protein activation GPU SIMT execution and branch divergence Gradient Gradient descent Grains and grain boundaries in polycrystalline materials Grand canonical ensemble and grand potential Graph representations for algorithms Graphs, vertices and edges Gravitational binding energy and escape speed Greatest common divisors and the Euclidean algorithm Greedy algorithms Green's functions for linear differential equations Griffith energy balance for brittle fracture Grinding and abrasive machining Gross and net primary productivity Grouped and depthwise-separable convolutions GTP-binding proteins as molecular switches Gyroscopic precession Hall-Petch grain-size strengthening Hamiltonian mechanics and canonical momentum Hamilton's equations and phase-space trajectories Hamming distance and error-control coding Happens-before and Lamport logical clocks Hardness and indentation testing Hardware interrupts Hardware timers and counters Hardy-Weinberg equilibrium as a null model of allele transmission Harmonic oscillator equation and sinusoidal solutions Hash tables Health checks, readiness and graceful service lifecycle Heap allocator design and fragmentation Heartbeats, failure detection and leases Heat capacity and sensible heating Heat engines, refrigerators and coefficients of performance Heat exchangers as control volumes Helmholtz free energy and natural variables of thermodynamic potentials Henderson-Hasselbalch relation for buffer pH Heritable variation as the raw material for evolutionary change Hermitian and unitary operators Hess's law and thermochemical reaction cycles Heterogeneous CPU-GPU memory and data transfer Heterogeneous equilibria and pure phases Heuristic evaluation of interfaces Hidden terminals and collision avoidance Hierarchical clustering and dendrograms Higher-order derivatives Higher-order functions and function composition High-pressure aluminium die casting Hindley-Milner type inference and let polymorphism Hoare logic and program assertions Homeostasis as dynamic negative-feedback regulation Homogeneous coordinates for affine transformations Homogeneous second-order linear ODEs with constant coefficients Homologous recombination by strand invasion and template-directed repair Homology, analogy and convergent evolution Hooke's law Hot working, cold working and forming temperature How the Web works HTML documents HTML forms and form submission HTMX HTTP Human-computer interaction and usability Huygens' principle and wavefront propagation Hybrid zones, reinforcement and outcomes of secondary contact Hydrogen bonding Hydrophobic effect and nonpolar association in water Hypercubes and high-dimensional corners Hyperparameters and model selection Hypothesis spaces and empirical risk minimization Hypothesis testing I²C addressed serial communication ICMP errors, reachability and path diagnostics Ideal operational amplifier model Ideal rocket equation Ideal transformer Idempotency and request deduplication Identical particles and exchange symmetry Identity and inverse matrices Image formation with mirrors and lenses Implication, equivalence and logical consequence Implicit differentiation Implicit surfaces and signed distance fields Improper integrals Improving Brayton-cycle performance Improving Rankine-cycle performance Impulse Incident response and post-incident learning Inclusion-exclusion principle Incomplete dominance, codominance and multiple alleles Incompressible Navier-Stokes equations Independence of events Independent assortment and crossover as sources of meiotic chromosome variation Independent assortment of unlinked loci in genetic crosses Indeterminate forms Induced electric dipoles and polarization of neutral matter Inductance Induction in a rotating magnetic field Induction machine construction Induction motor operation Induction motor torque-speed characteristic Inductive bias and the no-free-lunch principle Inductive definitions and structural induction Inductors in AC circuits Inequality constraints and Karush-Kuhn-Tucker conditions Inertial frames and the postulates of special relativity Inertia tensor and principal axes Inextensible-rope constraints in pulley systems Inferring physical relations by dimensional analysis Information and data Information architecture and navigation Initial and final value theorems for Laplace transforms Initial-value problems, existence and uniqueness Injection-molding cycle and pressure-driven filling Injection-mould part design, shrinkage and warpage Injection vulnerabilities and code-data separation In-phase and quadrature signal representation Input and output Inserting a dielectric into a capacitor at fixed charge or fixed voltage Insertion sort Instantaneous acceleration Instantaneous mechanical power from force and velocity Instantaneous velocity Instruction pipelining and pipeline hazards Instruction set architectures and microarchitectures Instrument response, bandwidth and loading Integers Integral control and elimination of persistent error Integrated rate laws and concentration-time behavior Integration techniques Integration with parameters Intensive, extensive and specific thermodynamic properties Interaction latency and perceived responsiveness Interatomic potential energy and equilibrium spacing Interfaces, contracts and information hiding Interference of light Intermediate value theorem Internal energy, heat and the first law of thermodynamics Internal shear force and bending moment in beams Interpolating orientations with quaternions Interpreter locks and free-threaded runtimes Interprocess communication Interrupt handlers and foreground-background concurrency Interspecific competition, competitive exclusion and resource partitioning Interval map distances from three-point crosses Intrinsic and doped semiconductors