| Mathematics 32AH |
| Calculus of Several Variables |
Instructor: Michael Hall, michaelhall@math.ucla.edu, MS 3955
Lectures: MWF 9-9:50, MS 6221
Office hours: MW 10-11 AM, Thursday 3:30-4:30 PM
Ususally, on Monday and Wednesday, office hours will be in the classroom (MS 6221) immediately following class.
TA Section: Robert Denomme, Tuesday 9-9:50, MS 6221
Textbook: R. Williamson, H. Trotter, Multivariable Mathematics, 4th Ed.,
Quizzes: There will be a quiz each week during Tuesday TA section. The two lowest quiz scores will be dropped.
Handouts: The Schwarz inequality, The Two Body Problem, Practice Midterm 1 (solutions), Extra Problems for the first midterm, Midterm 1 (solutions), Extra Problems 2, Practice Midterm 2 (solutions, with also problem 7 from Extra Problems 2), Midterm 2 (solutions), Practice Problems (partial solutions), Final Exam solutions
Homework: Homework will be collected each Friday at the beginning of lecture and returned in TA section. The two lowest homework scores will also be dropped. Late homework will not be accepted.
Homework Assignments:
Assignment Due Date Exercises Material Comments Solutions 1 Fri, Oct 1 1.1 #1,12,25
1.2 #3,25,27,31
1.3 #5,15,17,201.1-1.3 Added problem 1.2.31 on 9/26. Problem 1.3.20 uses 'p' to refer to two different points. 2 Fri, Oct 8 1.4 #16,18,19,29
1.5 #2,4,8,10,16,29
1.6 #1,4,8,15,261.4-1.6 3 Fri, Oct 15 4.1(A-D) #4,20,22(a),28,32
4.1F #6,10,20,22,24
8.2 #44.1(A-D), 4.1F, 8.2 Note that there are separate lists of exercises for 4.1(A-D) (pp. 182-184) and 4.1F (pp. 187-188). Only arc length is needed from 8.2. 4 Fri, Oct 22 8.3 #2,8,10,13,17
Problems 1-4 of the Extra Problems handout (above)8.2-8.3, Kepler's Laws 5 Fri, Oct 29 4.2(A-B) #1,11,23,25
4.2D #2,4,7,84.2(A-B), 4.2D 6 Fri, Nov 5 4.3 #1,2,4,6,11,12,14,26,36,38,42,46 4.3 7 Fri, Nov 12 4.4 #4,18,26
5.1 #12,15,25,42
5.2 #8,12,15,21,23,24,254.4,5.1,5.2 8 Fri, Nov 19 Complete Practice Midterm 2
5.3 #1,3,10
6.1 #3,20,23,27,385.3, 6.1 9 Mon, Nov 29 6.2A #1,4,6,10
6.2B #1,3,8.10
6.3 #1,4,12,14,166.2-6.3 The quiz will concern section 6.2 only. 10 Tues, Dec 7 6.4(A-D) #2,10,14,26,27,30,35
6.4E #3,6,106.4(A-D), 6.4E You may turn in the homework at the Final Exam, or earlier if you wish.
Examinations: There will be two mid-terms and a final exam.Midterm 1: Wednesday, October 20:
Material: Sections 1.1-1.6, 4.1, and 8.2-8.3 of the book, as well as Kepler's Laws.
Midterm 2: Wednesday, November 17:
Material: Sections 4.2-4.4, 5.1-5.3, 6.1 of the book
Final examination: Tuesday Dec 07, 11.30am-2.30pm.
You must take the final exam.Grading scheme: Maximum of:
Final 40%, Midterms 40% (20%-20%), Homework 10%, Quizzes 10%
Final 55%, Best midterm 25%, Homework 10%, Quizzes 10%
Grading disputes: Grades will be recorded on MyUCLA in a timely fashion. Please verify regularly that grades for all submitted assignments are present. Any grading complaints must be sumbitted within two weeks of the due date or exam date of the grade in question.
Calculators and other materials: You may use any resources you wish (textbooks, calculators, computers, friends, TAs, the SMC ...) to help you complete the homework so long as your use does not constitute plagiarism. The main point of the homework is to learn the material and prepare for the exams.
On the exams, no resources other than pencil and paper will be allowed.Rough Course Outline:
The actual content may deviate slightly.
Date Topics Fri, Sep 24 1.1-1.2 Vectors and Coordinates Mon, Sep 27 1.3 Lines and Planes Wed, Sep 29 1.4 Dot product Fri, Oct 01 1.5 Euclidean geometry Mon, Oct 04 1.6 Cross product Wed, Oct 06 4.1 Functions of a single variable Fri, Oct 08 4.1 Functions of a single variable Mon, Oct 11 8.2-8.3 Arc length, normal vectors, curvature Wed, Oct 13 8.2-8.3 Arc length, normal vectors, curvature Fri, Oct 15 Kepler's laws Mon, Oct 18 Kepler's laws Wed, Oct 20 FIRST MIDTERM Fri, Oct 22 4.2 Functions of several variables Mon, Oct 25 4.2 Functions of several variables Wed, Oct 27 4.3 Partial derivatives Fri, Oct 29 4.4 Parameterized surfaces Mon, Nov 01 5.1 Limits and continuity Wed, Nov 03 5.1 Limits and continuity Fri, Nov 05 5.2 Differentiability Mon, Nov 8 5.2 Differentiability Wed, Nov 10 5.3 Directional derivatives Fri, Nov 12 5.4 Derivative matrices Mon, Nov 15 Review Wed, Nov 17 SECOND MIDTERM Fri, Nov 19 6.1 Gradient fields Mon, Nov 22 6.2 The chain rule Wed, Nov 24 6.3 Implicit differentiation Mon, Nov 29 6.4 Extreme values Wed, Dec 01 6.4 Extreme values Fri, Dec 03 6.4 Extreme values Tue Dec 07, FINAL EXAM, 11:30AM-2:30PM