Math 225 - Introduction to Differential Equations

Class: MW 2:30PM - 3:45PM in Math & Psychology 106 (8/27-12/9/2025), Instructor: Bedrich Sousedik

Topics of this course include: solutions of first- and second order linear differential equations, non-linear exact and separable equations, integrating factors, homogeneous equations, higher-order linear equations, initial and boundary value problems, solutions as functions of the equation parameters, Laplace transforms, power series solutions for Bessel and Legendre equations, difference equations and numerical methods.

Recommended Preparation: MATH 251.

The detailed class syllabus (pdf) is here. However, look below to see the actual progress of the class.

errata

8/27 Introduction, (1.1-1.2) Classification of differential equations, ODEs.

9/1 Labor Day (no class).

9/3 (1.2) IVP, Picard's theorem, (2.1) First-order linear equations.

9/8 (2.1) First-order linear equations. Hw1 (due 9/15): 1.1/6,8; 1.2/7,11,15,41,42; 2.1/12,14,20.

9/10 (2.2) Separable equations.

9/15 Some applications: (2.3) Growth and decay. Quiz 1. Hw2 (due 9/22): 2.1/3,18,19; 2.2/22,24,29,30.

9/17 Some applications: (2.5) cooling and heating phenomena.

9/22 More applications of the first-order equations: continuos compounding. Hw3 (done in class, no quiz): 2.3/11,17,36 and 2.5/9,11.

9/24 (3.1) Introduction to second-order linear equations, (3.2) Fundamental solutions of the homogeneous equation. Hw4 (due 10/6): 3.1/17,18,43 and 3.2/5,6,20.

9/29 (3.3) Reduction of order. (3.4) Homogeneous equations with constant coefficients: real roots.

10/1 (3.4) Homogeneous equations with constant coefficients: real roots. (3.5) complex roots. Hw5 (due 10/13, Exam #1): 3.3/7,8,11, 3.4/14,18, 3.5/10,12, 3.6/8,12.

10/6 (3.6) Nonhomogeneous equations. (3.7) Solving nonhomogeneous equations: method of undetermined coefficients.

10/8 (3.7) Solving nonhomogeneous equations: method of undetermined coefficients.

10/13 Exam #1 (1.1-3.6).