Introduction to definite integration Introduction to differentiation Introduction to electric circuits Introduction to limits Introduction to linear systems Introduction to matrices Introduction to multiple integration Introduction to ordinary differential equations Introduction to physics Introduction to probability Introduction to series Introduction to sets and set operations Introduction to vectors Introduction to waves Inverse Laplace transforms and partial fractions Inverse lifting-line design for a target span loading Inverse trigonometric functions Inviscid potential flow around a circular cylinder Ionic bonding and electrostatic crystal cohesion Ionic equilibrium potentials and the Nernst equation Ionotropic and metabotropic neurotransmitter receptors Ion product $Q_{sp}$ and the precipitation threshold IP addressing IP routing IPv6 router discovery and stateless address autoconfiguration Iron-carbon phase diagram and steel microstructures Isentropic efficiencies of turbines and compressors Isentropic efficiency of nozzles Isentropic ideal-gas relations Isometric, concentric and eccentric skeletal-muscle contractions Isotopes and average atomic mass Iterative methods for linear systems JavaScript programming Joining-process families and joint design Joint random variables Judgments and inference rules Kelvin's circulation theorem for inviscid flow Kepler orbits from inverse-square gravity Kernel and image Kernel methods and the kernel trick Kernel modules, drivers and the trust boundary Kernel structure and user-space system services Keyboard focus and input-independent interaction Key exchange and forward secrecy Keyframe animation and interpolation Keys and relationships Keystone species, foundation species and indirect community effects Kinematic boundary condition for a moving fluid interface Kinetic energy Kinetic energy of translating and rotating rigid bodies Kinetic molecular model of an ideal gas Kirchhoff's circuit laws k-means clustering k-nearest neighbors Kruskal's minimum-spanning-tree algorithm Kullback-Leibler divergence Kutta condition and circulation selection at a sharp trailing edge Lagrangian duality and duality gaps Lagrangian mechanics Laplace transform Laplace transforms of derivatives Latent heat and phase-change enthalpy Lattice vibrations and phonons Law of large numbers Layer-2 loops and spanning-tree forwarding Lead and lag compensation Leader election and epochs Leading- and lagging-strand synthesis at DNA replication forks Learning curves and diagnosing generalization Least privilege Least squares as a Gaussian noise model Legendre transforms Lewis acids and bases as electron-pair acceptors and donors Lewis structures and the octet model Lewis symbols and valence-electron counting Lexical closures and captured environments L'Hôpital's rule Life-history trade-offs in survival, growth and reproduction Life tables, survivorship and age-specific reproduction Lift, induced drag, and span efficiency from lifting-line coefficients Ligand-gated ion channels as fast cell-surface receptors Ligand-receptor binding affinity and fractional occupancy Light as electromagnetic radiation Light, wavefronts and rays Likelihood and maximum likelihood estimation Limiting and excess reactants Limiting nutrients and controls on ecosystem productivity Linear and affine type disciplines Linear channel models and impulse responses Linear combinations Linear difference equations as discrete-time systems Linear differential equations and superposition Linear differential equations as continuous-time systems Linear drag and terminal velocity Linear independence Linear inequalities Linearity and time invariance of systems Linearizability and single-copy behavior Linear least-squares optimization Linear momentum Linear momentum balance for a control volume Linear ODE systems and eigenmodes Linear photosynthetic electron flow from water to NADPH Linear programming and feasible polyhedra Linear quadratic regulation Linear transformations Line integrals of scalar fields Line integrals of vector fields Lines and slope in the coordinate plane Link budgets and power margins Linked lists Linked loci and coupling versus repulsion phase Link-layer frames and MAC addressing Link-state routing Liouville's theorem in phase space Little's law for stable flow systems Load balancing in parallel computations Load sharing in preloaded bolted joints Local and global optima and stationary points Local conservation laws for fluid flow Local illumination and surface shading Locating, clamping and the 3-2-1 fixturing principle Lock-free and wait-free progress guarantees Logarithmic functions Logic gates and digital signals Logic programming with facts, rules and queries Logistic population growth and carrying capacity Logistic regression for binary classification Longitudinal wave equation in a slender elastic rod Loop invariants Loops and iteration Lorentz force Lossless source coding and the entropy bound Lower bounds for comparison sorting Low-power modes and wake-up sources Lubrication approximation for thin viscous gaps Luenberger state observers Machine data widths and runtime representations Machine-level control flow Machine-level function calls and calling conventions Magnetic circuits Magnetic core losses Magnetic dipole moment and torque of a current loop Magnetic field Magnetic field on the axis of a circular current loop Magnetic flux Magnetic force on a current-carrying conductor Magnetic hysteresis Magnetic materials Magnetic saturation Magnetomotive force and reluctance Manufacturing process families and capability envelopes Manufacturing process planning and operation routing Mapping over computational context MapReduce and shuffle-based data parallelism Matched filters and correlation