Math 21b - Multivariable Calculus

Information for students, Spring 2006

Click here for a PDF version of the info handout.

This is the second half of a year-long course known as "Intermediate Calculus: Linear Algebra and Calculus of Several Variables".

Class meets at: Goldsmith 117, MW 1-2 PM and Th 1-3 PM
Lecturer: Dmitry Kleinbock
Office: Goldsmith 207, phone 6-3059
Office Hours: Tue 11 AM-12 noon or 3-4 PM or by appt.
E-mail address: kleinboc@brandeis.edu
Grader: Hsin-Hong Lai, hhlai@brandeis.edu

Text: MULTIVARIABLE MATHEMATICS, 4th edition, by R. Williamson and H. Trotter, Prentice Hall, 2003.
We will cover Chapters 4-9 with some omissions. Chapters 1-3 contain an exposition of background material in linear algebra, which is a prerequisite for this course. Needless to say, the familiarity with single-variable calculus is also assumed.

Quiz 1: Thursday, Febuary 2, covering Section 4.1.
Quiz 2: Thursday, Febuary 17, covering Sections 4.2-4.4.
Quiz 3: Thursday, March 2, covering Sections 5.1-5.2.
Quiz 4: Thursday, March 9, covering Sections 5.3-5.4.
Midterm: Thursday, March 16, covering Chapters 4-5 and some of Chapter 6.
Click here for a PDF version of the midterm review sheet.
Quiz 5: Thursday, March 23, covering Sections 6.4A-C.
Quiz 6: Thursday, April 6, covering Sections 7.1-7.2.
Quiz 7: Wednesday, April 26, covering Section 7.4.
Quiz 8: Monday, May 1, covering Section 8.1.
Quiz 9: Wednesday/Thursday, May 3, covering Sections 9.1-9.2.
Review Session: Thursday, May 4, 2:30 - 3:30 PM, Goldsmith 117.
Final Exam: Monday, May 8, 9:15 AM - 12:15 PM, Goldsmith 117.
Click here for a PDF version of the final exam review sheet.

Homework assignments and deadlines:

1 Problems 3, 4, 5, 7, 10, 11, 14, 15, 19, 21, (*) 33 in Section 4.1D January 25
2 Problems 23, 24, 25 in Section 4.1D; 2, 3, 4, 9, 11, 14, 25(b) in Section 4.1F;
(*) compute the length of the piece of parabola y = x2/2, 0 < x < 1
(Hint: the easiest way is hyperbolic substitution, x = sinh u)
February 1
3 Problems 3, 8, 11, 14, 20, 22, 25 in Section 4.2B; 8 in Section 4.2D; 2, 4, 8, 10 in Section 4.3C;
(*) the hyperboloids x2 + y2- z2 = 1 and y2 + z2- x2 = 1 intersect in a curve in R3;
identify the curve and make a sketch of it
February 8
4 Problems 16, 17, 21, 23, 25, 30 in Section 4.3C; 2, 4, 5, 10, (*) 16 in Section 4.4B February 15
5 Problems 5, 6, 9, 10, 21, 22, 42ab(*)c in Section 5.1; 2, 7, 10, 16, 17, 18 in Section 5.2 March 1
6 Problems 2, 4, 8, 10, 12, (*) 20 in Section 5.3; 3, 4, 14, 18, 20, 22, 24, 26 in Section 5.4;
8, 9 in Section 6.1C
March 8
7 Problems 20, 22, 27, 28 in Section 6.1C; 2, 6, (*) 10, 20, 24 in Section 6.2A;
2, 6, 7, 8, 17 in Section 6.4D
March 15
8 Problems 10, 11, 12, 20, 24, 26, 27, (*) 31, 38 in Section 6.4D; 41, 42 in Chapter 6 Review March 22
9 Problems 4, 6, 10, 11, 12, (*) 17 in Section 6.4E; 1, 2, 20 in Section 7.1; 3, 7, 10 in Section 7.2 March 29
10 Problems 4, 8, 12, 16, 21 in Section 7.1; 2, 4, 8, 15, 17 in Section 7.2; (*) 6 in Section 7.3 April 5
11 Problems 1, 5, 6, 7, 10, 12, 14, 15, 26, (*) 27 in Section 7.4 April 12
12 Problems 2, 6, 7, 8, 11, 12, 13, 16, 17, (*) 23, 28, 30 in Section 8.1 April 26
13 Problems 1, 2, 6, 7 in Section 9.1, 4, 10, (*) 28 in Section 9.2;
1, 2, 3, 10, 12 in Chapter 9 Review
May 3

(*) stands for an optional problem.

Grades will be computed as follows:

Midterm exam, in class 20%
The final exam, as scheduled by registrar 50%
Quizzes, once every 1-2 weeks 15%
Graded homework 10%
Instructor's discretion 5%

The dates of the midterm exam and quizzes will be announced in advance. Each quiz will take 15-20 min. Homework is assigned once every week and is due the following week. Late homework will not be accepted and there will be no make-up quizzes. Instructor's discretion is my subjective evaluation of student's competence, based mainly on class participation (answering questions in class) and bonus points (for optional problems or exceptionally thoughtful analysis of tests/homework).

Have a great semester!