Instructor: J. D. Ward

Office: 305 Milner Hall

E-mail: jward@math.tamu.edu

Phone: 845-7554 (math office)

URL: http://www.math.tamu.edu/~joe.ward/

Office Hours: Wed. 1:30-4:00 or by appointment

Course: MATH 308 Differential Equations

Required Text: W.E. Boyce and R. C. DiPrima, Elementary Differential Equations: Ninth Edition, Wiley Custom 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, three in-class tests which will be within one class day of (Feb. 8 & March 7 & April 11 ) and a final exam (Friday, May 4, 3:00-5:00). The homework will count for 20%, each in-class test for 20% and the final for 20%. 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 2 (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

Help Sessions for homework and Matlab

Calclab Hours

Help with 308 homework: Mon., Wed. and Thurs. 7:00-9:30 PM, Bloc 102: Sunday 2:30-5:00 PM , Bloc 169

Help with matlab: Mon. thruough Thurs. 7:00-10:00 PM: Sunday 1:00-10:00 PM , Bloc 128

MATH 308 - Suggested Weekly Schedule

MATH 308. Differential Equations.(3-0) Credit 3.0. Ordinary differential equations, solutions in series, solutions using Laplace transforms, systems of differential equations. Prerequisites: MATH 251 or equivalent; knowledge of computer algebra system.

Suggested (Approximate) Schedule

• Chapter 1: 2-3 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

  1.1-1.3 should be covered in 2 days

• Chapter 2: 5-6 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
  • Do 2.4, 2.5 and 2.6 in two days, doing only one representative example from 2.5
• Chapter 3: 8 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: 6-7 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: 8 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: 6 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

The remaining lectures may come from either Chapter 8 (Numerical Methods) or Chapter 9 (Nonlinear Systems).

• Optional Track #1 - 4 days (Numerical Methods)
• Section 8.1. The Euler or Tangent Line Method
• Section 8.2. Improvements on the Euler Method
• Section 8.3. The Runge-Kutta Method
• Section 8.4. Multistep Methods
• Optional Track #2 - 4 days (Nonlinear Systems)
• Section 9.1. The Phase Plane; Linear Systems
• Section 9.2. Autonomous Systems and Stability
• Section 9.3. Locally Linear Systems
• Section 9.4, 9.5. Competing Species, Predator-Prey Equations

Add in three days for exams and this will give a total of 42 days.

Please send comments, questions, or suggestions to Alisa Baron at "alisa@math.tamu.edu".
Updated August 15, 2011 msp

MATH 308 - Suggested Homework Problems

All students should read the text, the lab manual, and study the online Chapter Notes before attempting the problems. Lab Manual and basic problems should be done by everyone. Advanced problems (marked with an asterisk '*') are optional and are for those students seeking A and B grades. Problems will be selected from those below and will be posted on my webpage each week.

• Chapter 1:
  • Section 1.1. 1-19 odd, 22, 23, 25, 29, 31
  • Section 1.2. 1-17 odd, 18*
  • Section 1.3. 1-23 odd, 29*, 30*, 31*
• Chapter 2:
  • Section 2.1. 1-25 odd, 27*, 30*, 38*
  • Section 2.2. 1-19 odd, 29*, 30*
  • Section 2.3. 1, 3, 5, 6, 9, 11, 17, 22, 27*, 31*, 32*
  • Section 2.4. 1-17 odd, 21, 24
  • Section 2.6. 5-15 odd, 19, 21, 25, 27
• Chapter 3:
  • Section 3.1. 7-23 odd
  • Section 3.2. 1-25 odd, 31, 35, 42*, 47*
  • Section 3.3. 7-23 odd, 27, 29, 33*, 34*
  • Section 3.4. 1-13 odd, 23-29 odd, 33*, 38*
  • Section 3.5. 1-17 odd, 27*, 30*
  • Section 3.6. 1-19 odd, 27*, 28*
  • Section 3.7. 1-19 odd, 26*, 30*
  • Section 3.8. 1-13 odd, 15*
• Chapter 6:
  • Section 6.1. 1-23 odd, 26*, 27*
  • Section 6.2. 1-23 odd, 27*
  • Section 6.3. 1-23 odd, 34*, 35*
  • Section 6.4. 1-15 odd, 16*
  • Section 6.5. 1-13 odd, 15*
  • Section 6.6. 1-19 odd
• Chapter 7:
  • Section 7.1. 1-17 odd, 18*
  • Section 7.2. 1-25 odd
  • Section 7.3. 1-23 odd, 31*, 33*
  • Section 7.4. 1-9 odd
  • Section 7.5. 1-27 odd
  • Section 7.6. 1-19 odd
  • Section 7.7. 1-11 odd
  • Section 7.8. 1-13 odd
  • Section 7.9. 1-11 odd
• Chapter 5:
  • Section 5.1. 1-23 odd
  • Section 5.2. 1-19 odd, 21*
  • Section 5.3. 1-15 odd, 22*, 23*
  • Section 5.4. 1-11 odd, 17-33 odd
  • Section 5.5. 1-13 odd, 14*, 16*
  • Section 5.6. 1-17 odd

• Optional Track #1 [Numerical Methods]
• Section 8.1. 1-11 odd, 15, 20
• Section 8.2. 1-11 odd, 14*, 15*, 22*
• Section 8.3. 1-11 odd, 14*
• Section 8.4. 1-15 odd

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• Optional Track #2 [Nonlinear Systems]
• Section 9.1. 1-11 odd, 20*, 21*
• Section 9.2. 1-11 odd, 17, 19
• Section 9.3. 1-15 odd, 19, 23, 25*, 27*
• Section 9.4. 1-5 odd, 8, 9, 13*, 15*
• Section 9.5. 1-7 odd, 14*, 15*, 16*

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Please send comments, questions, or suggestions to Alisa Baron at "alisa@math.tamu.edu".
Updated August 15, 2011 msp