receivers Material condition modifiers in GD&T Material derivative in fluid flow Material-extrusion additive manufacturing Material performance indices from design constraints Material selection by screening, ranking and supporting information Mathematical induction Mathematical statements and quantifiers Matrix addition and scalar multiplication Matrix multiplication Matrix representation of linear systems Matrix representation of linear transformations Matrix transpose and symmetric matrices Maximum a posteriori estimation as regularized inference Maximum-margin classifiers and support vector machines Maximum parsimony for comparing phylogenetic tree hypotheses Maxwell-Boltzmann velocity distribution Maxwell relations in thermodynamics Maxwell's equations Measurement-system analysis and gauge R&R Mechanical advantage Mechanical energy equation for incompressible pipe systems Mechanical power Mechanical waves Mechanical work Meiosis I as reductional segregation of homologous chromosomes Meiosis II as sister-chromatid segregation without intervening replication Meiotic homolog pairing, synapsis and crossover formation Membrane channels and carrier proteins Membrane electron-transport chains and redox-driven proton pumping Memoization Memory and storage Memory consistency and acquire-release synchronization Memory corruption and control-flow hijacking Memory-corruption exploit mitigations Memory latency, bandwidth and the memory wall Memory protection and page permissions Memory-safety vulnerabilities Mendelian segregation of alleles through meiosis and fertilization Mental models and conceptual models Merge sort Message authentication codes Message delivery semantics Message queues and publish-subscribe systems Metabolic pathways, flux and feedback regulation Metal casting and solidification Metallic bonding and delocalized electrons Method of joints for trusses Method of sections for trusses Metric tensor and curved spacetime Metropolis-Hastings sampling Microcontroller clocks and clock trees Microcontrollers and embedded systems Microscopic origins of magnetic susceptibility Microstructural imaging with optical and electron microscopy Microtubule polarity, dynamic instability and organizing centers Middleboxes and the end-to-end principle Milling and chip load per tooth Minimum spanning trees Missing data and imputation for machine learning Mitochondrial oxidative phosphorylation Mitosis and sister-chromatid segregation Mitotic spindle assembly and bioriented kinetochore attachment Mixed quantum states and density operators Mixing and frequency translation Mixing chambers and stream energy balances Model interpretability and feature importance Models of computation Modes and mode errors Modes of cell-cell signaling and target-cell specificity Modular arithmetic Modular inverses and linear congruences Mohr's circle and principal stresses Molarity and molar concentration Molar mass from a chemical formula Molar solubility from $K_{sp}$ Molecular conformations and rotation about single bonds Molecular polarity and intermolecular forces Molecular sequence evidence for phylogenetic inference Moment of inertia Moment of inertia of continuous mass distributions Momentum balance for variable-mass systems Monosaccharide structure, cyclization and anomers Monte Carlo estimation by random sampling Monte Carlo path tracing MOSFET operating regions and circuit model MOSFETs as electronic switches MOSFET structure and field-effect operation Motional electromotive force in moving conductors Motion of a charged particle in a uniform magnetic field Motor units and recruitment of skeletal-muscle force MTU, fragmentation and Path MTU Discovery Multiclass classification strategies Multicore parallelism and thread scheduling Multiple-degree-of-freedom vibration and normal modes Multiple linear regression Multivariable functions Multivariable limits Multivariate normal distributions Muscle twitches, temporal summation and tetanus Mutual exclusion, locks and deadlock Mutual inductance and coupled coils Mutual information Myelin and saltatory conduction NAD, NADP and FAD as reversible biological electron carriers Naive Bayes classification Natural numbers Natural selection from heritable differences in reproductive success Net ionic equations Network address and port translation Network congestion and congestion collapse Network data plane and control plane Network queues and the bandwidth-delay product Network sockets and endpoint lifecycle Neural networks and activation functions Neuromuscular junction and motor end-plate excitation Neuron structure and polarized information flow Neurotransmitter clearance and termination of chemical synaptic signals Neutrino mixing and oscillations Newtonian gravitation and gravitational fields Newton's laws of motion Newton's method for root finding Newton's method for unconstrained optimization Newton's shell theorem and gravity of spherical bodies Nitrification and denitrification as microbial nitrogen redox transformations Noether's theorem for mechanical symmetries Nonblocking sockets and readiness multiplexing Nondestructive testing and defect-detection physics Nondimensionalization and characteristic scales Nondisjunction and aneuploid chromosome numbers Nonhomologous end joining of DNA double-strand breaks Non-Newtonian fluid behaviour Nonrandom mating, inbreeding and genotype-frequency change No-penetration condition at impermeable moving boundaries Normal and shear strain Normal and shear stress Normal distribution Normal modes of two coupled oscillators No-slip condition at viscous solid walls Nozzles and diffusers Nuclear binding energy and mass defect Nuclear fission, chain reactions and fusion Nuclear reactions and Q-values Nucleation and growth in phase