LINEAR ANALYSIS, Math 309 A (3 credits)
Summer 2010

• Office : Padelford C-328
• Office Phone : (206) 685-1307
• E-mail : solomyak at math dot washington dot edu
• Office Hours : Mondays 1-2, Wednesdays 1-2, or by appointment

Course Information

• Text : W. Boyce and R. DiPrima, Elementary Differential Equations and Boundary Value Problems, 9th edition.
• Lecture : MWF 9:40-10:40, in CMU B006
• Homework (15% of overall grade) Weekly homework will be assigned, due on Fridays in class. No late homeworks will be accepted. The grader will typically grade only 3-4 problems from each homework assignment.
• Exams (85% of overall grade):
  • Quiz (10% of overall grade) : Friday, July 9
  • Quiz Answers; Figures (answers to #4 and #5)
  • Midterm (35% of overall grade) : Friday, July 23
    Practice Problems; Midterm answers ;

    Final Exam (40% of overall grade): last day of classes, Friday, August 20 in the usual classroom.

    Practice Problems ;
    

    Answers ;

    Optional Review on Thursday, August 19, 3:30-4:30, in C-401 PDL

    Additional office hour on Thursday, August 19, 1:10-2:20, in C-328 PDL

• Syllabus

• Homework 1 (due July 2)

• Homework 2 (due July 9)

• Homework 3 (due July 16)

• Homework 4 (due July 23)

• Homework 5 (due July 30)

• Homework 6 (due August 6)

• Homework 7 (due August 13)

Calendar/Announcements

8/13/2010:     Wave equation. READ Section 10.7. Practice problems (not collected or graded): Section 10.7: 1, 2, 4, 5, 6, 8, 14, 15.

8/11/2010:     Heat conduction problems (cont.) READ Section 10.6. Practice problems (not collected or graded): Section 10.6: 1, 3, 5, 7, 9, 10, 12, 14.

8/09/2010:     Heat conduction problems (cont.) READ Sections 10.5 and 10.6

8/06/2010:     Separation of variables; Heat Equation. READ Section 10.5

8/04/2010:     Even and odd functions; Cosine and Sine Fourier series. Worksheet 2. READ Section 10.4

8/02/2010:     Fourier convergence theorem. READ Section 10.3

7/30/2010:     Fourier series. READ Section 10.2

7/28/2010:     Start Intro to PDE's. Boundary value problems (BVP); eigenvalue problems for BVP. READ Section 10.1

7/26/2010:     Applications to population biology: competing species and predator-prey equations. READ Section 9.4 and 9.5 (optional)

7/23/2010:     Midterm Exam.

7/21/2010:     Autonomous systems, locally linear systems (I called them "almost linear" in class). READ selected parts of 9.2 and 9.3, skim the rest. You need to know the definitions on pages 497-499, at least on the intuitive level (witout epsilons and deltas); you can skip the rest of 9.2. In 9.3, read up to the damped pendulum example; the example is optional.

7/19/2010:     Phase plane, stability. READ Section 9.1

7/16/2010:     Non-homogeneous linear systems. Method of variation of parameters. Method of undetermined coefficients (summary)
Application: earthquake-induced vibrations of a multi-story building. READ Section 7.9 (you can skip the Laplace transform method).

7/14/2010:     Non-homogeneous linear systems. Methods of diagonalization and undetermined coefficients. READ Section 7.9 (you can skip the Laplace transform method).

7/12/2010:     Repeated eigenvalues (light coverage, skip Jordan form). Application: RLC-circuits (underdamped, overdamped, or critically damped). READ Section 7.8.

7/9/2010:     Quiz on 7.1-7.5 See practice problems.

7/7/2010:     More on phase portraits, direction fields. Fundamental matrices (light coverage, skip matrix exponentials). READ Section 7.7.

7/2/2010:     Complex eigenvalues; phase portrait is a spiral (stable or unstable), or a center (when the eigenvalues are pure imaginary). READ Section 7.6.

6/30/2010:     Homogeneous linear systems with constant coefficients. READ Section 7.5. ; Phase plane

6/28/2010:     General theory of homogeneous linear systems of ODE's (superposition principle, Wronskian, fundamental set of solutions). READ Section 7.4.

6/25/2010:     Linear independence for vectors and vector-functions. Eigenvalue problem. READ Section 7.3. ; Worksheet 1.

6/23/2010:     Matrices, matrix-functions, systems of algebraic equations. Complex Numbers. Section 7.2, begin Section 7.3. ; Complex numbers handout.

6/21/2010:     Instruction begins. Introduction to systems of ODE's. Section 7.1.