differential equation
Function meets slope
A differential equation is a mathematical equation containing derivatives—expressions that describe how a quantity changes relative to another.
In physics and engineering, differential equations model systems where rates of change matter: population growth, heat flow, orbital mechanics.
Newton's laws of motion are expressed as differential equations.
Solving one means finding the function whose derivatives satisfy the equation.
Function's rate of change
- integrationCombining into a whole
- ordinaryStandard, unremarkable
- partialFavoring one side
- linearArranged in straight succession
nonlinear · homogeneous · inhomogeneous · separable · exact · eigenvalue · eigenvector · coefficient
Mechanisms maintaining desired outputs
- signal processingMathematical manipulation of waveforms
- fluid dynamicsScience of flowing matter
- vibrationRapid oscillating movement
- stabilityResistance to displacement
feedback · frequency response · resonance · steady state · electrical networks · mechanical systems · aerospace · structural analysis
Imitation of real processes
- predictionForecast of coming events
- epidemiologyStudy of disease spread
- climate modelingSimulating long-term atmospheric behavior
- financial modelingMathematical business performance representation
pharmacokinetics · ecology · predator-prey · growth rate · decay rate · equilibrium · curve fitting · forecasting
Science of motion
- electrodynamicsStudy of charge interactions
- quantumSmallest discrete unit
- relativityHow observers differ
- thermodynamicsScience of heat-energy relationships
Newton's laws · pendulum · damping · oscillation · field · potential · energy · momentum
Numerical method using subdivisions
- substitutionExchange of one for another
- approximationNear but inexact value
- iterationRepeated procedural pass
- convergenceProcess of approaching sameness
derivative
Function's rate of change
- integrationCombining into a whole
- ordinaryStandard, unremarkable
- partialFavoring one side
linear · nonlinear · homogeneous · inhomogeneous · separable · exact · eigenvalue · eigenvector · coefficient · constant
control systems
Mechanisms maintaining desired outputs
- signal processingMathematical manipulation of waveforms
- fluid dynamicsScience of flowing matter
- vibrationRapid oscillating movement
stability · feedback · frequency response · resonance · steady state · electrical networks · mechanical systems · aerospace · structural analysis
simulation
Imitation of real processes
- predictionForecast of coming events
- epidemiologyStudy of disease spread
- climate modelingSimulating long-term atmospheric behavior
financial modeling · pharmacokinetics · ecology · predator-prey · growth rate · decay rate · equilibrium · curve fitting · forecasting
mechanics
Science of motion
- electrodynamicsStudy of charge interactions
- quantumSmallest discrete unit
- relativityHow observers differ
thermodynamics · Newton's laws · pendulum · damping · oscillation · field · potential · energy · momentum · diffusion
finite element
Numerical method using subdivisions
- substitutionExchange of one for another
- approximationNear but inexact value
- iterationRepeated procedural pass
- math problemsword problem, story problem, proof, derivation, inequality
- equationsquadratic formula
- computational mathalgorithm, linear algebra, calculus, finite element, matrices
- mathematical modelsgrowth model, prediction model, economic model, climate model, forecasting model
- differentialsderivative, rate of change
- special functionsgenerating function
differential equationalgebraic equation
Mathematical equality using variables
differential equationelementary algebra
Introductory symbol-based math
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