transformations Nuclei and nuclear size scales Nucleophiles, electrophiles and polar reaction sites Nucleosides, nucleotides and phosphate-rich nucleotide chemistry Nucleotide excision repair of helix-distorting DNA lesions NUMA memory locality Numerical approximation and error Numerical differentiation and finite differences Numerical feature scaling and standardization Numerical quadrature Numerical stability and backward error Nyquist criterion for zero intersymbol interference Nyquist-Shannon sampling theorem Nyquist stability criterion Object files, symbols and linking Object-oriented and data-oriented design trade-offs Objects and classes Observability of linear state-space systems Observability with logs, metrics and traces Observational equivalence Observer-based state feedback and the separation principle One-dimensional elastic collisions Online authentication guessing and rate limiting On-target debugging and hardware instrumentation Operating systems Operational amplifier limits and nonideal behavior Optical dispersion and prism spectra Optimization problems, objectives and feasible sets Optional and fallible computations as explicit context Orthogonality and projections Orthographic and perspective projection Osmolarity, tonicity and cell-volume responses Osmosis across selectively permeable membranes Outline fonts, glyphs and rasterization Overall equipment effectiveness and production losses Ownership, borrowing and lifetimes Oxidation and reduction as electron-transfer reactions Packet filtering and stateful firewalls Packets and protocol layers Packet scheduling and fair sharing Parallel-axis theorem for moment of inertia Parallel computations as dependency DAGs Parallel granularity and overhead Parallel prefix scans Parallel reductions Parallel speedup, efficiency and scaling Parameterized types, sum types and product types Parametricity and free theorems Parametric polymorphism Parametrized curves Parametrized surfaces Parasitism, mutualism and commensalism as interspecific associations Parity symmetry in quantum mechanics Parsing numeric text Parsing, semantic analysis and intermediate representations Partial derivatives Partial orders and Hasse diagrams Particle quantum numbers and conservation laws Partition functions and thermal averages Pascal's principle and hydraulic force transmission Passivation and localized corrosion Password hashing, salts and offline guessing Paths, cycles and connectedness in graphs Pattern matching and exhaustiveness Pedigree notation and inference of Mendelian inheritance patterns Peptide bonds and polypeptide backbone directionality Performance measurement and profiling Periodic trends in atomic size and electron binding Periodic waves and wave parameters Peripheral drivers and hardware abstraction Permissives and interlocks in machine control Permutations and combinations Perpendicular-axis theorem for planar bodies Perspective-correct interpolation of vertex attributes pH and pOH as logarithmic concentration scales Phase diagrams and equilibrium microstructures Phase portraits and stability of equilibria Phases and homogeneous regions of matter Phase transitions, order parameters and critical behavior Phasor circuit analysis Phasors Phospholipase C, IP3, DAG and calcium signaling Phospholipids and membrane-forming amphipathic structure Phosphorus cycling through rocks, soils, water and biomass Photon energy and selective absorption by matter Photophosphorylation driven by the thylakoid proton gradient Photosynthetic pigments and light-harvesting antennae Photosystem II and light-driven oxidation of water Photosystem reaction centers and photochemical charge separation Physical clocks, skew and clock synchronization Physical pendulum PID control Piecewise polynomial interpolation and cubic splines Pigeonhole principle Pipeline parallelism and throughput Pivoting and numerical Gaussian elimination Plane Couette-Poiseuille flow between parallel plates Plane polar coordinates and moving unit vectors Plane strain Plane stress PLC scan cycle and ladder logic Ploidy, homologous chromosomes and chromosome-set counting Point defects in crystalline solids Pointers, addresses and object lifetimes in C Point estimation Pointing targets and Fitts's law Poisson and Laplace equations as boundary-value problems Poisson brackets and Hamiltonian evolution Poisson distribution Poisson's ratio Polar form and Euler's formula Polarization by reflection and Brewster's angle Polarization of electromagnetic waves Pole placement by state feedback Poles and zeros of rational functions Polymer chain architecture and crosslinking Polymer chains, repeat units and degree of polymerization Polymer extrusion and die swell Polymer-melt viscosity and shear thinning in processing Polynomial functions Polynomial interpolation Polynomials Polyprotic acids and stepwise proton dissociation Polytropic ideal-gas processes Population size, density and demographic balance Populations, samples, parameters and statistics Position and displacement Post-replicative mismatch repair Postsynaptic potentials, reversal potentials and excitation versus inhibition Postzygotic barriers and reduced hybrid fitness Powder-bed fusion and scan-based consolidation Power and root functions Power series Power sets and Cartesian products Power spectral density of stationary random processes Power spectral density through LTI systems Poynting theorem and local electromagnetic energy conservation Poynting vector and intensity of electromagnetic waves Prandtl boundary-layer equations for steady incompressible flow Prandtl lifting-line equation for a finite wing Pratt parsing and expression precedence Predation and herbivory as consumer-resource interactions Predicting precipitation reactions from mixed aqueous