MATH 200 - Multivariable Calculus

Section 203, TTh 12:30-2:30, LSK 201
Office: MATH 229A
Office Hours: M 2:30 - 4:00; Th 2:00 - 3:30
Contact:

Weekly Schedule

Week 1
Jan. 3-5

10.1 (only up to "Cylinders") : Three-dimensional coordinate systems; 10.2: Vectors; basic operations with vectors; length of a vector, equation of a sphere in space, unit vector in a specified direction.

Intersecting Planes Demo in GeoGebra

Suggested problems:
10.1: 1-3, 7, 9, 12, 16.
10.2: 1-5, 8, 11, 15, 20, 23, 27, 31

Week 2
Jan. 8-12

10.3 Dot product; Using dot product to find an angle between lines. Application to finding forces. 10.4 Cross product. Using cross product to find a vector orthogonal to two given ones; cross product and area.

Quiz 1 on vectors. Quiz 1 Solutions

Suggested problems:
10.3: 1-3, 11, 15, 19, 31, 39.
10.4: 1-5, 9, 15, 27, 30, 31, 35, 39, 41.

Week 3
Jan. 15-19

10.5 and 10.6 Equations of lines and planes. Symmetric and parametric equations of a line in space. Equations for planes in space. Equations for a line of intersection of two planes, etc. Finding distances in space: distance from a point to a plane, etc.

Suggested problems:
10.5: 7, 11, 21, 27, 31.
10.6: 1, 2, 9, 11, 14, 15, 17, 19, 25, 29, 32.

Week 4
Jan. 22-26

10.1: Cylinders and quadric surfaces. Reading assignment: 9.1 (Conic Sections). 12.1 Functions of several variables. Domain and range. Level curves and level surfaces.

Quiz 2 on equations of lines and planes in space. Quiz 2 Solutions

Suggested problems:
10.1: 15, 17, 23-26, 27, 32.
12.1: 1-6, 7, 11, 17, 19, 21, 23, 26, 27, 29, 31.

Week 5
Jan. 29 - Feb. 2

Brief dicsussion of limits and continuity for functions of two variables. (reference: section 12.2 (we will not cover everything in this section; refer to lecture notes). 12.3, Partial derivatives; higher-order partical derivatives. 12.4 Differentials, tangent planes, and linear approximations.

Lecture Videos: Lecture 9

Suggested problems:
12.3: 1-4, 5, 13, 19, 29, 33.
10.4: 7, 10, (find equation of tangent plane to z=f(x, y) at given point for 11, 12) , 13, 15, (find linear approximation for 17, 18 at the given point).

Week 6
Feb. 5-9

12.5 Chain rule and implicit differentiation; start 12.6 -- directional derivatives. One additional topic to recall here: parametric equation of a segment connecting two points A and B.

Quiz 3 on partial derivatives and differentials. Quiz 3 Solutions

Suggested problems:
12.5: 1-5, 9, 17, 21, 29.

Week 7
Feb. 12-16

12.6 Directional derivatives and gradients, continued. 12.7 Geometric meaning of the gradient. Tangent planes to level surfaces. Tangent planes to graphs of functions of two variables, revisited.

Midterm Tuesday February 13th at 6:30pm

Suggested problems:
12.6: 1-6, 13, 15, 21, 23, 25, 27.
12.7: 17, 19, 21, 23.

Srping Break
Feb. 19-23

Spring Break!

Week 8
Feb. 26 - Mar. 2

Section 12.8 Critical points: the second derivative test, absolute maximum and minimum values. Lagrange multipliers (Secondary text #1, Section 14.8).

Suggested problems:
12.8, problems 1-4, 5, 7, 11, 13, 15, 17 (also 11, 13, 15, 19 from 14.7 in Whitman).
14.8 (from Whitman) 5, 10, 11, 12, 13, 15, 17 .

Week 9
Mar. 5-9

14.8 Lagrange multipliers, continued. (two constraints not included). Starting integration: 13.1 (the definitions; area; integral of a function of two variables over a rectangle. Iterated integrals (over a rectangle). Fubini theorem (without proof).

Quiz 4 on critical points. Quiz 4 Solutions

Help with multivariable algebra

Suggested problems:
see above for 14.8, see below for 13.1

Week 10
Mar. 12-16

13.1: double integrals over general regions. Interchanging the order of integration. Section 13.2.

Example of a complicated region of integration

A summary of integration techniques from Math 101.

Suggested problems:
13.1: 7, 9, 19, 21 (also see #3, 5, 10, 13, 15 from section 15.1 of Whitman) .
13.2: 1-4, 7, 9, 13, 17, 21, 25 (also see #17, 21, 23 from section 15.1 of Whitman)

Week 11
Mar. 19-23

13.3 Double integrals in polar coordinates. 13.4 Center of mass.

Quiz 5 on changing the order of integration in a double integral. Quiz 5 Solutions

Suggested problems:
13.3: 3, 4, 8, 13.
13.4: 1, 5, 6, 13, 24.

Week 12
Mar. 26-20

13.6 Triple integrals. Six different ways of writing a triple integral as an iterated integral. Applications. Triple integrals in cyindrical coordinates, see 14.4 (from Strang)

Suggested problems:
13.6: 5, 7, 9, 11, 13, 15, 19, 23.

Week 13
Apr. 4-6

Triple integrals in spherical coordinates 14.4 (from Strang); review.

Suggested problems:
Suggested problems: 14.4 (from Strang): 11, 13, 15, 19, 22, 23
A big list of tripple intergral problems with solutions