## Handouts

This page will consist of the class handouts, in reverse chronological orders by week.

### Week Twelve: April 27, 2009 — May 1, 2009

• Practice Problems for Sections 13.6–13.9 (Janet Chen) [Friday, May 1st] Extra problems from Janet Chen.
Revised 4:55 PM on Fri May 8. Janet says: I modified the vector fields in #4 and #8 (#4 was doable but slightly nicer now, and #8 was missing an x). Thanks to Eason for both.
• The Integral Theorems (Janet Chen) [Friday, May 1st] A worksheet, with solutions, from Janet Chen's section.
• Integral Theorems Review (Peter Garfield) [Friday, May 1st] A worksheet, with answers attached, from Peter Garfield's sections.
• Math 21a Notes (Jun Yin) [Posted Thursday, April 30th] By request, Jun Yin's notes (all 92 pages) from the semester.
• The Divergence Theorem (Janet Chen) [Wednesday, April 29th] A worksheet, with solutions, from Janet Chen's section.
• The Divergence Theorem (Peter Garfield) [Wednesday, April 29th] A worksheet, with answers attached, from Peter Garfield's sections. (It turns out that 1–1+2 is 2, not 1. This changes the answer to 6(a). Thanks Lilly! Corrected 2:35 PM on Sat May 9.)
• Stokes' Theorem (Janet Chen) [Monday, April 27th] A worksheet, with solutions, from Janet Chen's section.
• Stokes' Theorem (Peter Garfield) [Monday, April 27th] A worksheet, with answers attached, from Peter Garfield's sections. This is a slightly modified version of the worksheet used in class, as it has some typos corrected.

### Week Eleven: April 20, 2009 — April 24, 2009

• Flux Integrals (Janet Chen) [Friday, April 24th] A worksheet, with solutions, from Janet Chen's section.
• Flux Integrals (Peter Garfield) [Friday, April 24th] A worksheet, with answers attached, from Peter Garfield's sections. This is a modified version of the worksheet used in John Hall's sections as well.
• Curl and Divergence (Janet Chen) [Wednesday, April 22nd] A worksheet, with solutions, from Janet Chen's section.
• Curl and Divergence (Peter Garfield) [Wednesday, April 22nd] A worksheet, with answers attached, from Peter Garfield's sections. (The answer to 1(a)(iii) was wrong -- it was a vector, not a scalar. Thanks Helen! Corrected 2:35 PM on Wed Apr 22.)
• Green's Theorem (Janet Chen) [Monday, April 20th] A worksheet, with solutions, from Janet Chen's section.
• Green's Theorem (Peter Garfield) [Monday, April 20th] A worksheet, with answers attached, from Peter Garfield's sections. (The answer to 7(c) was wrong -- it should have been , not π/2. Thanks John! Corrected 12:05 PM on Thu Apr 30.)
• Extra Problems on Sections 13.1–13.4 (Janet Chen) [Monday, April 20th] A collection of practice problems from this Sections 13.1 through 13.4, courtesy of Janet Chen. Solutions will not be posted.

### Week Seven: March 16, 2009 — March 20, 2009

• Practice Problems For Week 7 (and Earlier) (Janet Chen) [Friday, March 20th] A collection of practice problems from this week (and earlier), courtesy of Janet Chen. Solutions will not be posted.
• More Extremal Problems (Janet Chen) [Friday, March 20th] A worksheet, with solutions, from Janet Chen's section.
• Global Extrema; Lagrange Multipliers II (Peter Garfield) [Friday, March 20th] A worksheet, with answers attached, from Peter Garfield's sections.
Correction: The answer to Problem 4 (Case 2) was incorrect and has been fixed (Apr 2 2:00 PM). Thanks Taylor!
• Lagrange Multipliers (Janet Chen) [Wednesday, March 18th] A worksheet, with solutions, from Janet Chen's section.
• Lagrange Multipliers (Peter Garfield) [Wednesday, March 18th] A worksheet, with answers attached, courtesy of Eric Wofsey from Peter Garfield's noon section.
Correction: The answer to Problem 4(a) was incorrect. The gradient of g was wrong in the z component. (Fixed Apr 2 2:00 PM). Thanks Taylor!
• Maxima and Minima (Janet Chen) [Monday, March 16th] A worksheet, with solutions, from Janet Chen's section.
• Extremal Points (Peter Garfield) [Monday, March 16th] A worksheet, with answers attached, from Peter Garfield's & John Hall's sections.

### Week Two: February 9, 2009 — February 13, 2009

• Quadric Surfaces (Janet Chen) [Friday, February 13th] A worksheet, with solutions, from Janet Chen's section.
• Graphs in Space (Peter Garfield) [Wednesday, February 11th] A worksheet, with solutions attached, from Peter Garfield's section.
• Functions and Graphs (Janet Chen) [Wednesday, February 11th] A worksheet, with solutions, from Janet Chen's section.
• Lines and Planes (Peter Garfield) [Monday, February 9th] A worksheet, with solutions attached, from Peter Garfield's section.
• Lines and Planes (Janet Chen) [Monday, February 9th] A worksheet, with solutions, from Janet Chen's section.

### Week Zero: January 28, 2009 — January 30, 2009

• The introductory meeting slides [Wednesday, January 28th] The overheads from the mandatory introductory meeting for students in Math 21a on Wednesday, January 28th are available for download.
• Syllabus [Wednesday, January 28th] The course syllabus. This is really just an abbreviated version of this web site, so browse around here instead.