ions Prefix-free codes and Huffman coding Pressure as normal force per area Pressure projection for incompressible fluid simulation Pressure, temperature, and molecular speed from kinetic theory Pressure-volume and temperature-entropy process diagrams Pressure-volume boundary work with varying pressure Pressure-volume work at constant external pressure Prezygotic barriers to gene flow Primary active transport and ATP-driven membrane pumps Prim's minimum-spanning-tree algorithm Principal component analysis Priority inversion and priority inheritance Priority queues Probability calibration and proper scoring rules Process capability indices Cp and Cpk Processes Processor execution and machine instructions Producer-consumer queues and bounded buffers Product and sum types Program decomposition and modules Programmable rasterization pipelines and shaders Projectile motion under uniform gravity Prokaryotic and eukaryotic cell organization Prokaryotic operons and transcriptional gene regulation Proof by contrapositive and contradiction Propagation of measurement uncertainty Proportional control Protein phosphorylation and dephosphorylation as reversible regulatory switches Protein primary and secondary structure Protein tertiary structure, quaternary structure and folding forces Proton-motive force across biological membranes Prototyping and iterative interaction design Public-key cryptography and key pairs Pull production and kanban WIP limits Pull-up and pull-down resistors for digital signals Pulse-code modulation Pulse-width modulation Pumps and incompressible-flow work Punnett squares and probability calculations for monohybrid crosses Pure functions and immutable data Pure-substance phase diagrams and saturation Pyruvate oxidation to acetyl-CoA Python programming Quadratic drag and terminal speed Quadratic equations Quadratic forms and matrix definiteness Quadrature amplitude modulation Qualitative solubility rules for ionic compounds Quantum angular momentum Quantum entanglement and local measurement statistics Quantum heat capacity of solids Quantum observables and operators Quantum probability current and continuity Quantum scattering amplitudes and partial waves Quantum states and probability amplitudes Quantum tunneling through potential barriers Quarks, leptons and hadrons Quarter-chord aerodynamic center in thin-airfoil theory Quaternion algebra Quenching and tempering of steels Quicksort and partitioning QUIC streams and connection migration Quorums and quorum intersection Radial dynamics in circular motion Radiative heat exchange and view factors Radicals and rational exponents Radioactive decay and nuclear activity Raft consensus Random and systematic measurement effects Random forests Random processes as time-indexed random variables Random sampling and sampling bias Random variables Random vectors and covariance matrices Rank and nullity Raster images, pixels and resolution Rational expressions Rational functions Rational numbers Rayleigh scattering and wavelength-dependent light scattering Rays and geometric intersection tests Ray tracing for visibility, shadows and reflections RC charging and discharging transients Reaction enthalpy and thermochemical equations Reaction Gibbs energy under nonstandard conditions Reaction quotient and direction toward equilibrium Reaction stoichiometry from balanced equations Reading potential-energy diagrams Reading rooted phylogenetic trees by topology Real numbers and intervals Real thermodynamic cycle analysis Real-time constraints, deadlines and jitter Real-time operating systems Receptor tyrosine kinases and the Ras-MAPK signaling cascade Reciprocal lattices Recognition, recall and cognitive load Recombinant gametes from crossing over between linked loci Recombination frequency from linked-locus test-cross progeny Recovery, recrystallization and grain growth after deformation Recurrence relations and recursive definitions Recursion Recursive types and algebraic data types Refactoring and technical debt Reference counting and ownership cycles References, object identity and heap-allocated values Reflection of light Refraction and Snell's law Regression evaluation metrics Regularized optimization and penalty terms Relational data model Relations between sets Relativistic energy and momentum Relativity of simultaneity and Lorentz transformations Remote procedure calls Repeatability, reproducibility and robustness of measurements Replicated chromosomes, sister chromatids, centromeres and kinetochores Replicated logs and state machine replication Replication slippage and repeat-length variation Reproducible builds and immutable artifacts Residual connections and deep networks Resistance and Ohm's law Resistance spot welding Resistive circuit analysis Resistors in AC circuits Resolution and backtracking in logic programming Resonance Resonance and delocalized bonding in Lewis structures Resource exhaustion and denial of service Resting membrane potential from selective ion permeability Retarded electromagnetic potentials Reverse transcription from RNA templates into DNA Reversible reactions and dynamic chemical equilibrium Reynolds lubrication equation for thin films Reynolds number and flow regimes Reynolds transport theorem for a fixed control volume Ribosome-catalyzed translation of mRNA into polypeptide Ridge and lasso regression Right-triangle trigonometry Rigid-body degrees of freedom and constraints RL current growth and decay transients RMS values RNA strand structure, base pairing and folding RNA transcription from DNA templates ROC and precision-recall curves Rollback and forward recovery Rolling, blue-green and canary deployments Rolling of metal strip and plate Rolling without slipping kinematics Rooted trees Root locus Rotating magnetic