Math 2255 SyllabusMATH 2255 CALCULUS III 4 CREDIT HOURS
Prerequisite: MATH 2254
A continuation of Calculus with an introduction to Multivariate Calculus: Topics include: vectors in two and three dimensions, dot and cross product, lines and planes in space, cylindrical and spherical coordinates, vector functions, tangents and normals, velocity and acceleration, arclength and curvature, functions of several variables, partial derivatives, chain rules, directional derivatives and gradients, tangent planes, extrema and optimization, multiple integrals in rectangular, polar, cylindrical, and spherical coordinates.
Text: Calculus,7E by James Stewart, 7th edition (Brooks/Cole) ISBN: 9780538497817
The following schedule and homework are suggested and will vary with instructor. Students should consult with their instructor regarding exam dates and homework requirements.
Week 
Topic 
Sections (in Stewart) 
Homework 
Exam 
1 
3D Coordinate Systems and Vectors 
12.1 12.2 
Pg.814: 1, 4, 7—19odd, 23, 25, 29, 33, 36, 38, 41 Pg. 822: 1, 4, 5—23 odd, 24, 25, 27, 29, 31, 38, 47 

2 
The Dot and Cross Products 
12.3

Pg. 830: 3—9 odd, 14, 17, 19, 21, 23, 27, 29, 31, 33, 35, 39, 41, 51, 61, 63 Pg. 838: 1—19 odd, 25—37odd, 39, 45 

3 
Lines, Planes, Cylinders and Quadric Surfaces 
12.5

Pg. 848: 3—11 odd, 15, 19, 21, 25—39 odd, 45, 47, 49, 51—59 odd, 61, 69, 71, 73 Pg. 856: 1, 3, 5, 7, 11—19odd, 21—28, 29—35 odd, 41, 42, 45 

4 
Vector Functions and Space Curves 
13.1 
Pg. 869: 1—6, 7, 9, 11, 17, 19, 27, 40, 41, 43, 47 
Exam I 
5 
Derivatives/Integrals of Vector Functions, Arc length and Curvature 
13.2 13.3 
Pg. 876: 1—13 odd, 17, 19, 21, 35—41 odd Pg. 884: 1, 3, 5, 11, 13, 15, 17—23 odd, 25, 27, 31, 43, 47, 48, 49, 55, 57, 59 

6 
Motion in Space, Multivariate Functions, Limits and Continuity 
13.4 14.1

Pg. 894: 3—15 odd, 19, 22, 23, 25, 27, 37—41 odd Pg. 912: 7, 9, 11, 13—19 odd, 25, 27, 29, 31, 32, 43, 45, 53, 59—64, 65, 66 Pg. 923: 1, 5—19 odd, 25, 29—41 odd 

7 
Partial Derivatives, Tangent Planes and Linearization 
14.3 14.4 
Pg. 935: 11, 15—39 odd, 42, 45, 47, 49, 52, 53—67 odd Pg. 946: 1, 3, 5, 11, 13, 15, 17, 21, 25, 27, 29, 31, 33 

8 
The Chain Rule

14.5 
Pg. 954: 1—13 odd, 17, 19, 21—29 odd, 31, 33, 35, 39 
Exam II 
9 
Directional Derivatives, Extreme Values 
14.6 14.7 
Pg. 967: 5—17 odd, 19, 21, 23, 25, 29, 33, 41, 43, 45 Pg. 977: 1, 2, 5—15 odd, 19, 29, 31, 33, 39, 41, 43, 45, 49 

10 
Lagrange Multipliers, Introduction to Double Integrals 
14.8 15.1 
Pg. 987: 1—13 odd, 15, 17, 19, 27, 2935 odd Pg. 1005: 1, 3, 11, 12, 13 

11 
Iterated Integrals, Double Integrals over General Regions 
15.2 15.3 
Pg. 1011: 1, 3—21 odd, 25, 27, 29, 35 Pg. 1019: 1—9 odd, 11, 12, 13, 15, 17, 19, 21, 23, 25, 27, 31, 35, 37, 43—53 odd, 55, 57, 59 

12 
Polar Coordinates 
15.4 
Pg. 1026: 1—4, 5, 7, 9, 11, 15—25 odd, 29, 31, 37 
Exam III 
13 
Applications of Double Integrals, Surface Area* 
15.5 15.6*

Pg. 1036: 1—13 odd, 1723 odd Pg. 1040: 119 odd 

14 
Triple Integrals Triple Integrals in Cylindrical 
15.7 15.8

Pg. 1049: 1—15odd, 19, 21, 27, 29, 31, 33, 35, 39, 41, 47 Pg. 1055: 1—13 odd, 15, 17, 19, 21, 23, 25, 28, 29, 30 

15 
Triple Integrals in Spherical Coordinates 
15.9

Pg. 1061: 1—15 odd, 17, 21, 23, 25, 27, 29, 35, 39, 40 
Exam IV 
*This section is optional.