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: MWF 12-1:25, BLOC 128

Required Text: W.E. Boyce and R. C. DiPrima Elementary Differential Equations (Ninth Edition) Wiley 2009.

Tests

Test 1: Friday, July 3.

Test 2: Monday, July 27.

Final Examination: Tuesday, August 11, 1-3 pm.

Syllabus: The course covers all or part of Chapters 1-7 of the text. A schedule is given below. For the computer component of the course, we will learn and use Matlab.

Grading System: Your grade will be based on homework/quizzes, two in-class tests, and a final examination. The homework/quizzes will count for 25% of your grade, each in-class test for 25%, and final for 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 once or twice 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: The instructor will give make-ups (or satisfactory equivalents) only in cases authorized under TAMU Regulations. In borderline cases, the instructor will decide whether or not the excuse is authorized. Also, if you miss a test, quiz, or cannot turn in a homework, contact your instructor as 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 Disability Services, B118 Cain Hall, (979) 845-1637."

Approximate Schedule

• Chapter 1: 2 days
• Section 1.1. Some Basic Mathematical Models; Direction Fields
• Section 1.2. Solutions of Some Differential Equations
• Section 1.3. Classification of Differential Equations
• Chapter 2: 4 days
• Section 2.1. Linear Equations; Method of Integrating Factors
• Section 2.2. Seperable Equations
• Section 2.3. Modeling with First Order Equations
• Section 2.4. Differences Between Linear and Nonlinear Equations
• Section 2.5. Autonomous Equations and Population Dynamics
• Section 2.6. Exact Equations and Integrating Factors
• Chapter 3: 6 days
• Section 3.1. Homogeneous Equations with Constant Coefficients
• Section 3.2. Solutions of Linear Homogeneous Equations; the Wronskian
• Section 3.3. Complex Roots of the Characteristic Equation
• Section 3.4. Repeated Roots; Reduction of Order
• Section 3.5. Nonhomogeneous Equations; Method of Undetermined Coefficients
• Section 3.6. Variation of Parameters
• Section 3.7. Mechanical and Electrical Vibrations
• Section 3.8. Forced Vibrations
• Chapter 6: 3 days
• Section 6.1. Definition of the Laplace Transform
• Section 6.2. Solution of Initial Value Problems
• Section 6.3. Step Functions
• Section 6.4. Differential Equations with Discontinuous Forcing Functions
• Section 6.5. Impulse Functions
• Section 6.6. The Convolution Integral
• Chapter 7: 5 days
• Section 7.1,7.2 Introduction and Review of Matrices
• Section 7.3. Linear Algebraic Equations: Linear Independence, eigenvalues, Eigenvectors
• Section 7.4. Basic Theory of Systems of first Order Linear Equations
• Section 7.5. Homogeneous Linear systems with Constant Coefficients
• Section 7.6. Complex Eigenvalues
• Section 7.7. Fundamental Matrices
• Section 7.8. Repeated Eigenvalues
• Section 7.9. Nonhomogeneous Linear Systems
• Chapter 5: 4 days
• Section 5.1. Review of Power Series
• Section 5.2. Series Solutions near an Ordinary Point, Part I
• Section 5.3. Series Solutions near an Ordinary Point, Part II
• Section 5.4. Euler Equations; Regular Singular Points
• Section 5.5. Series Solution near a Regular Singular Point, Part I
• Section 5.6. Series Solution near a Regular Singular Point, Part II

If time remains, selected topics from Chapter 8 (Numerical Methods) or Chapter 9 (Nonlinear Systems) will be covered.