LINEAR ANALYSIS, Math 309 A (3 credits)
Winter 2009

• Office : Padelford C-328
• Office Phone : (206) 685-1307
• E-mail : solomyak at math dot washington dot edu
• Office Hours : Tuesdays 11-12 in C-328, or by appointment
• Problem Work Sessions (PWS): Thursdays 2:30-4:20 in Padelford C-401 In the PWS, you work on problems, and I will be there to answer your questions.

Course Information

• Text : W. Boyce and R. DiPrima, Elementary Differential Equations and Boundary Value Problems, 8th edition.
• Lecture : MWF 10:30-11:20, CMU 230
• Homework (20% of overall grade) (Almost) weekly homework will be assigned, due on Fridays in class. No late homeworks will be accepted. The grader will typically grade only 2-3 problems from each homework assignment.
• Exams (80% of overall grade):
  • Quiz (10% of overall grade) : Friday, January 23,
  • Midterm (25% of overall grade) : Friday, February 13
  • Final Exam (45% of overall grade): 8:30-10:20 a.m. Monday, March 16, in the usual classroom

• Syllabus

• Homework 1 (due Jan 16)

• Homework 2 (due Jan 23)

• Homework 3 (due Jan 30)

• Homework 4 (due Feb 6)

• Homework 5 (due Feb 20)

• Homework 6 (due Feb 27)

• Homework 7 (due Mar 6)

• Final Practice Problems

Solutions of Practice Problems: page 1;   page 2;   page 3;   page 4;   page 5;  page 6;  page 7;  page 8;  page 9;  page 10;   page 11

Calendar/Announcements

Monday, 3/16/2009:     8:30-10:20, FINAL EXAM

Sunday, 3/15/2009:     1:30-2:20, Office hour in C-328; 2:30-3:20, Review in C-36.

3/13/2009:     Review (see practice problems).

3/11/2009:     Laplace's equation (Section 10.8). Will NOT be on the Final.

3/9/2009:     D'Alembert solution of the wave equation; worksheet.

3/6/2009:     Wave Equation (cont.). Practice problems (not collected or graded): Section 10.7: 5, 6, 8, 23.

3/4/2009:     Wave Equation. Practice problems (not collected or graded): Section 10.7: 1, 2, 4, 14, 15.

3/2/2009:     Other Heat Conduction Problems. Practice problems (not collected or graded): Section 10.6: 1, 3, 5, 7.

2/27/2009:     Heat Conduction Problems. Practice problems (not collected or graded): Section 10.5: 2, 6, 8, 11, 16.

2/25/2009:     Even and Odd functions. Practice problems (not collected or graded): Section 10.4: 1, 2, 3, 4, 5, 6, 7, 9, 10, 13, 31, 32, 33, 34.

2/23/2009:     Fourier Convergence Theorem. Practice problems (not collected or graded): Section 10.3: 2, 4, 7.

2/20/2009:     Fourier Series (end).

2/18/2009:     Fourier Series. Practice problems (not collected or graded): Section 10.2: 13, 15, 29.

2/13/2009:     Midterm

2/11/2009:     Review. Answers to selected practice problems;   Solution of problems 1,2(b): page 1;   page 2;   page 3;   page 4;  

2/9/2009:     Boundary Value Problems, Section 10.1.

2/6/2009:     Predator-Prey equations. Practice problems (not collected or graded): Section 9.5: 2, 3, 4.

2/4/2009:     Phase Plane, Stability. Practice problems (not collected or graded): Section 9.1: 17, 18, 19, 20 , 21, Section 9.2: 5, 8 (see what you can do without a computer).

2/2/2009:     Application: earthquake-induced vibrations (not from the Textbook).

1/30/2009:     Homework 3 is due. 7.9: Non-homogeneous linear systems continued; Methods of Undetermined Coefficients and Variation of Parameters. Practice problems (not collected or graded): look at all the problems 1-12 in 7.9 and decide which ones can be solved by the Methods of Undetermined Coefficients. Without actually solving them, write down the form in which you would look for the particular solution.

1/28/2009:     7.9: Non-homogeneous linear systems; Method of Diagonalization (Example 1). See also pages 417-419 on Diagonalization.

1/26/2009:     7.7: Fundamental Matrices (up to the middle of page 416), 7.8: Repeated eigenvalues (up to the middle of page 426).

1/23/2009:     Quiz on 7.1-7.5.

1/21/2009:     Review, start repeated eigenvalues. Practice problems (not collected or graded), Section 7.8: 1, 3, 5.

1/16/2009:     Complex eigenvalues. Complex numbers handout. Practice problems (not collected or graded), Section 7.6: 1, 9, 15.

1/14/2009:     Homogeneous linear systems with constant coefficients, phase plane. Phase Plane handout. Practice problems (not collected or graded), Section 7.5: 1, 5, 9, 14, 16.

1/12/2009:     Basic theory of systems of first order linear homogeneous ODE's: Wronskian and the fundamental solution set. Practice problems (not collected or graded), Section 7.4: 4, 5, 6.

1/09/2009:     Eigenvalue problem, diagonalization. Read 7.3 and the subsection on diagonalizable matrices on pages 417--419 from 7.7 (you can also read Section 4.7 from the Math 308 text). Practice problems (not collected or graded), Section 7.3: 18, 19, 24. For each of the problems, decide if the matrix is diagonalizable, and if yes, diagonalize it.

1/07/2009:     Review of matrices, matrix-functions, linear independence. Practice problems (not collected or graded), Section 7.2: 2, 8, 10, 11, 15, 23. Section 7.3: 2, 6, 7, 8, 10.

1/05/2009:     Instruction begins. Introduction to systems of ODE's. Practice problems (not collected or graded), Section 7.1: 2, 4, 6, 7, 8, 9.