fields Rotating reference frames and inertial forces Rotational and irrotational fluid flow Rotational dynamics Rotational kinetic energy Rotational work and power about a fixed axis Rotation matrices in two and three dimensions Round-trip estimation and retransmission timers Routh-Hurwitz stability criterion Row operations and echelon form RuBisCO and fixation of carbon dioxide into 3-phosphoglycerate Runge-Kutta methods Russell's paradox and axiomatic set theory Safety and liveness properties of concurrent systems Sampling continuous domains on discrete grids Sampling continuous-time signals Sampling distributions Sarcomere length–tension relationship and filament overlap Saturated mixtures and vapor quality Scalar and vector potentials in electromagnetism Scaling laws and order-of-magnitude estimates Scattering cross sections and angular distributions Scene graphs and hierarchical transformations Scheduling and context switching Scheduling policies for concurrent tasks Schmid's law and critical resolved shear stress Scientific notation and powers of ten Scope and local state Secondary active transport and coupled cotransport Secondary production and trophic transfer efficiency Second messengers as intracellular signaling intermediates Second-order LTI systems, natural frequency and damping ratio Second-order tensors in anisotropic materials Second-order tests for unconstrained optima Second partial derivatives and the Hessian matrix Secret-key lifecycle and key rotation Secure channels and TLS Security goals: confidentiality, integrity and availability Selective permeability of lipid bilayers Self-information Semantics-preserving program transformations Semantic versioning and deprecation Semiconservative DNA replication from origins of replication Sensitivity and disturbance rejection in feedback systems Separable first-order differential equations Sequence alignment as a hypothesis of positional homology Sequence numbers, acknowledgements and retransmission Sequences Sequential process control with state machines Series RLC circuits and resonance Server-side HTML templating Service level indicators and objectives Set-reset latches and stored state Setup time, batch size and changeover trade-offs Sex chromosomes, autosomes and hemizygous loci Sexual selection through differences in mating and fertilization success Shannon entropy Shannon-Hartley capacity of an AWGN channel Shannon's noisy-channel coding theorem Shared derived characters, outgroups and clade diagnosis Shear-force and bending-moment diagrams Shear modulus Shear stress in beams Sheet-metal bending, bend allowance and springback Sheet-metal formability and forming-limit diagrams Sheet-metal shearing, blanking and punching Shells and the command line Side channels and observable implementation effects Sigma and pi bonding in single and multiple bonds Signal amplification, branching and integration in signaling networks Signal constellations and decision regions Signal energy and average power Signal handling and graceful shutdown Signal inner products and orthogonal waveforms Signal termination, receptor desensitization and adaptation Signal-to-noise ratio SIMD vector processing Similarity solution for one-dimensional diffusion into a semi-infinite domain Simple compressible systems and the state postulate Simple harmonic motion Simple linear regression Simple pendulum and the small-angle period Simply typed lambda calculus Simultaneous multithreading and logical processors Single-degree-of-freedom vibration models Single-variable functions Sintering and densification of particulate materials Sinusoidal AC voltage and current Sinusoidal quantities Skeletal animation and linear blend skinning Skeletal-muscle excitation–contraction coupling through T-tubules and sarcoplasmic reticulum Skeletal muscle fibers, myofibrils and sarcomere organization Skeletal-muscle relaxation by calcium reuptake into the sarcoplasmic reticulum Slicing, build orientation and support structures in additive manufacturing Sliding-filament mechanism of sarcomere shortening Sliding windows and receiver flow control Slip in induction machines Small-angle approximations Small oscillations about stable equilibrium Small-signal linearization around an operating point Small-step operational semantics Softmax and categorical probabilities Software-defined networking Software dependency management and lockfiles Software specifications and invariants Solubility product equilibria and $K_{sp}$ Solubility, saturation and supersaturation Solutions, solutes and solvents Solution treatment, precipitation hardening and overaging Solvation and the dissolution process Solving initial-value ODEs with Laplace transforms Solving linear equations Solving linear recurrence relations Sound waves Source-channel separation theorem Source preprocessing and translation units Spacetime curvature and the Einstein field equations Spacetime interval and proper time Span Sparse matrices and sparse linear systems Spatial and temporal memory locality Spatial anti-aliasing in raster graphics Species concepts and reproductive isolation Species richness, evenness and community diversity Specific heats at constant volume and pressure Specific stiffness and specific strength Spectral efficiency in digital communication Speed of longitudinal sound waves in a fluid Spherical harmonics Spherical mirrors Spin one-half and the Stern-Gerlach experiment SPI synchronous serial communication Spontaneous and induced DNA lesions SQL injection and parameterized queries SQL joins and aggregation SQL queries SQL schema definition Stability of linear state-space systems Stability of numerical time-stepping methods Stack allocation and stack discipline Stacks and queues Standard enthalpies of formation