AMS 20 & 20A: Mathematical Methods For Engineers II


Instructor: Dongwook Lee (dlee79 _at_ ucsc _dot_ edu), Applied Mathematics and Statistics, Baskin Engineering 353C

TAs: Youngjun Lee (ylee109 _at_ ucsc _dot_ edu) and Jayashree Sridhar (jsridha1_at_ ucsc _dot_ edu)

Lectures: Tue and Thu, 9:50 am - 11:25 am in Classroom Unit 001

Lab Sections: There are four mandatory computer lab/discussion sections led by TAs. Students are required to attend one of these four sections. Lab/discussion sections will be used to take Quizzes, and learn MATLAB programming for the course, review lectures, and solve practice problems. 

  • Monday 3:30 - 4:30 pm at Ming Ong (Merrill Room 103) led by TA Youngjun Lee
  • Monday 4:30 - 5:30 pm at Ming Ong (Merrill Room 103) led by TA Youngjun Lee
  • Tuesday 3:30 - 4:30 pm at Social Science 1 Room 135 led by TA Jayashree Sridhar
  • Tuesday 4:30 - 5:30 pm at Social Science 1 Room 135 led by TA Jayashree Sridhar
  • No lab sections in the first week. 


Tutor: Jesus Bobadilla (jebobadi _at_ ucsc _dot_ edu). Sign up for tutoring sessions at

  • Three 1hr tutoring sessions (You need to sign up to see the location of each session)
    • Monday: 1:30 pm -- 2:30 pm
    • Wednesday: 4:15 pm -- 5:15 pm
    • Friday: 9:30 am -- 10:30 am

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:

  • Prof. Dongwook Lee: Mon 10:30 am -- 11:30 am & Th 3:30 pm -- 4:30 pm, BE 353C
  • TAs:
    • Youngjun Lee, Tue 1:00 pm -- 2:00 pm & Wed 3:00 pm -- 4:00 pm, both at BE 312 C/D
    • Jayashree Sridhar, Wed 9:00 am -- 11:00 am (BE 312C/D)
  • Remember that all TAs and the instructor are available to help you during office hours (you are welcome to attend office hours of any of the TAs, not just your own). If you cannot make any of the office hours, please contact the instructor by email and arrange to meet at another time.


 Course Objectives

The course provides fundamentals of Ordinary Differential Equations (ODEs) and systems of ODEs with an emphasis on engineering applications. 

Grading Policy

Homework: (see more on the Homework tab) 

  • Homework will be due weekly at the beginning of class on one of the class days. Homework will be posted online (see the Homework Assignments tab). 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.


Quizzes: (see more in the Homework tab) -- All quizzes will be given in Lab sections.

  • AMS 20 students: there will be six quizzes for AMS 20.
  • AMS 20A students: only the first three of them (Quiz 1 ~ Quiz 3) are required for AMS 20A.


Two in-class exams: (see more in the Quizzes and Exams tab) 

  • Midterm exam (only for AMS 20): Feb 13, Tue, in-class.
  • Final exam (both for AMS 20 and AMS 20A): Mar 22, Thu (8 am -- 11 am).



  • AMS 20  :  
    • Method 1: Homework 20%, Quizzes 10%, Midterm 30% and Final 40%
      • All class activities (classes, labs, six quizzes, homework sets, midterm and final exams)
      • AMS 20 students can drop one lowest homework score and one lowest quiz score.
    • Method 2: 100% Final only
    • Final grade = max (Method 1 score, Method 2 score)
  • AMS 20A:  Homework: 30%   Quizzes: 10%  Final 60%
    • All class activities (classes, lab sessions, quiz 1 ~ quiz 3, homework sets) for Week 1 ~ Week 6
    • No midterm exam
    • Final exam only on the topics for Week 1 ~ Week 6
    • AMS 20A students can drop either one lowest homework score or one lowest quiz score.
    • Required participation:


Curving: There will be a curve of your final grade. The policy on curving is such that the class average will be decided to be between C+ and C.


Passing grades: Your overall curved score must be C or above in order to pass the class.


Academic Honesty (zero-cheating policy): 

  • Any form of cheating or dishonest academic activities (using notes, books, smartphones, tablet PCs, or electronic devices; copying from someone else, etc. on in-class quizzes or exams) will not be tolerated and such students will receive a failing grade. Any students with such activities, if caught by the instructors or classmates, will be reported to the AMS department and her/his college provost.
  • See more explanation at


A List Of Course Topics

Note: AMS 20A students are NOT required to attend classes from week 7 to week 10

Click the Class Schedules tab to see more details

  • 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 (Feb 13, Tue, in-class)
  • Week 6: Higher order linear equations.
  • Week 7: Laplace transforms and initial value problems, discontinuous forcing functions, and review. Review of linear algebra
  • Week 8: Systems of first order linear ODEs. Homogeneous cases with constant coefficients (distinct real eigenvalues and complex eigenvalues).
  • Week 9: Homogeneous cases with constant coefficients repeated eigenvalues.
  • Week 10: Nonhomogeneous systems of first order linear ODEs, engineering applications.
  • Final exam (Mar 22, Thu, in class, 8 am -- 11 am for AMS 20; 8 am -- 9:30 am for AMS 20A)

Students With Disabilities

UC Santa Cruz is committed to creating an academic environment that supports its diverse student body. If you are a student with a disability who requires accommodations to achieve equal access in this course, please submit your Accommodation Authorization Letter from the Disability Resource Center (DRC) to me privately during my office hours or by appointment, preferably within the first two weeks of the quarter. At this time, I would also like us to discuss ways we can ensure your full participation in the course. I encourage all students who may benefit from learning more about DRC services to contact DRC by phone at 831-459-2089, or by email at