Differential Equations
Math 308-503 (MWF 10:20-11:10...BLOC 128) - Spring 2012
- 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
- 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).
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
- 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*
Please send comments, questions, or suggestions to Alisa Baron at
"alisa@math.tamu.edu".
Updated August 15, 2011 msp