Differential Equations

Math 308-503 — Spring 2011

Instructor: Dr. Francis J. Narcowich, Professor of Mathematics
Office: 302 Milner Hall
E-mail: fnarc@math.tamu.edu
Phone: (979) 845-7369
URL: /~francis.narcowich/
Office Hours: MWF 11:20-12:20, and by appointment.

Catalogue Description: MATH 308. Differential Equations. (3-0). Credit 3. I, II S. Ordinary differential equations, solutions in series, solutions using Laplace transforms, systems of differential equations. Prerequisites: MATH 251 or equivalent; knowledge of computer algebra system.

Time & Place: Section 503: MWF 10:20-11:10, BLOC 128

Required Text: James R. Brannan and William E. Boyce, Differential Equations: An Introduction to Modern Methods and Applications , 1st ed., John Wiley & Sons, Hoboken, NJ, 2007.

Supplementary Materials:

Tests
  • Test 1: Wednesday, February 16, 2011
  • Test 2: Friday, March 25, 2011
  • Test 3: Wednesday, April 27, 2011
  • Final Examination: 8-10 a.m., Tuesday, May 10, 2011
  • Syllabus: The course covers all or part of Chapters 1-6 and Appendices A and B in the Brannan/Boyce book. For the computer component of the course, we will use Matlab. For a schedule, which may change due to contingencies and unforseen circumstances, see the table below.

    Grading System: Your grade will be based on three in-class tests, homework, and a final examination. Each in-class test will count for 20% of your grade; the homework & quizzes, for 15%; and the final examination will count for the remaining 25%. Your letter grade will be assigned this way: 90-100%, A; 80-89%, B; 70-79%, C; 60-69%, D; 59% or less, F.

    Homework and Quizzes: Homework will be collected about once a week. Occasionally, quizzes may be given. You may discuss homework problems with each other. However, all submitted work must be your own. Submitting the work of others is cheating. Late homework will not be accepted.

    Make-up Policy: I will give make-ups (or satisfactory equivalents) only in cases authorized under TAMU Regulations. In borderline cases, I will decide whether or not the excuse is authorized. Also, if you miss a test, quiz, or cannot turn in a homework, contact me at fnarc@math.tamu.edu soon as possible. Normally, this is the next business day, unless there are extenuating circumstances.

    Academic Integrity

    Copying Course Materials:   "All printed hand-outs and web-materials are protected by US Copyright Laws. No multiple copies can be made without written permission by the instructor."

    Aggie Honor Code:   "An Aggie does not lie, cheat, or steal or tolerate those who do."

    Americans with Disabilities Act Policy Statement: "The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe that you have a disability requiring an accommodation, please contact the Department of Student Life, Services for Students with Disabilities, in Room 126 of the Koldus Building or call 845-1637."

    Schedule

    Date Section Topic
    1/19/11 1.1 Basic Mathematical Models; Direction Fields
    1/21/11 1.2 Solutions of Some Differential Equations
    1/24/11 2.1 Linear Equations; Method of Integrating Factors
    1/26/11 2.2 Separable Equations
    1/28/11 2.3 Modeling with First Order Equations
    1/31/11 2.4-2.5 Linear vs. Nonlinear Equations, Autonomous Equations
    2/2/11 2.5-2.5 Autonomous Equations, Exact Equations
    2/4/11 3.1 Systems of Two Linear Algebraic Equations
    2/7/11 3.2 Systems of Two First Order Linear Differential Equations
    2/9/11 3.3 Homogeneous Linear Systems with Constant Coefficients
    2/11/11 3.4, Appen. B Complex Eigenvalues
    2/14/11 N/A Catch up. Review
    2/16/11 N/A Test 1
    2/18/11 4.1-4.2 Definitions and Examples, 2nd Order Linear Homogeneous Equations
    2/21/11 4.3 Linear Homogeneous Equations with Constant Coefficients
    2/23/11 4.4 Characteristic Equations with Complex Roots
    2/25/11 4.5 Mechanical and Electrical Vibrations
    2/28/11 4.6 Nonhomogeneous Equations: Method of Undetermined Coefficients
    3/2/11 4.8 Variation of Parameters
    3/4/11 5.1 Definition of the Laplace Transform
    3/7/11 5.2 Properties of the Laplace Transform
    3/9/11 5.3 Inverse Laplace Transform
    3/11/11 N/A Catch up.
    3/14 - 3/18 N/A Spring Break
    3/21/11 5.4 Solving Differential Equations with Laplace Transforms
    3/23/11 N/A Catch up. Review.
    3/25/11 N/A Test 2
    3/28/11 5.5 Discontinuous Functions with Laplace Transforms
    3/30/11 5.6 Differential Equations with Discontinuous Forcing Functions
    4/1/11 5.7-5.8 Impulse Functions and Convolutions
    4/4/11 A.1 Matrices
    4/6/11 A.2 Linear Algebraic Equations
    4/8/11 A.2 Linear Independence and Rank
    4/11/11 A.3 Determinants and Inverses
    4/13/11 A.4 The Eigenvalue Problem
    4/15/11 6.1-6.2 Definitions, Examples and Basic theory
    4/18/11 6.3 Homogeneous Linear systems with Constant Coefficients
    4/20/11 6.5 Fundamental Matrices and the Exponential of a Matrix
    4/22/11 N/A Reading day
    4/25/11 N/A Catch up. Review.
    4/27/11 N/A Test 3
    4/29/11 6.6 Nonhomogeneous Linear Systems
    5/2/11 N/A Review
    5/10/11 N/A Final exam (8-10 a.m.)

    Updated: January 15, 2011 (fjn)