Mathematical Methods for Engineers II

Feb. 25, 2013: We will have a quiz next week (week 8) in the lab sections. The quiz will cover higher order linear ODES and system of 1st order linear ODES.

Final Exam: Thursday, March 21 from 4:00pm to 7:00pm

Jan. 30th, 2013: We will have our midterm exam on Feb. 12th during the regular lecture time. The exam covers everything we learned on 1st order and 2nd order ODES. Note that AMS20A students are not required to take the midterm exam.

Jan. 22, 2013: We will have a quiz next week (week 4) in the lab sections. The quiz covers everything we learned on 1st order ODES.


AMS 20/20A – Mathematical Methods for Engineers II. The course provides fundamentals of Ordinary Differential Equations (ODEs) and systems of ODEs with strong emphasis on engineering applications. 

Instructor: Qi Gong, Associate Professor, BE 361A, email:

TA: Furutani, Aya, email:

Lecture: TuTH 6:00PM - 7:45PM, Kresge Clrm 321

Sections: There are three lab/discussion sections. Students are required to attend one of these three sections. Lab/discussion sections will be used to teach MATLAB programming needed for the course, review lectures, and solve practice problems.

  • Section 01A: Tuesday, 4:00PM-5:45PM, J Baskin Engr 109
  • Section 01B: Wednesday, 2:00PM-3:45PM, J Baskin Engr 109
  • Section 01C: Thursday, 9:00AM-10:45AM, J Baskin Engr 109

Textbook: Elementary Differential Equations, William Boyce and Richard DiPrima, Wiley, 9th Edition.

Office Hours

  • Qi Gong: Monday, Wednesday, Thursday: 12:30PM – 2:00PM, BE 361A
  • Furutani, Aya, Thursday and Friday: 2:30pm - 3:30pm, BE 312C/D

Homework: The homework will always be due on Tuesday by 11:00am. Homework should be deposited in the AMS20/20A drop-box (map of the drop-box). Late homework is NEVER accepted. Please print your name clearly, and write down your lab section number on the first page. Homework will be returned to you during the lab sections. 


  • AMS 20:    Homework: 20%   Quizzes: 10%  Midterm: 30%   Final 40%
  • AMS 20A:  Homework: 30%   Quizzes: 10%  Final 60%

Academic Honesty: See explanation at

Course Webpage:

Tentative Schedule  (AMS 20A students are not required to attend class from week 6 to week 10)

  • Week 1 Introduction and basic mathematical models involving ODEs.
  • Week 2 First order linear ODEs; integrating factor method; separable equations, existence and uniqueness of solutions.  
  • Week 3 Homogeneous second order linear ODEs. Existence and Uniqueness, Principle of Superposition, Wronskian, fundamental Solutions
  • Week 4 Homogeneous linear ODEs with constant coefficients, nonhomogeneous linear ODEs, method of variation of parameters
  • Week 5 Method of undetermined coefficients, mechanical examples of second order linear ODEs, high order linear equations.

        Midterm exam

  • Week 6 Higher order linear equations. Review of linear algebra
  • Week 7 Systems of first order linear ODEs. Homogeneous cases with constant coefficients (distinct real eigenvalues and complex eigenvalues).
  • Week 8 Homogeneous cases with constant coefficients repeated eigenvalues).
  • Week 9 Nonhomogeneous systems of first order linear ODEs, engineering applications, introduction to Laplace transform
  • Week 10 Laplace transform and initial value problems, discontinuous forcing functions, and review.

Instructors and Assistants