AMS 20 (Winter 2009)

Mathematical Methods for Engineers II

Qi Gong

AMS 20 – 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

Prof. Qi Gong (qigong@soe.ucsc.edu), Baskin Engineering 143

Teaching Assistants

Chan, Derek (dchan@soe.ucsc.edu)

Lubinsky, Michael (mlubinsk@soe.ucsc.edu)

Text Book

Elementary Differential Equations and Boundary Value Problems, William Boyce and Richard DiPrima, Wiley, 8^th or 9^th Edition. ISBN: 0-471-43338-1.

Lectures

Tuesday and Thursday, 6:00pm to 7:45pm, Thim Lecture 001

Sections

There are two discussion/lab sections. Sections will be used to teach MATLAB programming needed for the course and solve practice problems.

Ming Ong PC (Merrill Room 103- Left side)

1: Tuesdays, 12:00-2:00pm (Chan, Derek)

2: Thursdays, 3:00-5:00pm (Chan, Derek)

Office Hours

Qi Gong: Wednesday, 11:00 - 12:00, Thursday, 12:00 - 1:00, BE 143.

Lubinsky, Michael: Tuesday and Thursday 10:00 - 12:00, BE 144.

Homework

Homework will be due weekly on Thursday at the beginning of class. Late homework is NEVER accepted. Please print your name clearly on the first page.

Grading

For AMS 20: Homework: 20% Quizzes: 10% Midterm: 30% Final 40%

For AMS 20A: Homework: 20% Quizzes: 20% Final 60%

Academic Honesty

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

Course Webpage

http://www.soe.ucsc.edu/classes/ams020/Winter09/

Tentative Schedule

• Week 1, Introduction and basic mathematical models involving ODEs.

Homework: read Chapter 1 except for Section 1.2.

Exercises

• Week 2, First order linear ODEs; integrating factor method; separable equations.

Read Sections 1.2, 2.1, 2.2, and 2.4

Homework Exercises Homework Solutions

Things you need to know after week 2

a. Know how to classify differential equations.

b. Know what an initial value problem is; and how to show a given

function is a solution.

c. Know the general format of linear differential equations.

d. If the differential equation is linear, compute the integrating factor, and

then the general solution.

e. If it's nonlinear, is it separable? If it's separable, you will need to

compute two different integrals.

f. It is crucial to know integration of basic functions and integral methods

from your calculus course. For Example, various substitutions,

integration by parts, and partial fractions will all be utilized.

g. Existence and uniqueness of solutions to linear first order ODE's.

h. Existence and uniqueness of solutions to nonlinear first order ODE's.

• Week 3, Homogeneous second order linear ODEs with constant coefficients.

Read Sections 3.1, 3.2, 3.3, 3.4, and 3.5

Homework Exercises Homework Solutions

• Week 4, Nonhomogeneous linear ODEs. Method of variation of parameters and

method of undetermined coefficients.

Read Sections 3.6, 3.7, 3.8, and 3.9

Homework Homework Solutions

• Week 5, Mechanical examples of second order linear ODEs.

Things You Should Know about 2nd Order ODEs

Midterm Exam: Thurs, Feb. 5^th, 6:00-7:45, Thim Lecture 001.

(Midterm covers all material we have discussed up to this point)

• Week 6, High order linear equations. Review of linear algebra

Read Chapter 4, Sections 7.2, and 7.3

Homework Homework Solutions

Things you should know about high-order ODEs

• Week 7, Systems of first order linear ODEs. Homogeneous cases with constant

coefficients.

Read Sections 7.1, 7.4, 7.5 and 7.6

Homework Homework Solutions

• Week 8, Nonhomogeneous systems of first order linear ODEs.

Read Sections 7.7, 7.8 and 7.9

Homework Homework Solutions

Things you should know about system of ODEs

• Week 9, Laplace transform and initial value problems.

Read Sections 6.1 and 6.2

Homework Homework Solution

• Week 10, Discontinuous forcing functions, engineering applications and review.

Read Sections 6.3 and 6.4

Things you should know about Laplace transform

AMS 20A students are not required to attend class from week 7 to week 10.

“If you qualify for classroom accommodations because of a disability, please submit your Accommodation Authorization from the Disability Resource Center (DRC) to me during my office hours in a timely manner, preferably within the first two weeks of the quarter. Contact DRC at 459-2089 V, 459-4806 TTY.”