TSJC Differential Equation

Course Syllabus Content

Current Schedule

Instructor – Robert Philbin                           Course Title: Differential Equations

Office:  Davis 238                                                     Course Number: MAT 265

Phone:  846-5518                                                     Credit Hours:    3

Email: robert.philbin@trinidadstate.edu                          Clock Hours:    45

Semester:  Spring 2007

Catalog Description:

Emphasizes techniques of problem solving and applications.  Topics include first, second, and higher order differential equations, series methods, approximations, systems of differential equations, and Laplace transforms.

PREREQUISITE: MAT 202

COREQUISITE: MAT 203

Policies, attendance and program-specific

Attendance is expected. Missed tests cannot be made up. Cheating may result in reduction of grade or withdrawal from the course.

OBJECTIVES: detail

  1.       Solve first order differential equations by separation of variables.
  2.       Determine when unique solutions exist.
  3.       Solve exact differential equations.
  4.       Find an integrating factor.
  5.       Use an integrating factor to solve an equation of the form: M dx + N dy = 0.
  6.       Find the Wronskian determinant.
  7.       Use the Wronskian determinant to prove linear independence.
  8.       Recognize a homogenous equation.
  9.       Find the general solution of a homogenous differential equation.
  10.       Recognize a nonhomogeneous equation.
  11.       Find the general solution of a nonhomogeneous equation.
  12.       Solve differential operators using operators.
  13.       Solve differential equations where the auxiliary equation has distinct roots.
  14.       Solve differential equations where the auxiliary equation has repeated roots.
  15.       Solve differential equations where the auxiliary equation has imaginary roots.
  16.       Solve linear nonhomogeneous equations using the method of undetermined coefficients.
  17.       Solve linear nonhomogeneous equations using the method of reduction of order.
  18.       Solve linear nonhomogeneous equations using the method of variation of parameters.
  19.       Use the operator 1/f(D) to solve linear nonhomogeneous equations.
  20.       Define Laplace transform.
  21.       Find the transforms of elementary functions, exponential functions, periodic functions, and derivatives.
  22.       Find the derivatives of transforms.
  23.       Find and use inverse transform to find a function.
  24.       Solve equations and applications using Laplace transforms and inverse transforms.
  25.       Solve homogenous systems with constant coefficients.
  26.       Solve nonhomogeneous systems.
  27.       Solve systems of linear differential equations using Laplace transform.
  28.       Use power series to represent linear differential equations.
  29. .

Assessment Procedures and Grading:

  • There are four components to the evaluation. They are as follows; homework, class participation and attendance, chapter and part of chapter tests, and the final exam. The weight for each is shown below:
  • 25% - Homework        (20% of problems in text)
  • 10% - Class participation and attendance - You are expected to ask questions, answer question, assist in solving problems, discuss, and learn how to use the software.
  • 50% - Chapter Tests and Section Tests
  • 15% - Final Exam
  • The grading cutoffs are 90, 80, 70, 60 for A, B, C, D, respectively.

Methods of conducting class

Class will be conducted by using lectures, recitation, and demonstrations of electronic methods. There is no lab component but the student is expected to do the electronic methods in the computer labs.

Required Supplies:

The student is expected to have a graphing calculator that can handle matrices and determinants as a minimum. The math lab has some available for your use when taking a test. If you have a computer and you intend to continue your mathematics program or engineering program might look into purchasing Maple for your computer.

Required Text: Elementary Differential Equations, 7th edition, by Boyce and DiPrima

Course schedule of topics by weeks

  1. Intro and Separable Equations: C1.1-2.2 - C1.1-.3,2.1 (6,5,5,5) Due M 1/20
  2. First Order Differential Equations: C2.3-2.6 - C2.2-2.4 (5,4,4) Due M 1/27
  3. Intro Second Order DEs: C2.7-3.2 - C2.5-2.9 (4,0,2,2,2) Due W 2/5
  4. Second Order DEs: C3.3-3.6 - C3.1-2.4 (8,7,5,8) Due F 2/14
  5. Second Order DEs: C3.7-3.9 - C3.5-3.9 (8,6,5,3,3) Due W 2/19
  6. Higher Order DEs: C4.1-.4 (4+4+3+3) - Due R 3/13 - Test in MathLab R 3/13
    C4.2 E2, C4.4 P5, C4.4 P12
  7. Series Solutions: C5.1-4 Test/Project Due F 3/28
  8. Laplace Transforms: C6:1-3
  9. Laplace Transforms: C6:4-6 HW Due T 4/8
  10. Systems of First Order DEs: C7.1-3 (4,0,4 from {15..24}) - Due F 4/25
  11. Systems of First Order DEs: C7.4-6 (0,5,4) - Due W 4/30
  12. Systems of First Order DEs: C7.7-9 (0,3,2) - Due F 5/2
  13. Numerical Methods: C8.1-3,6
  14. NonLinear DEs: C9.1-.5 - see Maple pendulum
    (2 from {1..12},2,1,1,1) - Due F 5/2
  15. More NonLinear: C9.6-.8
  16. May 5-8: Final exam week Take Home Part Due W 5/7, see SIR
    M 5/5 C7 test
    M 5/6 C9 test
    M 5/7 C6 test + GenEdMath

Census date – Jan. 29, 2007, Withdrawal Date – Apr. 26, 2007 The census date is thhe last date that the student can withdraw without having to pay for the course. The withdrawal date is the last date that the student can withdraw with a "W".

TSJC Mission Statement:

          Trinidad State Junior College enriches the academic, technical, and cultural life of our diverse community.  We are committed to offering traditional and alternate approaches to education, providing quality instruction, and promoting lifelong learning.