MAP 2302 - Differential Equations

Mathematics Department

Credit(s): 3
Contact Hours: 47
Effective Term Fall 2019 (565)

Requisites

Prerequisite MAC 2312 with a minimum grade of C

Course Description

This course covers the basic methods and fundamental theorems of ordinary differential equations with applications in the natural sciences and engineering. Topics include solutions of first order differential equations, solutions of nth order linear differential equations, solutions by power series, Laplace transforms, and systems of linear differential equations.

Learning Outcomes and Objectives

  1. The student will apply the definitions of terms used in differential equations by:
    1. identifying the order and linearity of various differential equations.
    2. determining linear dependence and independence.
    3. identifying non-homogeneous and homogeneous linear equations.
    4. performing Laplace and inverse Laplace transforms.
    5. identifying the general solution and particular solution of a differential equation.
    6. creating auxiliary equations.
    7. analyzing initial value problems and boundary value problems.
  2. The student will find the solution of various types of differential equations by:
    1. using first-order techniques to solve separable, exact, linear, Bernoulli, and homogeneous differential equations.
    2. solving homogeneous linear equations with constant coefficients.
    3. constructing a second solution from a known solution.
    4. using the methods of undetermined coefficients and variation of parameters.
    5. solving Cauchy-Euler equations.
    6. using the Laplace transform to solve initial-value problems.
    7. obtaining power series solutions to differential equations with variable coefficients.
    8. solving systems of linear differential equations.
  3. The student will analyze models from science and engineering using the methods of solving differential equations by:
    1. setting up and solving problems utilizing Newton’s law of cooling.
    2. encountering various exponential growth and decay applications.
    3. examining applications that pertain to vibration of a spring.
    4. setting up and solving mixture problems.

Criteria Performance Standard

In order to earn a grade of C or better, the student will achieve at the 70% level or higher on classroom measures. Upon successful completion of the course the student will, with a minimum of 70% accuracy, demonstrate mastery of each of the above stated objectives through classroom measures developed by individual course instructors.

History of Changes

Revised 6/30/83, 8/84 DBT 4/18/85 Effective Session 19851 DBT 11/20/86 Effective Session 19862 DBT 11/20/90 Effective Session 19911 3 YR C&I Review 8/94 C & I 11/11/97 DBT 12/15/97 Effective Session 19981 Effective Session 19981 Format by mr 9/01 for 3 Year Review 2001. 3 Year Review 2005 eff20061(0370). 3 Year Review 2009 C&I Approval: 03/17/1998, BOT Approval: 04/20/1998, Effective Term: Fall 2006 (370).
C&I Approval: 02/14/2019, BOT Approval: 03/19/2019, Effective Term: Fall 2019 (565)

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