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: qigong@soe.ucsc.edu

**Teaching Assistants:**

- Sky Trigueiro, Email: striguei@ucsc.dot.edu
- Mattew Simms, Email: mmsimms@soe.ucsc.edu

**LSS Tutor:** Jason Vranek (jvranek@ucsc.edu). Sign up for a tutoring section at: http://lss.ucsc.edu/programs/small-group-tutoring/index.html

**Lectures:** MoWeFr 12:30PM - 1:40PM, Steven Acad 150

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

- Section 01A: Tuesday, 1:30PM-3:15PM, BE 109
- Section 01B: Wednesday, 3:00PM-4:45PM, BE 109
- Section 01C: Thursday, 3:00PM-4:45PM, BE 109
- Section 01D: Friday, 6:30PM-8:30PM, MingOng Cmp Lb 103

**Office Hours**

- Qi Gong: Tuesday and Thursday, 12:00PM to 1:30PM , BE 361A
- Matthew Simms: Monday 3:00 - 4:00pm, Thursday 5:00 - 6:00pm, Friday 10:00 - 11:00am, at BE 312C/D

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

**Homework:** Homework will be due weekly on Wednesday 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.

**Quizzes:** All quizzes will be given in Lab sections.

**Grading:**

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

**Academic Honesty:** See explanation at http://www.ucsc.edu/academics/academic_integrity/index.html

**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 (only for AMS 20)

- 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:

- AMS 20: Monday, June 6th, 4:00pm - 7:00 pm
- AMS 20A: Monday, June 6th, 4:00pm - 5:30 pm

**Students with disabilities:** If you have special needs, we will accommodate you. The Disability Resource Center offers services that are confidential and free of charge. After you contact the Disability Resource Center, bring your Accommodation Authorization form to me after class or during office hours and we will discuss your accommodations.