Spring, 2004

**GSI:** Jiangang Yao

**Office:** 1039 Evans

**Office Hours:** M 4-5pm and Th 1-2pm

**Mailbox:** 940 Evans

**Prerequisites:** Math 1B

**Syllabus:** Honors version of Math 54. The course has two
parts.

__Part I: Linear algebra__. Vectors; matrices; solving linear
equations. Invertible matrices; determinants. Vector
spaces, bases, dimension and rank. Inner product spaces,
orthogonality, least-squares approximation. Eigenvalues and
eigenvectors; linear transformations.

__Part II: Differential equations__. Review of linear
ordinary differential equations in one variable. Systems of
linear differential equations; solution of systems with constant
coefficients. Introduction to Fourier series with applications
to partial differential equations.

**Required Texts:**

- Hill,
*Elementary Linear Algebra*(3rd Ed.) - Boyce and DiPrima,
*Elementary Differential Equations and Boundary Value Problems*(7th Ed.)

**Homework, exams and grading policy:** Weekly homework
assignments posted on the course web page and due in discussion
section on Fridays (or in the GSI's mailbox by noon Friday).
Each homework set will contain some straightforward exercises, to
check your understanding of the basic subject matter, and some more
challenging problems, requiring a measure of creativity to solve.

Homework ground rules: feel free to discuss the homework problems and
your ideas for solutions with other students. However, if you
work together with others, each of you must write up your solutions
independently, without copying from solutions worked out jointly.

Percentage contribution of homework and exams to the overall course
grade will be Homework 20%, Midterm exams 20% each, Final exam 40%.

- 1st Midterm Exam: Tues, Feb. 24
- 2nd Midterm Exam: Tues, Apr. 13
- Final Exam: Wednesday, May 19, 8:00-11:00am (exam group 12), Room 110 Wheeler

- Assignment 1, due Friday, Jan. 30. Solutions
- Assignment 2, due Friday, Feb. 6. Solutions
- Assignment 3, due Friday, Feb. 13. Solutions
- Starting Tues., Feb. 10, Math H54
**lecture moves to room 7 Evans Hall** - The class will
**not meet on Thurs., Feb. 12** - Assignment 4, due Friday, Feb. 20.
Corrected Problem A to refer to section
**2.4**, Ex. 22. Solutions - Midterm 1 is Tuesday, Feb. 24 in class. Here are some review problems, with solutions. Jiangang will hold a review session Sunday, Feb. 22, 3-5pm, Room 31 Evans Hall.
- Exam 1 Solutions
- Assignment 5, due Friday, March 5. Solutions
- Assignment 6, due Friday, March 12. Solutions
- Assignment 7, due Friday, March 19. Solutions
- Assignment 8, due Friday, April 2. Solutions
- Assignment 9, due Friday, April 9. Solutions
- Midterm 2 is Tuesday, April 13, in class. Jiangang will hold a review session Sunday, April 11, 3-5 pm in 5 Evans Hall. Here are review problems, with solutions.
- Exam 2 Solutions
- In the lecture on Thursday, April 15, we'll discuss the use of orthogonal polynomials to compute polynomial approximations to general functions. Here is an interesting example.
- Assignment 10, due Friday, April 23. Solutions
- Assignment 11, due Friday, April 30. Solutions
- Assignment 12, due
**Monday**, May 10.**Note:**Problem A was not stated correctly, fixed now. If you downloaded the assignment before Thursday afternoon (May 6), please fetch it again. Solutions - Final exam is Wed., May 19, 8-11am in Room 110 Wheeler. Jiangang will hold a review session Saturday, May 15, 7-9pm in Room 31 Evans. Here are some review problems, with solutions.
- Final exam solutions

Jiangang's office hours for finals week:

Tu, W 5-6pm 818 Evans see Han Fei

Th, F 5-6pm 1039 Evans

Tu(May 18) 4-6pm 818 See Han Fei