Differential Equations, Course Information
Course Number and Title
MAP 2302: Differential Equations
Cata log Description
Topics include ordinary differential equations, the Laplace transform,
differential operators,
systems of equations , orthogonal trajectories, electric ne tworks , and inverse
transforms. A grade
of C or higher is required for this course to be used as a General Education
course. Course is
designated as a Gordon Rule course . (*)
Credit and Contact Hours
303
Transferability
Yes
Prerequisites
A grade of C or better in MAC 2312
Corequisites
N one
MAP2302 Student Learning Outcomes
1. De termine the intervals where a Differential Equation is guaranteed to have a
unique solution.
2. Identify the order of a differential equation and recognize if the
differential
equation is ordinary (or partial) and linear (or nonlinear).
3. Solve first order differential equations using the techniques of separation
of
variables, linear equations , exact equations, homogeneous substitution , and
Bernoulli’s substitution.
4. Determine a second linearly independent solution from a known solution.
5. Solve higher order linear differential equations that are homogeneous with
constant
coefficients.
6. Solve higher order linear differential equations that are homogeneous with
variable
coefficients using the Cauchy Euler equation.
7. Solve higher order linear differential equations that are nonhomogeneous with
constant coefficients using the techniques of undetermined coefficients,
annihilators, variation of parameters, and Laplace Transforms.
8. Solve higher order linear differential equations that are nonhomogeneous with
variable coefficients using the techniques of variation of parameters and the
CauchyEuler equation.
9. Use differential equations to model and solve application problems such as
spring
mass systems and LRC circuits.
Textbook and Suggested Schedule Effective: Fall 2009
though Summer 2012
Textbook
Zill, Dennis (2009) A First Course in Differential Equations with Modeling
Applications, (9th
Edition) Florence, KY., Cengage Learning
0495108243
Suggested Course Schedule for MAP2302
Class 
Ch./Sec. 
Topic 
1 
1.1 
Definitions and Terminology 
2 
1.21.3 
Initial Value Problems; Mathematical Models 
3 
2.2 
Separable Variables 
4 
2.3 
Linear Equations 
5 
2.4 
Exact Equations 
6 
2.5 
Solutions by Substitutions 
7 

Test #1 
8 
3.1 
First Order Linear Equations – Linear Models 
9 
4.1 
Preliminary Theory: Linear Equations 
10 
4.2 
Reduction of Order 
11 
4.3 
Homogeneous Linear Equations with Constant Coefficients 
12 

Test #2 
13 
4.4 
Undermined CoefficientsSuperposition Approach (Optional) 
14 
4.5 
Undetermined CoefficientAnnihilator Approach 
15 
4.6 
Variation of Parameters 
16 
4.7 
CauchyEuler Equation 
17 

Test #3 
18 
5.1 
Spring Mass SystemsUndamped, Damped, Driven Motion 
19 
5.1 
Spring Mass SystemsUndamped, Damped, Driven Motion 
20 
5.2 
Boundary Value Problems (Optional) 
21 
6.16.2 
Solutions about Ordinary Points & Singular Points 
22 

Test #4 
23 
7.1 
Definition of Laplace Transform 
24 
7.2 
Inverse Transform & Transforms of Derivatives 
25 
7.3 
Operational Properties – I 
26 
7.4 
Operational Properties – II 
27 
7.6 
Systems of Linear Equations (Optional) 
28 

Test #5 
29 
8.18.2 
Systems of Equations  Preliminary Theory; Homogeneous Linear 


Systems with Constant Coefficients (Optional) 
30 
8.38.4 
Variation of Parameters; Matrix Exponential (Optional) 


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