TRI-COUNTY TECHNICAL COLLEGE 

COURSE SYLLABUS

Catalog Course Description:  This course includes the following topics:  solution

of linear and elementary non-linear differential equations by standard methods

with sufficient linear algebra to solve systems; applications; series; Laplace

transform; and numerical methods.

Entry Level Skills:  Algebra, Trigonometry and Calculus

Prerequisites:  Completion of MAT 141, Analytic Geometry and Calculus II

Corequisites:  None

Text(s):    Differential Equations with Boundary-Value Problems, 6^th  edition, by Dennis G. Zill and Michael R. Cullen, Brooks/Cole Publishing Company, 2005.

Equipment:  Graphing Calculator (TI-89 or TI-92 Plus)

Broad categories of this course include:

1.         various solution techniques to first-order differential equations and applications.

2.         various solution techniques to second-order differential equations, applications and modeling.

3.         series solutions of second-order linear equations.

4.         various solution techniques to nth-order linear equations and applications.

5.         use Laplace transformations to solve differential equations and applications.

6.         solving systems of first-order linear equations.

7.         knowledge and use of several numerical methods involving differential equations.

8.         positively function and contribute to collaborative group activities.

Course Competencies and Objectives/Major Course Topics:

Unit 1:  Introduction, First Order Differential Equations, Application of First Order Differential Equations

Upon completion of this unit (Sections 1.1-3, 2.1-5, 3.1-3), the student should be able to:

1.         Define and recognize a differential equation.

2.         Describe how differential equations are derived.

3.         Define and solve an initial-value problem.

4.         Solve a differential equation by separation of variables.

5.         Define a homogeneous function of degree n.

6.         Solve a first-order differential equation using an appropriate substitution.

7.         Recognize and solve an exact differential equation.

8.         Define the general form of a linear differential equation of order n.

9.         Find the general solution of a first-order linear differential equation subject to the initial condition.

10.     Recognize and solve the Bernoulli equation.

11.     Solve applications involving linear first-order differential equations including growth, decay, cooling, circuits, and chemical mixtures.

12.     Solve applications involving nonlinear first-order differential equations including population growth, and chemical reactions.

Unit 2:  Higher Order Linear Differential Equations

Upon completion of this unit (Sections 4.1-9), the student should be able to:

1.         define and recognize an initial-value and a boundary-value problem.

2.         define homogeneous and nonhomogeneous differential equations.

3.         define fundamental set of solutions, general solutions, and particular solutions.

4.         solve a homogeneous linear differential equation with constant coefficients.

5.         solve a homogeneous linear differential equation with constant coefficients.

6.         solve a given differential equation by variation of parameters.

7.         recognize and solve a Cauchy-Euler equation.

8.         solve a system of linear differential equations.

Unit 3:  Applications of higher order differential equations, power series solutions, numerical methods.

Upon completion of this unit (Sections 5.1, 6.1, 2.6, 9.1-2), the student should be able to:

1.         write a second-order differential equation describing free damped motion.

2.         write a second-order differential equation describing free undamped motion.

3.         define transient term, or solution, and steady-state solution.

4.         write a second-order differential equation for an L-R-C series electrical circuit.

5.         solve applications of second-order differential equations involving simple harmonic motion, damped motion, forced motion, electric circuits, and other analogous systems.

6.         define an ordinary and a singular point of a second-order differential equation.

7.         define a regular singular point and an irregular singular point.

8.         determine the singular points of a second-order differential equation.

9.         use a power series to solve a differential equation.

10.     compute approximate solutions using Euler’s method.

11.     use the three-term Taylor formula to obtain an approximate solution.

12.     apply the Runge-Kutta method to find solutions to a given problem.

Unit 4:  The Laplace transform, Systems of linear first-order differential equations

Upon completion of this unit (Sections 7.1-4, 8.1-2), the student should be able to:

1.         define the Laplace transform and linear transform, or linear operator.

2.         evaluate the Laplace transform of a given function directly for the definition of Laplace transform.

3.         determine the inverse Laplace transform of a given function using a Laplace transform table.

4.         evaluate the Laplace transform of a given function using a table of Laplace transform.

5.         apply the first and second translation theorem, and define the unit step function.

6.         write a given function in terms of the unit step function, and find the Laplace transform of that function.

7.         find the Laplace transform to solve a given periodic function.

8.         use the Laplace transform to solve a given integral equation or integrodifferential equation.

9.         solve and verify the solution to a system of linear differential equations.

10.     rewrite a given differential equation as a system of differential equations.

11.     find the eigenvalues and eigenvectors of a given matrix.

12.     rewrite a given system of differential equations in matrix form and visa versa.

13.     verify that a vector is a solution of a given system of differential equations.

14.     find the general solution of a given homogeneous linear system of differential equations.

 Grade Calculation Method:   

 Grades for this course will be determined based upon the following criteria:

                 Four unit tests                                                    =         60 – 80 %

                  Homework/ Other assignments                  =            0 – 20 %

                  Comprehensive Final Exam                        =            15 – 20%

                                                TOTAL                                                      100%

  Prepared by_Gerald L. Marshall__   Date written or revised:_3/1/06__