Review of Common ODE

1.1 Differential Equations and Mathematical Models

1.2 Integrals as General and Particular Solutions

1.3 Slope Fields and Solution Curves

1.4 Separable Equations and Applications

1.5 Linear First-Order Equations

1.6 Substitution Method and Exact Equations

2.1 Population Models

2.3 Acceleration-Velocity Models

2.4 Numerical Approximation Euler’s Method

2.5 A Closer Look at the Euler Method

3.1 Introduction Second-Order Linear Equations

3.2 General Solutions of Linear Equations

3.3 Homogeneous Equations with Constant Coefficients

3.4 Mechanical Vibrations

3.5 Nonhomogeneous Equations and Undetermined Coefficients

3.6 Forced Oscillations and Resonance

4.1 First-Order Systems and Applications

4.2 The Method of Elimination

5.1 Matrices and Linear Systems

5.2 The Eigenvalue Method for Homogeneous Systems

5.3 A Gallery of Solution Curves of Linear Systems

5.5 Multiple Eigenvalue Solutions

5.6 Matrix Exponentials and Linear Systems

5.7 Nonhomogeneous Linear Systems

7.1 Laplace Transforms and Inverse Transforms

7.2 Transformation of Initial Value Problems

7.3 Translation and Partial Fractions

7.4 Derivatives, Integrals, and Products of Transforms

7.5 Periodic and Piecewise Continuous Input Functions

7.6 Impulses and Delta Functions