**Welcome to the Home Page of MAth 0200 (Multivariable
Calculus for Physiscs/Engeneering)!**

** Instructors:** Alexander Braverman, Paul Carter and Edward Newkirk

**Book:** Edwards and Penney, Multivariable calculus, 6th
edition.

The plan is to cover Chapters 12-15 from the book. I.e. the approximate plan is as follows:

1)A thorough discussion of vectors in 3-dimensional space, equations of lines, planes, 3-dimensional curves and their curvature, some surfaces.

2) Partial derivatives, linear approximations, maxima and minima in the multivariable case, constrained optimization and Lagrange multipliers.

3) Multivariable integration: line and surface integrals, applications to geometry (such as area and volume computations etc.)

4) Multivariable versions of the fundamental theorem of calculus: Green's theorem, divergence theorem and Stokes theorem.

**Midterms:** There will be two midterms (tentatively) on October 7 and November 10 at 7pm.

**The final grade:** Your final grade will be computed as follows:

Midterms: 15% each

Homework: 20%

Final exam: 50%

** Midterm 1 information: ** The exam will be in List 120. You are allowed to bring one sheet of paper
with any formulas or text of your choice (but it has to bw written by you!).

Practice midterm 1 (This is an actual midterm given in this course in 2011

Actual midterm

Solutions

Practice final

**Homework:**

Here are the homeworks for the course (the assignments will usually be posted here Thursdays and they will be due the following Thursday at the recitation section)

**Assignment 1 (due 9/11):**

**12.1:** 34, 46, 47; **12.2:** 26, 40, 56; **12.3:** 2, 14;

**Assignment 2 (due 9/18):**

**12.3:** 18, 20, 36 **12.4:** 2, 14, 48, 54; **
12.5:**2, 40, 44;

**Assignment 3 (due 9/25):**
**12.5:** 50, 58, 64; **12.6:** 2, 8, 14, 54 (just find the curvature,
forget about center of curvature);
** 13.2:** 36, 41, 48;

** Assignment 4 (due 10/2):**
** 13.4:**17, 32;
**13.5:**12, 16, 25; ** 13.6:** 2, 32; ** 13.7:** 2, 6, 20.

** Assignment 5 (due 10/9):**

**Chapter 12, Miscellaneous problems:** 19, 15, 21

**Chapter 13, Miscellaneous problems:** 11, 16, 18

**13.7:** 26, 34, 46;

**Assignment 6 (due 10/16):**
**13.8:**8, 22, 34, 60
**13.9:** 2, 14, 40, 44, 62;

**Assignment 7 (due 10/23):**

**13.10:** 6, 10, 28, 30;
in problems 6 and 10 sketch the level curves ("contour plot") of
f.

**Assignment 8 (due 10/30):**
**14:2:** 2, 16, 18, 26, 28
** 14.3:** 4, 20, 28, 44

** 14.4:** 4, 22, 24, 32 ** 14.5:** 13,20, 41

**Assignment 10 (due 11/6):**

** 14.5:** 12, 26;

**14.6:** 2, 8, 12, 16, 31, 32

** 14.8:** 2,, 4, 10

**Assignment 11 (due 11/13):**
An old midterm

**14.9:** 2,6,8 **
**

** Assignment 12 (due 11/20):
15.2: ** 2, 12, 36, 40;

** 15.3** 2, 5, 30

** 15.4: ** 2, 12, 18, 22;

** Assignment 13 (due 12/4): **

** 15.5** 2, 5, 10, 30;

** 15.6:** 2, 4, 10, 13

** 15.7: ** 2, 8