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Differential Equations

15 topics · study sheets, quizzes, and tests.

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Go through each topic step by step, with 10 timed practice problems after every section.

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Topics

1.

First-Order Equations

Separable equations and integrating factors

StudyQuizUnit Test
2.

Exact Equations & Substitutions

Exactness tests, integrating factors, Bernoulli and homogeneous types

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3.

Second-Order Linear Equations

Characteristic roots: oscillate, decay, or both

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4.

The Wronskian & Variation of Parameters

Independence certificates, and the method that handles any forcing

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5.

Nonhomogeneous Equations & Resonance

Undetermined coefficients, and what forcing does

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6.

Systems of Differential Equations

Eigenvalues run the phase portrait

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7.

Nonlinear Systems & Linearization

Jacobians, predator–prey, competition, and the pendulum

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8.

Laplace Transforms

Turning calculus into algebra

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9.

Laplace II: Steps, Impulses & Convolution

Piecewise forcing, hammer blows, and the convolution theorem

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10.

Series Solutions

Power series where formulas fail

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11.

Frobenius & Special Functions

Singular points, indicial equations, Bessel and Legendre

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12.

Models & Qualitative Behavior

Growth, cooling, mixing, and equilibria

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13.

Existence, Uniqueness & Bifurcations

Picard's theorem, phase lines with parameters, harvesting collapse

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14.

Boundary Values & Fourier Series

Eigenvalue problems, sine series, the heat and wave equations

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15.

Numerical Methods: Euler to Runge–Kutta

Heun, RK4, error orders, and stability ceilings

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