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Math 2255 Syllabus

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

3-D 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


12.4

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


12.6

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


14.2

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, 29-35 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, 17-23 odd

Pg. 1040: 1-19 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.

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