This course is a study of ordinary differential equations, including linear equations, systems of equations, equations with variable coefficients, existence and uniqueness of solutions, series solutions, singular points, transform methods, boundary value problems, and applications.
Fundamentals of Differential Equations 9th Edition (Nagle) - Chapters 1-9
Textbook Link| Full Differential Equations Notes |
| Chapter 1 - Introduction to Differential Equations (1/21/25 - 1/26/25) |
Background Solutions and Initial Value Problems Direction Fields The Approximation Method of Euler |
Notes |
| Chapter 2 - First-Order Differential Equations (1/27/25 - 2/4/25) |
Separable Equations Linear Equations Exact Equations Special Integrating Factors Substitutions and Transformations |
Notes |
| Chapter 3 - Mathematical Models and Numerical Methods Involving First-Order Equations (2/4/25 - 2/7/25) |
Compartmental Analysis Numerical Methods: A Closer Look at Euler's Algorithm Higher-Order Numerical Methods: Taylor and Runge-Kutta |
Notes |
| Chapter 4 - Linear Second-Order Equations (2/13/25 - 2/25/25) |
Introduction: The Mass-Spring Oscillator Homogeneous Linear Equations: The General Solution Auxiliary Equations with Complex Roots Nonhomogeneous Equations: the Method of Undetermined Coefficient The Superposition Principle and Undetermined Coefficients Revisited Variation of Parameters Variable-Coefficient Equations |
Notes |
| Chapter 5 - Introduction to Systems (2/25/25 - 2/27/25) |
Differential Operators and the Elimination Method for Systems Solving Systems and Higher-Order Equations Numerically |
Notes |
| Chapter 6 - Theory of Higher-Order Linear Differential Equations (3/17/25 - 3/26/25) |
Basic Theory of Linear Differential Equations Homogeneous Linear Equations with Constant Coefficients Undetermined Coefficients and the Annihilator Method Method Of Variation of Parameters |
Notes |
| Chapter 7 - Laplace Transforms (3/26/25 - 4/12/25) |
Definition of the Laplace Transform Properties of the Laplace Transform Inverse Laplace Transform Solving Initial Value Problems Transforms of Discontinuous Functions Transforms of Periodic and Power Functions Convolution Impulses and the Dirac Delta Function Solving Linear Systems with Laplace Transforms |
Notes |
| Chapter 8 - Series Solutions of Differential Equations (4/17/25 - 4/24/25) |
Introduction: The Taylor Polynomial Approximation Power Series and Analytic Functions Power Series Solutions to Linear Differential Equations Equations with Analytic Coefficients Method of Frobenius |
Notes |
| Chapter 9 - Matrix Methods for Linear Systems (4/24/25 - 5/8/25) |
Introduction Review 1: Linear Algebraic Equations Review 2: Matrices and Vectors Linear Systems in Normal Form Homogeneous Linear Systems with Constant Coefficients Complex Eigenvalues Nonhomogeneous Linear Systems |
Notes |