# 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
3-0-3

Transferability
Yes

Prerequisites
A grade of C or better in MAC 2312

Co-requisites
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
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
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

Textbook
Zill, Dennis (2009) A First Course in Differential Equations with Modeling Applications, (9th
Edition) Florence, KY., Cengage Learning
0-495-10824-3

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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