and reaction enthalpy Standard Gibbs free energy changes for chemical reactions Standard molar entropy and reaction entropy Standard states in chemical thermodynamics Standard uncertainty from repeated measurements Standing acoustic modes in open and closed pipes Standing waves Star and delta connections State feedback and closed-loop state dynamics State-transition matrices and the matrix exponential Static analysis, formatting and linting Static and kinetic dry friction Static equilibrium Stationary phase and the classical limit Statistical entropy and the arrow of time Statistical strength and Weibull failure of brittle materials Steady creeping flow and the Stokes equations Steady-state approximation for reaction intermediates Steady-state tracking error and system type Step sizes and line search in descent methods Stiff differential equations and implicit time stepping Stochastic gradient descent and mini-batch optimization Stochastic linear state-space models Stoichiometry of gaseous reactants and products Stoichiometry with solution concentrations Stokes drag and terminal settling of a sphere Stokes' first problem: an impulsively started plate Stokes' theorem Strain energy and Castigliano's theorem Stream function for two-dimensional incompressible flow Stream sockets, framing and partial I/O Strength, ductility and toughness Strengthening mechanisms in metals Stress concentrations around notches and holes Stress-intensity factors and linear-elastic fracture mechanics Stress-strain curves and elastic-plastic behaviour Stress transformation in plane stress Strong and weak acids and bases in water Structured application logging Structured data and schemas Sturm-Liouville eigenvalue problems Subspaces Substitutional and interstitial solid solutions Substrate-level phosphorylation as direct ATP formation Subtyping and subsumption Superconductivity and Cooper pairing Superposition of waves Superscalar and out-of-order instruction execution Supervised learning and loss functions Support reactions Surface and interfacial energy in materials Surface integrals Surface normals, orientation and winding Surface-profile measurement and roughness filtering Surface tension of liquid interfaces Surface texture, roughness and waviness Switch bounce and debouncing Symbolic execution and path conditions Symmetric encryption and secret keys Symmetric thin-airfoil lift distribution and the 2π lift slope Symmetry reduction of the incompressible Navier-Stokes equations Sympatric speciation and polyploid reproductive isolation Symplectic integration of Hamiltonian dynamics Synchronous generator operation Synchronous machine construction and excitation Synchronous motor operation Systems as mappings between signals Systems of first-order ordinary differential equations Tail calls and proper tail recursion Task parallelism and fork-join execution Taylor and Maclaurin series TCP and UDP TCP congestion window and congestion control TCP connection establishment and teardown Temperature and thermal equilibrium Temperature dependence of equilibrium constants and the van 't Hoff equation Template-directed nucleic-acid synthesis and 5′→3′ polymerization Temporal and spatial summation of synaptic inputs Tension in a massive rope Tensor components under a change of basis Test crosses for inferring an unknown dominant-phenotype genotype Text encodings Texture coordinates and texture mapping Texture filtering and mipmaps The 50% recombination limit and hidden multiple crossovers The air-standard Diesel cycle The air-standard Otto cycle The Buckingham Pi theorem The CAP theorem and network partitions The Carnot cycle and reversible performance limits The Clapeyron equation for phase equilibrium The CMOS inverter The curse of dimensionality in machine learning The Dirac delta distribution The electron-volt as an energy unit The equipartition theorem The free-electron Fermi gas The Gamma function and generalized factorials The genetic code, codons and reading frames The Gibbs relations for simple compressible substances The heat equation The hydrogen atom The hydrologic cycle as movement of water through ecosystems The ideal Brayton cycle The ideal-gas law The ideal Rankine cycle The incompressible-substance approximation The infinite square well The Joule-Thomson effect The Kalman filter The microcanonical ensemble The nitrogen cycle across atmospheric, inorganic and organic pools The nuclear liquid-drop model and semi-empirical mass formula The nuclear shell model and magic numbers Theoretical, actual and percent reaction yield The periodic table, groups and recurring valence patterns The p-n junction and depletion region The quantum harmonic oscillator The quantum uncertainty relation The rendering equation and global illumination Thermal conduction and Fourier's law Thermal expansion of solids Thermal fluctuations and response functions Thermally activated processes and Arrhenius behavior Thermal shock and thermally induced fracture Thermal strain and constrained expansion in solids Thermodynamic coupling of chemical reactions Thermodynamic property tables and interpolation Thermodynamic systems, states and properties Thermodynamic work modes The Schrödinger equation The simplex method for linear programming The Standard Model of particle physics The steady-flow energy equation The substitution lemma for typing The unit circle The vapor-compression refrigeration cycle The variational method in quantum mechanics The Zeeman effect The z-transform Thin-airfoil vortex-sheet formulation and flow-tangency equation Thin lenses Threads within a process Threat models, assets and adversaries Three-dimensional rotations with unit quaternions Three-phase power Three-point test crosses for inferring gene order Throttling processes and