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Ordinary Differential Equations
MA26600 Spring 2026
Jakayla Robbins
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\( \newcommand{\N}{\mathbb N} \newcommand{\Z}{\mathbb Z} \newcommand{\Q}{\mathbb Q} \newcommand{\R}{\mathbb R} \newcommand{\set}[1]{\{{#1}\}} \newcommand{\gint}[1]{\llbracket #1 \rrbracket} \newcommand{\mean}[1]{\overline{#1}} \newcommand{\median}[1]{\widetilde{#1}} \newcommand{\spc}[1]{\underline{\hspace{#1}}} \newcommand{\del}{\partial} \newcommand{\intfact}{e^{\int P(x) \, dx}} \newcommand{\defn}{\stackrel{\textrm{def}}{=}} \newcommand{\laplace}[1]{\mathscr{L}\set{#1}} \newcommand{\laplaceinv}[1]{\mathscr{L}^{-1}\set{#1}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \newcommand{\fillinmath}[1]{\mathchoice{\underline{\displaystyle \phantom{\ \,#1\ \,}}}{\underline{\textstyle \phantom{\ \,#1\ \,}}}{\underline{\scriptstyle \phantom{\ \,#1\ \,}}}{\underline{\scriptscriptstyle\phantom{\ \,#1\ \,}}}} \)
Front Matter
Course Documents
Course Information
Extra Resources
Lecture Notes
Lesson 1, Introduction to Differential Equations
Lesson 2, Using Integration to Solve Simple Differential Equations
Lesson 3, Slope Fields and Sketching Solution Curves
Lesson 4, Separable Differential Equations and Applications
Lesson 5, First-order Linear Differential Equations, Part I
Lesson 6, First-order Linear Differential Equations, Part II
Lesson 7, Substitution Methods
Lesson 8, Exact Differential Equations and More Substitutions
Lesson 9, Population Growth Models
Lesson 10, Equilibrium Solutions and Stability
Lesson 11, Acceleration, Velocity, and Resistance
Lesson 12, Euler’s Method, A Numerical Method for Solving IVP’s
Lesson 13, Second-Order Linear Differential Equations
Lesson 14, General Solutions of Linear Equations
Lessons 15 and 16, Homogeneous Equations with Constant Coefficients
Lesson 17, Mechanical Vibrations
Lesson 18, The Method of Undetermined Coefficients
Lesson 19, Variation of Parameters
Lessons 20 and 21, Forced Oscillations and Resonance
Lessons 22 and 23, Systems of Differential Equations and Applications
Lesson 24, Matrices and Linear Systems
Lessons 25-27, Linear Systems of Differential Equations with Constant Coefficients: The Eigenvalue Method
Lesson 28, Pictures of Solution Curves of Linear Systems
Lesson 29, Matrix Exponentials and Linear Systems
Lesson 30, Nonhomogeneous Linear Systems of Differential Equations
Lesson 31, Laplace Transformations and Inverse Laplace Transformations
Lesson 32, Laplace Transformations of Initial Value Problems
Lesson 33, Translation of Laplace Transforms and Partial Fractions
Lesson 34, Derivatives, Integrals, and Products of Laplace Transforms
Lesson 35, Piecewise Continuous Input Functions
Lesson 36, Impulses and Delta “Functions”
Ordinary Differential Equations
MA26600 Spring 2026
Jakayla Robbins
Department of Mathematics
Purdue University
Last Updated: March 27, 2026
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