LINEAR ANALYSIS, Math 309 C (3 credits)
Winter 2011

• Office : Padelford C-8B
• E-mail : gbzhuang at u dot washington dot edu
• Office Hours : Wednesdays 3:30-5:30, or by appointment

Course Information

• Text : W. Boyce and R. DiPrima, Elementary Differential Equations and Boundary Value Problems, 9th edition.
• Lecture : MWF 1:30-2:20, in LOW 205.
• Prerequisites : Math 307 and Math 308.
• Structure : I plan to cover Chapters 7 and 10, and also a bit of Chapter 9 if we have time.
• Homework : Homework is due on Friday (starting from the second week) unless otherwise stated. No late homeworks will be accepted. The lowest homework score will be automatically dropped.
• Exams : One sheet of handwritten notes is allowed on the midterms, and two sheets of notes are allowed on the final.
  • Midterm 1 is on Feb 4th, 2011 in class. I plan for it to cover Chapter 7.
  • Midterm 2 is on Feb 28th, 2011 in class. I plan for it to cover Chapter 10.
  • The final exam is on March 14, 2011, from 2:30 to 4:20 pm, at LOW 205. It will be comprehensive, but the emphasis will be on the material we cover after the second exam.
• Grading : 20% each midterm; 40% final exam; 20% homework.
• How to succeed in this class : Math 309 is a tough course, significantly harder than even Math 307 and 308. The problems tend to be long and involved, and the class may require more time than you have spent on previous classes. Here are some suggestions.
  • Pay attention to "Calendar/Announcement" on this webpage. I will say which material we will cover in the coming class. Read the section ahead of time. In lecture, I will cover the textbook fairly closely, and I will presume that you have read it already.
  • If you find something confusing, ask me about it as soon as you can. If you fall behind, it is much harder to catch back up.
  • Keep your Math 308 book and review it as necessary. We will do some review of linear algebra in class, but you may need to review some more on your own.
  • Make sure you review for homework and exams when solutions are available, and if you make a mistake, work out the problem again to make sure you have it right. You need lots of practice to master the material.

Links to Homework Problems

• Homework 1 (due Jan 14)

• Homework 2 (due Jan 21)

• Homework 3 (due Jan 28)

• Homework 4 (due Feb 4)

• Homework 5 (due Feb 18)

• Homework 6 (due Feb 25 )

• Practice problems for Chapter 9

Calendar/Announcements

2/22/2011:     Laplace equations II. Section 10.8. Midterm II prep.

2/18/2011:     Laplace equations. Section 10.8.

2/16/2011:     More on wave equations. Section 10.7.

2/14/2011:     Wave equations. Section 10.7.

2/11/2011:     Heat conduction equations with insulated ends. Section 10.6.

2/09/2011:     Heat conduction equations II. Section 10.5.

2/07/2011:     Heat conduction equations I. Section 10.5.

2/04/2011:     Midterm I.

2/01/2011:     Even and Odd functions. Section 10.4.

1/31/2011:     Fourier Convergence Theorem. Section 10.3.

1/28/2011:     Fourier series: introduction. Section 10.2. Midterm I prep.

1/26/2011:     Two-point boundary value problems Section 10.1.

1/24/2011:     Method of variation of parameters for non-homogeneous systems. Section 7.9.

1/21/2011:     More on fundamental matrix. Repeated eigenvalues. Section 7.8.

1/19/2011:     More on phase portrait. Start on fundamental matrix. Section 7.7.

1/14/2011:     Complex eigenvalues. Section 7.6.

1/12/2011:     Homogeneous linear systems with constant coefficients. Section 7.5. Phase plane.

1/10/2011:     General theory of homogeneous linear systems of ODE's (Wronskian, fundamental set of solutions). Section 7.4.

1/7/2011:     Systems of algebraic linear equations, linear independence, eigenvalues and eigenvectors. Section 7.3.

1/5/2011:     Matrices, matrix-functions, systems of algebraic equations. Complex Numbers. Section 7.2, begin Section 7.3. ; Complex numbers handout.

1/3/2011:     Instruction begins. Introduction to systems of ODE's. Section 7.1, begin Section 7.2.