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Class Notes

Part 1

First Order ODEs

Sections 1.2 & 1.3: Introduction to Differential Equations

Section 2.1: Integrals as Solutions

Section 2.2: Slope Fields

Section 2.3: Separable Equations

Section 2.4: Linear Equations

Section 2.6: Substitution

Section 2.7: Autonomous Equations

Section 2.8: Numerical Methods-Euler's Method

Section 2.9: Exact Equations

Higher-Order Linear Homogeneous Equations

Section 4.1: Second Order Linear ODEs

Section 4.4: Second Order Linear ODEs with Constant Coefficients

Section 4.8 Free Mechanical Vibrations

Section 4.5: Higher Order Linear ODEs

Section 4.6 Reduction of Order

Part 2

Non-Homogeneous Equations

Section 4.2: Undetermined Coefficients (Part 1)

Section 4.3: Undetermined Coefficients (Part 2)

Section 4.7 Variation of Parameters

Section 4.10 Forced Oscillations and Resonance

Laplace Transforms, Series Solutions, and Systems of ODEs

Section 8.1: The Laplace Transform

Section 8.2: Transforms of Derivatives: Solving ODEs

Section 8.3: Convolution

Section 8.4: Dirac Delta and Impulse Response

Section 9.1: Power Series

Section 9.2: Series Solutions of Linear ODEs

Section 5.1 Introduction to Systems of ODEs