Mathematical Methods for Engineers II

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:

Teaching Assistant: Harleigh Marsh, Email:

Lecture: TuTH 4:00PM - 5:45PM, Merrill Acad 102

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: Monday, 6:00PM-8:00PM, Soc Sci 1 135
  • Section 01B: Tuesday, 6:00PM-8:00PM, Soc Sci 1 135
  • Section 01C: Wednesday, 6:00PM-8:00PM, Soc Sci 1 135

Textbook: Elementary Differential Equations, William Boyce and Richard DiPrima, Wiley, 10th Edition. You can get the UCSC custom version to save the cost.

Office Hours

  • Qi Gong: Tuesday and Wednesday, 11:00AM to 12:30PM , BE 361A
  • Harleigh Marsh: Thursday 6:00PM -7:00PM, Friday 3:00PM - 4:00PM, BE 312C-D

Homework: Homework will be due weekly on Tuesday at the beginning of class. Homework will be posted online. Late homework is NEVER accepted. For each homework, a selected set of problems will be graded. The graded homework will be returned to you in lab sections. Please print your name, lab section number, and Student ID clearly on the first page of your homework.


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

Academic Honesty: See explanation at

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

  • Week 1 Introduction and basic mathematical models involving ODEs, First order linear ODEs, and integrating factor method.
  • Week 2 Nonlinear 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.

     Final Exam: Wednesday, March 18, 8:00 - 11:00 am



Students with disabilities: If you qualify for classroom accommodations because of a disability, please get an Accommodation Authorization from the Disability Resource Center (DRC) and submit it to me in person outside of class (e.g., office hours) within the first two weeks of the quarter. Contact DRC at 459-2089 (voice), 459-4806 (TTY), or for more information on the requirements and/or process.

Instructors and Assistants