(4/29/2006) SPRING 2006

HANDOUTS

EXAM 1

Here is a PowerPoint summary of Chapter 4

Here is a derivation of Snell's Law

Here are some Boundary Problem examples

Here are two Lagrange Multiplier examples from Physics

Here is a PowerPoint summary of Chapter 5

Here are answers to Examination I

EXAM 2

Note that Sections 5.4 and 5.5 will be on Examination II

Here is additional material on Green's Theorem: Green's Theorem - Page 1 Green's Theorem - Page 2 Green's Theorem - Page 3 Green's Theorem - Page 4 Green's Theorem - Page 5 Green's Theorem - Page 6

Answers from the back of the book for Section 8.12 are: 1. 3; 3. 0; 5. 75pi; 7. 48pi; 9. 56/3; 11. 2/3

Here are answers to Examination II

EXAM 3

Note that the Divergence Theorem and Stokes's Theorem will be on Examination III

Here is additional material on the Divergence Theorem: Divergence Theorem - Page 1 Divergence Theorem - Page 2 Divergence Theorem - Page 3 Divergence Theorem - Page 4 Divergence Theorem - Page 5 Divergence Theorem - Page 6 Divergence Theorem - Page 7

Answers from the back of the book for Section 8.16 are: 1. 3/2; 3. 12a^5pi/5; 5. 256pi; 7. 62pi/5; 9 4pi(b-a); 11. 128

And, finally, here is additional material on Stokes's Theorem: Stokes's Theorem - Page 1 Stokes's Theorem - Page 2 Stokes's Theorem - Page 3 Stokes's Theorem - Page 4 Stokes's Theorem - Page 5 Stokes's Theorem - Page 6 Stokes's Theorem - Page 7

Answers from the back of the (different) book for Section 9.9 are: 1. 5; 3. +-4(1-e)^4; 5. +-4/3; 7. 36pi; 9. -4pi; 11. 0; 13. -sqrt(3)/10

Actually, here is even better material on Surface & Stokes's Theorem with answers on the last page.

Here are problems 7,12,15 on page 334 done. Try them yourself first and then check your answers. Stokes Page 334

Here is a PowerPoint summary of the Infinite Series material.

Here are answers to Examination III

EXAM 4

Here is a PowerPoint summary of the Complex Numbers material.

Here is a PowerPoint summary of the Complex Variables material.

Here are the notes of the lecture on April 10th. I see that the graph paper background interferes with the material so I'll use whiter paper next time.
In addition, I see that I did not make use of the entire sheet available and I'll try to fix that also.

Here are the notes of the lecture on April 12th.

Here is some material on Poles and Zeros from another book: Poles and Zeros - Page 1 Poles and Zeros - Page 2 Poles and Zeros - Page 3 Poles and Zeros - Page 4 Poles and Zeros - Page 5 Poles and Zeros - Page 6 Poles and Zeros - Page 7 Poles and Zeros - Page 8 These show one of the important applications of this material!

Here are some exercises on Cauchy Integrals

Here are notes for the lecture April 17th on Laurent Series

Application of Contour Integrals may be seen here as a PowerPoint slide.

Here are notes for the lecture an April 19th Now visible (4/23).

Notes of the review session of April 24th are available here as PowerPoint slides.

Here are answers to Examination IV