differential equations
Calculus with unknowns
Differential equations are mathematical equations that relate a function to its derivatives—expressions describing how quantities change.
They model phenomena where rates of change matter: population growth, heat flow, planetary motion, electrical circuits.
Solving the differential equation gives us the position of the particle at any time.
A first course in differential equations typically follows calculus.
Combining into a whole
- ordinaryStandard, unremarkable
- partialFavoring one side
- linearArranged in straight succession
- nonlinearNot in sequence
homogeneous · nonhomogeneous · first-order · second-order · eigenvalues · eigenvectors · Dirichlet problem · separable
Repeated back-and-forth movement
- vibrationRapid oscillating movement
- motionChange in position
- trajectoryPath of moving object
- velocityDirected rate of motion
acceleration · damping · resonance · stability · harmonic · frequency · amplitude · phase
Complete disorder and confusion
- perturbationState of being unsettled
- stochasticRandomly determined, statistically describable
- singularitiesPoints where quantities become infinite
- bifurcationDivision into two branches
turbulence · instability · Lyapunov exponents · intractable · sensitive dependence · strange attractor
Numerical method using subdivisions
- simulationImitation of real processes
- substitutionExchange of one for another
- linearizationApproximating nonlinear with linear
Simulating long-term atmospheric behavior
- epidemiologyStudy of disease spread
- fluid dynamicsScience of flowing matter
- pharmacokineticsDrug fate in body
- mechanicsScience of motion
heat transfer · orbital mechanics · signal processing · structural engineering · electromagnetism · predator-prey · radioactive decay · diffusion
integration
Combining into a whole
nonlinear · homogeneous · nonhomogeneous · first-order · second-order · eigenvalues · eigenvectors · Dirichlet problem · separable · exact
oscillation
Repeated back-and-forth movement
- vibrationRapid oscillating movement
- motionChange in position
- trajectoryPath of moving object
velocity · acceleration · damping · resonance · stability · harmonic · frequency · amplitude · phase · waveform
chaos
Complete disorder and confusion
- perturbationState of being unsettled
- stochasticRandomly determined, statistically describable
- singularitiesPoints where quantities become infinite
bifurcation · turbulence · instability · Lyapunov exponents · intractable · sensitive dependence · strange attractor
finite element
Numerical method using subdivisions
- simulationImitation of real processes
- substitutionExchange of one for another
- linearizationApproximating nonlinear with linear
climate modeling
Simulating long-term atmospheric behavior
- epidemiologyStudy of disease spread
- fluid dynamicsScience of flowing matter
- pharmacokineticsDrug fate in body
mechanics · heat transfer · orbital mechanics · signal processing · structural engineering · electromagnetism · predator-prey · radioactive decay · diffusion · acoustics
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differential equationsalgebraic equations
Mathematical statements with variables
linear equations · polynomial equations · quadratic equations · simultaneous equations · arithmetic
differential equationselementary algebra
Introductory symbol-based math
difference, indifferent, equation, differently, indifference, differing, derivative, differentiate, differential