Math 441. Differential Equations
Syllabus for Instructors

Text: Boyce and DiPrime, Elementary Differential Equations and Boundary Value Problems, 8th Edition, John Wiley & Sons, Inc., 2005.

Subject Chapter-Section Class
Hours
Introduction 1.1, 1.2, 1.31
First order linear equations 2.1 (plus Exercise 38 on pg. 41)1
Separable and exact equations

2.2, 2.6 (plus a statement and discussion of
the implicit function theorem for F(x,y) = c).

1
Integrating factors and
homogeneous equations
2.6 (plus Exercise 30 on pg. 49)2
Differences between linear and nonlinear equations 2.4, Bernoulli Equations on pg. 77 1
Modeling with first order equations 2.3 2
Autonomous equations and population dynamics 2.5 2
The Picard existence and uniqueness theorem 2.9 (plus an introduction to uniform convergence) 4
The basic theory or nth order linear differential equations

Sections 3.1, 3.2 and3.3 should be done in
conjunction with Sections 4.1 and Exercises 20 and 25 on pg. 223-224
so that the basic theory is developed for nth order equations and not just for 2nd order equations.

6
nth order linear equations with constant coefficients 3.1, 3.4, 3.5, 4.2 3
Undetermined coefficients and variation of parameters for nth order equations 3.6, 3.7, 4.3, 4.4 2
Applications 3.8, 3.9 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, 5.5 (plus Exercise 23 on pg 278) 2
Series solutions near a regular singular point (I, II) 5.6, 5.7 2
Bessel's equation 5.8 2
Introduction to systems7.11
Solving 2 x 2 systems with constant coefficients 7.5 (Restrict attention to 2 x 2 systems) 1
Stability and asymptotic stability and Liapounov's Method 9.2, 9.6 3
Leeway and Exams   4
TOTAL   44

Course Description: This course can be described as a "semi-honest" introduction to differential equations. Even though the "cookbook" methods are covered, each of them is proved. In addition, the basic existence and uniqueness theorem is proved fully (and honestly). The student is also given an introduction to uniform convergence and to the implicit function theorem. It should be emphasized that all theorems and methods covered should be proved in class. As a general rule, this course should be taught on a higher level than Math 385, since many mathematics majors and computer science majors take Math 441.

Courses webpage
Department of Mathematics

Last modified November 29, 2005