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Differential
Equations (92.236)
Detailed Course Syllabus
The tables below represent a working course syllabus that lists
the subjects to be treated and the homework assignment number
for each subject. The sequence of subjects follows your textbook
by Edwards and Penny (3rd Edition) quite closely. Minor alterations
in sequence may be made to fit the schedule as needed. The specific
HW problems for each assignment are given in a separate file (see
HW assignments). Many of the HW problems require the use of Matlab
for function evaluation, plotting, and overall analysis and interpretation
of the problem. Some of the assignments will also highlight the
numerical and symbolic solution capabilities within Matlab. One
or more Projects are also required in addition to the HW assignments
indicated below (usually after the completion of Chapter 1 and/or
Chapter 4).
Chapter
I: First Order Differential Equations

Section

Topic

Assignment
#

1.1

Differential
Equations and Mathematical Models

HW#1

1.2

Integrals
as General and Particular Solutions

HW#2

1.4

Separable
Equations and Applications

HW#3

1.3

Slope
Fields and Solution Curves

HW#4

1.5

Linear
FirstOrder Equations

HW#5

1.6

Substitution
Methods and Exact Equations

HW#6

Exam
#1 on Sections 1.1  1.6

Chapter
II: Mathematical Models and Numerical Methods

Section

Topic

Assignment
#

2.4

Numerical
Approximation: Euler's Method

HW#7

2.5

Closer
Look at the Euler Method

HW#8

2.6

The
RungeKutta Method

2.1

Population
Models

HW#9

2.2

Equilibrium
Solutions and Stability

2.3

AccelerationVelocity
Models

Chapter
III: Linear Equations of Higher Order

Section

Topic

Assignment
#

3.1

Introduction:
SecondOrder Linear Equations

HW#10

3.2

General
Solution of Linear Equations

HW#11

3.3

Homogeneous Equations with Constant Coefficients

Exam
#2 on Sections 2.1  2.6 and Sections 3.1  3.3

3.5

Nonhomogeneous
Equations and the Method of Undetermined Coefficients

HW#12

3.4

Mechanical
Vibrations

HW#13

3.6

Forced
Oscillations and Resonance

3.7

Electrical
Circuits

3.8

Boundary
Value Problems and Eigenvalues (not done in detail)

No
HW

Chapter
IV: Introduction to Systems of Differential Equations

Section

Topic

Assignment
#

4.1

First
Order Systems and Applications

HW#14

4.3

Numerical
Methods for Systems

Chapter
VII: Laplace Transform Methods

Section

Topic

Assignment
#

7.1

Laplace
Transforms and Inverse Laplace Transforms

HW#15

7.2

Transformation
of Initial Value Problems

Exam
#3 on Sections 3.4  3.8, Sections 4.1  4.3, and Sections
7.1  7.2

7.3

Translation and Partial Fractions

HW#16

7.4

Derivatives,
Integrals, and Products of Transforms

Last
updated by Prof. John R. White (January 2007)
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