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: Chris Phelps, Email:

Learning Support Services (LLS) Tutor: Corey Abraham, Email: Sing-up for tutoring at

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 homework, and solve practice problems.

  • Section 01A: Tuesday, 3:00PM-4:45PM, MingOng Cmp Lb 103
  • Section 01B: Wednesday, 4:00PM-5:45PM, MingOng Cmp Lb 103
  • Section 01C: Thursday, 3:00PM-4:45PM, MingOng Cmp Lb 103

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

Office Hours

  • Qi Gong: Tuesday 2:30 - 3:30 pm and Thursday 1:00 - 3:00 pm, BE 361A
  • Chris Phelps: Tuesday 1:30 - 2:30 pm, 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. Graded homework will be returened 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 class 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: Monday, June 9, 7:30 - 10:30 pm

Students with disabilities: If you qualify for classroom accommodations because of adisability, 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) with in 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