# Syllabus Math 441

## Math 441. Differential Equations Instructor Syllabus

Text: Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems, 10th Edition, John Wiley & Sons, Inc., 2012.

 Subject Chapter-Section Class Hours Introduction 1.1, 1.2, 1.3 1 First order linear equations 2.1 (Exercise 38 on pg. 41) 1 Separable and exact equations 2.2, 2.6 1 Integrating factors and homogeneous equations 2.6 (Exercise 30 on pg. 49) 2 Differences between linear and nonlinear equations 2.4, Bernoulli Equations 1 Modeling with first order equations 2.3 2 Autonomous equations and population dynamics 2.5 2 The Picard existence and uniqueness theorem 2.8 4 The basic theory or nth order linear differential equations 3.1, 3.2, 3.3, 4.1 6 nth order linear equations with constant coefficients 3.1, 3.3, 3.4, 4.2 3 Undetermined coefficients and variation of parameters for nth order equations 3.5, 3.6, 4.3, 4.4 2 Applications 3.7, 3.8 1 Review of power series 5.1 1 Series solutions near an ordinary point 5.2, 5.3 2 Regular singularities, Euler equations 5.4 2 Series solutions near a regular singular point (I, II) 5.5, 5.6 2 Bessel's equation 5.7 2 Introduction to systems 7.1 1 Solving linear systems with constant coefficients 7.5 1 Stability and Liapunov's Method 9.2, 9.6 3 Leeway and Exams 4 Total number of lectures 40

Approved by R. Muncaster 7/16/12.