Math 279
Differential Equations
I. Course Description
An introduction to ordinary differential equations and their applications. Topics
include first-order equations, second- and higher- order linear equations,
vibrational motion, electrical circuits, power series solutions, Laplace transforms,
systems of equations, numerical methods, and matrix methods for systems of
equations.
II. Prerequisites
Math 173-174 (Calculus with Analytic Geometry I-II) or equivalent.
III. Introduction
This course is an introduction to ordinary differential equations and their
applications. In this course, it is expected that the student will not only become
proficient in solving many classes of differential equations by hand calculations, but
will become familiar with how to solve differential equations using symbolic
manipulation software available for computers today. Additionally, the student
should acquire an ability to model real world situations in terms of differential
equations.
IV. Instructional Materials
Textbook: A First Course in Differential Equations with Modeling Applications
(6th edition) by Dennis G. Zill;
Brooks/Cole (ITP) Publishing Company, 1997.
Optional: Student’s Solutions Manual by Warren S. Wright.
Required: Scientific calculator or graphing calculator (preferred).
V. COURSE CONTENT
Chapter One: Introduction to Differential Equations
1.1 Definitions and Terminology
1.2 Initial-Value Problems
1.3 Differential Equations as Mathematical Models
Chapter Two: First-Order Differential Equations
2.1 Separable Variables
2.2 Exact Equations
2.3 Linear Equations
2.4 Solutions by Substitution
Chapter Three: Modeling with First-Order Differential Equations
3.1 Linear Equations
3.2 Nonlinear Equations
Chapter Four: Differential Equations of Higher Order
4.1 Preliminary Theory: Linear Equations
4.2 Reduction of Order
4.3 Homogeneous Linear Equations with Constant Coefficients
4.4 Undetermined Coefficients-Superposition Approach
4.6 Variation of Parameters
4.7 Cauchy-Euler Equation
4.8 Systems of Linear Equations
4.9 Nonlinear Equations
Chapter Six: Series Solutions of Linear Equations
6.1 Review of Power Series; Power Series Solutions
6.2 Solutions About Ordinary Points
6.3 Solutions About Singular Points
Chapter Seven: Laplace Transforms
7.1 Definition of the Laplace Transform
7.2 Inverse Transform
7.3 Translation Theorems and Derivatives of a Transform
7.4 Transforms of Derivatives, Integrals, and Periodic Functions
7.5 Applications
Chapter Eight: Systems of Linear First Order Differential Equations
8.1 Preliminary Theory
8.2 Homogeneous Linear Systems with Constant Coefficients
8.3 Variation of Parameters
8.4 Matrix Exponential
Chapter Nine: Numerical Methods for Ordinary Differential Equations
9.2 Euler Methods
9.3 Runge-Kutta Methods
Assignments and Test Schedule for
A First Course in Differential Equations by Zill (6th edition)
SECTION
PAGE
ASSIGNMENT
1.1
1.2
1.3
8
15
25
1-11 odd, 15,17,19,23,31,37,45,49
1-17 odd
1-11 odd
2.1
2.2
2.3
2.4
35
42
51
57
1,3,5,9,11,23,31,33,39,41,43
1-17 odd,25,27
1-21 eoo, 27,37,41,45
11,7,9,11,13,15,17,21
3.1
TEST 1
68
11,3,5,9,13,21
4.1
4.2
4.3
4.4
4.6
4.7
4.8
4.9
TEST 2
106
112
119
130
146
152
160
165
1,5,9,11,15,17,21,23,25,33
1-21 eoo
1-41 eoo
1,5,11,13,19,23,29,33
1,7,11,15,21,25
1,3,5,7,11,15,19,23,25
1,3,9,13
3,5,7
6.1
6.2
6.3
221
229
242
1,3,5,7,11,15,19
3,7,15,17
1-11 odd, 23
7.1
7.2
7.3
7.4
7.5
265
272
281
284
301
11,15,19-37 odd
1-33 odd
1-21 odd,37-41 odd
formulas 1,2,3
1-13 odd, 17
8.1
8.2
8.3
TEST 3
327
341
347
1,3,7-23 odd
1,5,7,19,23,31
1,5
tba