Math 252: Applied Differential Equations

Lecture Notes from Previous Years

Here are the lecture notes for Winter, 2021.

Chapter 1. Introduction to Differential Equations

• Section 1.1: Definitions and Terminology
• Section 1.2: Initial-Value Problems

Chapter 2. First-Order Differential Equations

• Section 2.2: Separable Variables
• Section 2.3: Linear Equations
• Section 2.4: Exact Equationsworks.
• Sections 2.2 to 2.4: Methods Covered Thus Far
• Section 2.5: Solutions by Substitution

Chapter 3. Modeling with First-Order Differential Equations

• Section 3.1: Linear Models (revised 2023/01/26 to correct errors)

Chapter 4. Higher-Order Differential Equations

• Section 4.1: Preliminary Theory - Linear Equations
• Section 4.2: Reduction of Order
• Section 4.3: Homogeneous Linear Equations with Constant Coefficients
• Section 4.4: Undetermined Coefficients
• Section 4.6: Variation of Parameters
• Section 4.7: Cauchy-Euler Equations

Chapter 5. Modeling with Higher-Order Differential Equations

• Section 5.1: Linear Models: Initial-Value Problems

Chapter 6. Series Solutions of Linear Equations

• Section 6.1: Review of Power Series
• Section 6.2: Solutions about Ordinary Points

Chapter 7. Laplace Transforms

• Section 7.1: Definition of the Laplace Transform
• Section 7.2: Inverse Transforms and Transforms of Derivatives
• Section 7.3: Operational Properties I
• Section 7.4: Operational Properties II – We are only doing the derivatives of transforms. Omit convolutions.
• Section 7.5: The Dirac Delta Function

Chapter 8. Systems of Linear First-Order Differential Equations

• Section 8.1: Preliminary Theory - Linear Systems
• Section 8.2: Homogeneous Linear Systems