Differential Equations
Math 308302 — Summer 2015
Catalogue Description: MATH 308. Differential
Equations. (30). 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 121:25, 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, 13 pm.
Syllabus: The course covers all or part of
Chapters 17 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 inclass tests, and a final examination. The
homework/quizzes will count for 25% of your grade, each inclass
test for 25%, and final for 25%. Your letter grade will be assigned
this way: 90100%, A; 8089%, B; 7079%, C; 6069%, 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.
Makeup Policy: The instructor will give makeups
(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
handouts and webmaterials 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
antidiscrimination 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) 8451637."
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.