Mat
22b-22
(CRN 75840)
Ordinary
Differential
Equations
Summer
Session
II
2010
Instructor: Ricky
Kwok
Office: MSB
2232
Email: rkwok at math dot
ucdavis dot edu
Class webpage:
www.math.ucdavis.edu/~rkwok/22b
Course Information
Dates: August 2nd - September 10th
Times: MWF 12:10 - 1:50pm
Location: Olson
158
Textbook:
Elementary
Differential Equations and Boundary Value
Problems (8th Edition)
by W.
E. Boyce and R. C. DiPrima
Office Hours: MW 3:00 -
4:00pm and by appointment
Department
Syllabus
Course Outline
Introduction (Chapter 1)
- (1.1, 1.2, 1.3) Introduction and Terminology, direction
fields, discussion and solution of some ODE
First
Order
Differential
Equations
(Chapter
2)
- (2.1) Linear equations; integrating factors
- (2.2) Separable equations
- (2.3, 2.4) Modeling, mechanics; Linear versus non-linear
equations
- (2.5) Autonomous equations; Population dynamics
- (2.7) Numerical approximations: Euler's method
- (2.8) Existence and uniqueness theorem
- (2.9) First order difference equations
Second
Order
Linear
Equations
(Chapter
3)
- (3.1) Homogeneous second order equations with constant
coefficients
- (3.2, 3.3) Fundamental solutions, linear independence,
Wronskian
- (3.4) Complex roots
- (3.5) Repeaed roots; Reduction of order
- (3.6) Nonhomogenous equations; Method of undertermined
coefficients
- (3.7) Vaiation of Parameters
- (3.8, 3.9) Applications to oscillating systems
Laplace
Transform
(Chapter
6)
- (6.1) Definition of Laplace Transform
- (6.2) Solution of initial value problems with Laplace
Transform
Systems
of
First
Order
Linear
Equations (Chapter 7)
- (7.1) Introduction to system of linear ODE
- (7.2, 7.3) Review of related linear algebra
- (7.4) Basic theory of first order linear systems
- (7.5) Homogeneous linear systems with constant coefficients
- (7.6) Complex eigenvalues
- (7.7) Fundamental matrices
- (7.8) Repeated eigenvalues
- (7.9) Nonhomogeneous linear systems
Grading
20%
Homework: I will assign homework after every two lectures so to keep
you up to speed with material. Late homeworks
will not be accepted.
30%
Midterm (August 20): At the end of the third week, we
will have a midterm covering the first three chapters, or what I can
get done up until that point.
50%
Final Exam (September 10) : We will have an in class final during the
last scheduled lecture. The exam will be cumulative, but will
emphasize chapters six and seven.
Philosophy
Homework
I strongly
encourage collaboration among students. However, please write up
solutions to homeworks by yourself.
If you have a specific question, please come to office hours!
Exams
Review all homework problems and be sure you can solve them on your own
without referring back to solutions.
Do this with the help of a few classmates; explaining topics to each
other is a strong indication you all understand the material.
Exam Information
No calculators or any electronic device will be
allowed for any exam. You will be graded on organization,
presentation and clarity.
No make-up exams will be allowed. A missed exam
will result in a zero for the score.
CODE OF ACADEMIC CONDUCT
Honor and Academic Integrity: UC Davis Traditions Since 1911
All members of the academic community are responsible for the academic
integrity of the Davis campus. Existing policies forbid cheating on
examinations, plagiarism and other forms of academic dishonesty.
Academic dishonesty is contrary to the purposes of the University and
is not to be tolerated. A code of conduct for the campus community must
exist in order to support high standards of behavior. Under the Code of
Academic Conduct, adopted in 1976, students, faculty, and
administration share responsibility for academic integrity at UC Davis.
The Code requires students to act fairly and honestly, and is based on
a student honor code established in 1911. Examples of academic
misconduct include:
- Receiving or providing unauthorized assistance on examinations
- Using or having unauthorized materials out during an examination
- Plagiarism - using materials from sources without citations
- Altering an exam and submitting it for re-grading
- Fabricating data or references
- Using false excuses to obtain extensions of time
Schedule
(tentative)
Week
|
Monday
|
Wednesday
|
Friday
|
1
|
8-2
Syllabus
+ 1.1, 1.2, 1.3
|
8-4
2.1, 2.2
|
8-6
2.3,
2.4, 2.5
|
2
|
8-9
2.7,
2.8
|
8-11
2.9,
3.1
|
8-13
3.2, 3.3, 3.4
|
3
|
8-16
3.5, 3.6
|
8-18
3.7,
3.8, 3.9
|
8-20 Midterm
|
4
|
8-23
Go
over midterm + 6.1
|
8-25
6.2,
7.1
|
8-27
7.2,
7.3
|
5
|
8-29
7.3,
7.4
|
9-1
7.5,
7.6
|
9-3
7.7,
7.8
|
6
|
9-6 Labor Day
Holiday (No Class)
|
9-8
7.9
+ review
|
9-10 Final
Exam
in
Olson 158
|