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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


A grade of C or better in MAC 2312

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 non-linear).
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
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
Cauchy-Euler 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

Zill, Dennis (2009) A First Course in Differential Equations with Modeling Applications, (9th
Edition) Florence, KY., Cengage Learning

Suggested Course Schedule for MAP2302

Class Ch./Sec. Topic
1 1.1 Definitions and Terminology
2 1.2-1.3 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 Coefficients-Superposition Approach (Optional)
14 4.5 Undetermined Coefficient-Annihilator Approach
15 4.6 Variation of Parameters
16 4.7 Cauchy-Euler Equation
17   Test #3
18 5.1 Spring Mass Systems-Undamped, Damped, Driven Motion
19 5.1 Spring Mass Systems-Undamped, Damped, Driven Motion
20 5.2 Boundary Value Problems (Optional)
21 6.1-6.2 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 8.1-8.2 Systems of Equations - Preliminary Theory; Homogeneous Linear
    Systems with Constant Coefficients (Optional)
30 8.3-8.4 Variation of Parameters; Matrix Exponential (Optional)
    Final Exam
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