valves Time- and frequency-division multiplexing Time-dependent perturbations and transition rates Time dilation and length contraction Time-independent quantum perturbation theory Timeouts, retries and duplicate requests Timer interrupts and preemptive multitasking Time-temperature-transformation and continuous-cooling diagrams Tipping stability and the support base Tolerance stack-ups in assemblies Tooling cost, unit cost and production-volume break-even Topological ordering of directed acyclic graphs Torque Torsional pendulum Torsion of circular shafts Total internal reflection Trace of matrices and linear operators Tracing and generational garbage collection Trailing vorticity and downwash of a finite lifting wing Training, validation, and test sets Transfer functions and state-space realizations Transformer architecture Transformer equivalent circuit Transformer losses and efficiency Transient control-volume energy balances Transient-response performance specifications Translating accelerating frames and inertial force Transposable elements as mobile sources of genome variation Transverse and longitudinal waves Trapezoidal and Simpson quadrature rules Tree pruning and complexity control Trees and forests as graphs Tree traversal orders Triangle meshes and indexed geometry Triangle rasterization and pixel coverage Trigonometric Fourier series and orthogonal coefficient projection Trigonometric functions Trigonometric identities Triose-phosphate output and carbohydrate synthesis from photosynthetic carbon tRNA charging and codon-anticodon decoding Trophic levels, food chains and food webs True stress and true strain TrueType hinting bytecode and its interpreter Trusses and axial member forces Trust boundaries and the trusted computing base Tunneling and overlay networks Turbines Turing machines and computability Turning operations on a lathe Twin paradox and elapsed proper time Two-dimensional collision analysis Two-dimensional doublet potential flow Two-dimensional source and sink potential flows Type constraint generation Type safety through progress and preservation Typing judgments and static semantics UART asynchronous serial communication Uncertainty budgets and reporting measurement results Uncountability and Cantor's diagonal argument Underfitting, overfitting, and the bias-variance tradeoff Uniform circular motion and centripetal acceleration Uniform distribution Unix-like systems Unix process creation, program replacement and termination Unix signals Unsupervised learning Untyped lambda calculus URLs and web resources Usability testing with representative tasks User mode, kernel mode and system calls Users, tasks and context of use Using Ampère's law for ideal solenoids and toroids Using Gauss's law with spherical, cylindrical, and planar symmetry Variable-amplitude fatigue and cumulative damage Variables and values Variance and standard deviation Variance in parameterized and function types Vat photopolymerization Vector addition and scalar multiplication Vector clocks and concurrent updates Vector embeddings Vector fields Vector graphics and resolution-independent geometry Vector kinematics Vector norms and distance Vector spaces Velocity and acceleration in plane polar coordinates Velocity and acceleration of points in planar rigid-body motion Velocity potential for incompressible irrotational flow Verification and validation of physical simulations Version control Vibrating strings and harmonic modes Virtual address spaces and page tables Virtualization and containers Viscoelasticity, creep and stress relaxation in polymers Viscosity and Newtonian fluids Viscous damping in mechanical vibration Viscous diffusion of momentum in unsteady parallel shear flow Visual hierarchy, grouping and scanning Volatile hardware-register access in C Voltage-gated ion channels and electrical excitability Volume integrals Volume of an n-dimensional ball von Karman momentum-integral equation for a boundary layer Vortex-sheet strength as circulation density Vortex tubes and filament-strength constraints Vorticity and local rotation in a fluid Vorticity transport in incompressible Newtonian flow Voxels and volumetric grids VSEPR theory and molecular geometry Watchdog timers and fault recovery Water autoionization and the ion-product constant Wave energy and intensity Wavefunctions and the Born rule Wave interference Wave propagation and wave speed Wear mechanisms in contacting materials Web application architecture Web application development Web applications in Go Web origins and the same-origin policy Web sessions and secure cookies Weighted graphs and path cost Weighted least squares with measurement uncertainties Weld discontinuities and acceptance criteria Weld heat-affected zones and metallurgical transformations Welding residual stress and distortion Wetting, contact angle and capillary action White noise Wide-sense stationarity and autocorrelation Wi-Fi association and roaming Wireless shared media and Wi-Fi Work by a variable force in one dimension Work-energy theorem Work, span and critical-path parallelism Work-stealing schedulers X-linked recessive and dominant inheritance patterns X-ray diffraction for crystal and phase identification Young-Laplace pressure across curved interfaces Young's modulus and linear elasticity

No matching units

Arrows go from each prerequisite to the units that depend on it. Hover or focus a unit to highlight its path.

Calculating derivatives
Multivariable functions
Partial derivatives
Differentiability of multivariable functions
Action and the Euler-Lagrange equations
Feynman's sum over paths
Noether's theorem for mechanical symmetries
Curl
Stokes' theorem
Covariant derivatives, connections and geodesics
Spacetime curvature and the Einstein field equations