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

**TA:** Furutani, Aya, email: afurutan@soe.ucsc.edu

**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, 9^{th} 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.

**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

**Course Webpage: **http://courses.soe.ucsc.edu/courses/ams20/Winter13/01

**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,

**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

**Week 5**Method of undetermined coefficients, mechanical examples of second

** **** 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

**Week 10**Laplace transform

- Qi Gong (qgong) (Instructor)
- Aya Rita Furutani (afurutan) (Assistant)