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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).
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Chapter
I: First Order Differential Equations
|
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Section
|
Topic
|
Assignment
#
|
|
1.1
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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
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Slope
Fields and Solution Curves
|
HW#4
|
|
1.5
|
Linear
First-Order Equations
|
HW#5
|
|
1.6
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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
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The
Runge-Kutta Method
|
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2.1
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Population
Models
|
HW#9
|
|
2.2
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Equilibrium
Solutions and Stability
|
|
2.3
|
Acceleration-Velocity
Models
|
|
Chapter
III: Linear Equations of Higher Order
|
|
Section
|
Topic
|
Assignment
#
|
|
3.1
|
Introduction:
Second-Order 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
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Last
updated by Prof. John R. White (January 2007)
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