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Thomas W. Judson

The ODE Project

Differential equations with a systems-first flavor: first-order equations, linear systems and the phase plane, second-order equations, and the Laplace transform. The problems practice both solving equations exactly and reading long-run behavior straight from a system’s structure.

The ODE Project

205 exercises15 sections

Status

Sections

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A First Look at Differential Equations

91

Modeling with Differential Equations31

Separable Differential Equations23

First-Order Linear Equations24

Existence and Uniqueness of Solutions13

Systems of Differential Equations

5

Modeling with Systems5

Linear Systems

58

Linear Algebra in a Nutshell38

Planar Systems10

Complex Eigenvalues2

Repeated Eigenvalues8

Second-Order Linear Equations

2

Homogeneous Linear Equations1

The Laplace Transform

49

The Laplace Transform21

Solving Initial Value Problems13

Delta Functions and Forcing6

Adapted from The ODE Project © 2019–2025 Thomas W. Judson. Licensed under CC BY 4.0. Source: The ODE Project. Imported at revision 7935458.