**Instructor: J. D. Ward****Office:**305 Milner Hall**E-mail:**`jward@math.tamu.edu`**Phone:**845-1169**URL:**`http://www.math.tamu.edu/~joe.ward/`**Office Hours**: MW 1:00-2:30 or by appointment

**Catalogue Description and Syllabus:** MATH 308 * Differential Equations *

**Required Text**: J. R. Brannan and W.E. Boyce,
*
Differential Equations: An Introduction to Modern Methods and Applications, Wiley 2009*.

**Prerequisites**
*
Math 251 or equivalent; knowledge of Matlab or Maple would be helpful*.

**Course Objectives**: to expose the students to the basics of linear ODEs and to nourish an appreciation for
the potential of application of ODEs to various engineering problems.

**Grading System & Tests:** Your grade will be
based on homework, two in-class tests which will be within one class day of (**February 28 & April 13**) and a final exam (**Friday, May 6, 7:30-9:30 am**). The
homework will count for 25%, each in-class test for 25% and the 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.

** Note: Q-drop deadline is Monday, April 4 (5 P.M.). **

**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 a student MUST contact me BEFORE missing an exam (only emergencies
allowed if contact after the exam).

**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."

**Homework:** You may consult with each
other on homework problem sets, BUT only submit work which is in your
own words AND be sure to cite any sources of help (either texts or
people). Late homework will *not* be accepted. The homework problems
will be announced in class and can be found on my homepage
http://www.math.tamu.edu/~jward

** Americans with Disabilities Act **

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 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.

** Academic Integrity Statement **

Honor Council Rules and Procedures

**MATH 308.** Differential Equations.(3-0) Credit 3.0. Ordinary differential equations, solutions using Laplace transforms, systems of differential equations.

** Suggested Schedule**

- Chapter 1: 1 days
- Section 1.1. Some Basic Mathematical Models; Direction Fields
- Section 1.2. Solutions of Some Differential Equations

- Chapter 2: 4 days
- Section 2.1. Linear Equations; Method of Integrating Factors - one day
- Section 2.2. Seperable Equations - one day
- Section 2.3. Modeling with First Order Equations - one day
- 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
- Do 2.4, 2.5 and 2.6 in two days, doing only one representative example from 2.5

- Chapter 3: 4 days
- Section 3.1. Systems of Two Linear Algebraic Equations - one day
- Section 3.2. Systems of Two First Order Linear Differential Equations - one day
- Section 3.3. Homogeneous Linear Systems with Constant Coefficients - one day
- Section 3.4. Complex Eigenvalues - one day
- Section 3.6. A Brief Introduction to Nonlinear Systems - one day

- Chapter 4: 4 days
- Section 4.1. Definitions and Examples
- Section 4.2. Theory of Second Order Linear Homogeneous Equations (Cover 4.1 and 4.2 in one day)
- Section 4.3. Linear Homogeneous Equations with Constant Coefficients - one day
- Section 4.4. Characteristic Equations with Complex Roots - one day
- Section 4.5. Mechanical and Electrical Vibrations - optional
- Section 4.6. Nonhomogeneous Equations: Method of Undetermined Coefficients - one day
- Section 4.7. Forced Vibrations, Frequency Response, and Resonance - optional
- Section 4.8. Variation of Parameters - one day

- Chapter 5: 6 days
- Section 5.1. Definition of the Laplace Transform - one day
- Section 5.2. Properties of the Laplace Transform - one day
- Section 5.3. The Inverse Laplace Transform - one day
- Section 5.4. Solving Differential Equations with Laplace Transforms - one day
- Section 5.5. Discontinuous Functions with Laplace Transforms - one day
- Section 5.6. Differential Equations with Discontinuous Forcing Functions - one day
- Section 5.7. Impulse Functions - one day
- Section 5.8. Convolution Integrals and Their Applications - one day
- Section 5.9. Linear Systems and Feedback Control - optional

- Chapter A (Appendix A): 3 days
- Section A.1. Matrices
- Section A.2. Systems of Linear Algebraic Equations, Linear Independence, and Rank
- Section A.3. Determinants and Inverses
- Section A.4. the Eigenvalue Problem

- Chapter 6: 4 days
- Section 6.1. Definitiions and Examples
- Section 6.2. Basic Theory of First order Linear Systems
- Section 6.3. Homogeneous Linear systems with Constant Coefficients
- Section 6.4. Complex Eigenvalues
- Section 6.5. Fundamental Matrices and the Exponential of a Matrix
- Section 6.6. Nonhomogeneous Linear Systems