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Calculus III

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3-D Geometry and Vectors


Corresponding Chapters
Briggs [1e]     - Ch. 11
Stewart [5e]     - Ch. 12
Stewart [6e]     - Ch. 13

Three-Dimensional Coordinate Systems

Stewart [5e]: 12.1
Stewart [6e]: 13.1

Problems:
Stewart [6e], 13.1
    #5, 9, 11, 13, 15, 21, 27, 37, 38, 41.

Vectors

Stewart [5e]: 12.2
Stewart [6e]: 13.2


Problems:
Briggs 11.1: Vectors in the Plane
    #15, 18, 19, 21, 26, 29, 31, 32, 35, 37.

Briggs 11.2: Vectors in 3D
    #2, 3, 5, 8, 11, 19, 22, 24, 29, 32, 35.

Stewart 6e, 13.2
    #3, 7, 11, 17, 19, 21, 25, 29, 31, 33, 37, 43.

Dot Product

Briggs: 11.3
Stewart [5e]: 12.3
Stewart [6e]: 13.3

Problems:
Briggs 1e, 11.3
    #4, 10, 11, 14, 18, 19, 23, 26, 33.

Stewart 6e, 13.3
    #1, 7, 9, 11, 19, 23, 27, 31, 39, 47, 53, 59.

Cross Product

Briggs: 11.4
Stewart [5e]: 12.4
Stewart [6e]: 13.4

Problems:
Briggs [1e], 11.4
    #4, 8, 9, 11, 13, 17, 18, 20, 21, 24, 25, 26, 27, 29, 31, 33, 35, 45, 55, 56.

Stewart [6e], 13.4
    #5, 7, 9, 11, 15, 23, 25, 29, 35, 39, 43, 45.

Equations of Lines and Planes

Briggs: 11.5?
Stewart [5e]: 12.5
Stewart [6e]: 13.5

Problems:
Stewart [6e], 13.5
    #3, 5, 9, 15, 19, 25, 31, 39, 43, 45, 51, 53, 61, 63, 65, 67.

Cylinders and Quadric Surfaces

Stewart [5e]: 12.6
Stewart [6e]: 13.6

Problems:
Briggs [1e], 11.5
    #9, 11, 13, 15, 19, 35, 41, 43, 47, 51.

Stewart [6e], 13.6
    #1, 9, 19, 21, 23, 27, 29, 35, 41, 43, 45.

Vector Functions and Space Curves

Stewart [5e]: 13.1
Stewart [6e]: 14.1
Derivatives and Integrals - Stewart [6e]: 14.2

Problems:

Briggs [1e], 11.5
    #9, 11, 13, 15, 19, 35, 41, 43, 47, 51.

Stewart [6e], 14.1
    #1, 5, 11, 15, 19, 25, 33, 35, 39.

    Derivatives and Integrals
    Stewart [6e], 14.2
        #5, 13, 16, 19, 21, 25, 31, 35, 39, 49.

Arc Length and Curvature

Briggs: 11.8 & 11.9
Stewart [5e]: 13.3
Stewart [6e]: 14.3
Problems:

Stewart [6e], 14.3
#3, 11, 13, 19, 27, 29, 37, 39, 55.

    Arc Length
    Briggs [1e], 11.8
        #7, 9, 10, 11, 13, 14, 15, 17, 19, 21, 27, 31, 36, 39.

    Curvature & Normal Vectors
    Briggs [1e], 11.9
        #3, 7, 9–17, 19, 21, 25, 27, 29, 31, 33, 35, 37, 38, 39, 40, 41, 54, 56, 63, 75.

Velocity and Acceleration

Briggs: 11.7
Stewart [5e]: 13.4
Stewart [6e]: 14.4

Problems:

Briggs [1e], 11.7
    #7, 9, 11, 12, 13, 14, 16, 22, 25, 28, 35, 51, 53, 57 (a,b).

Stewart [6e], 14.4
    #5, 7, 11, 15, 19, 25, 33, 39.

Cylindrical and Spherical Coordinates

Stewart [5e]: 12.7

Problems:
???

Partial Derivatives

Corresponding Chapters
Briggs [1e]    - Ch. 12
Stewart [5e]     - Ch. 14
Stewart [6e]     - Ch. 15

Functions of Several Variables

Stewart [5e]: 14.1
Stewart [6e]: 15.1

Problems:

Stewart [6e], 15.1
    #1, 3, 5, 9, 13, 17, 23, 29, 30, 31, 43, 55, 61, 63.

Limits and Continuity

Briggs: 12.3
Stewart [5e]: 14.2
Stewart [6e]: 15.2

Problems:

Briggs [1e], 12.3
    #8, 11–23, 25, 27, 29, 30, 31–45 ,48–59.

Stewart [6e], 15.2
    #1, 3, 7, 11, 15, 19, 23, 35, 37, 39.

Partial Derivatives

Briggs: 12.4
Stewart [5e]: 14.3
Stewart [6e]: 15.3
Briggs 12.4
    #3, 7–37, 43, 45, 47, 49, 51, 53, 55, 65.
        (Highlights: #3, 7, 10, 11, 13, 15, 17, 19, 21, 26, 35, 36, 43, 47, 53.)

Stewart [6e], 15.3
    #1, 3, 5, 7, 17, 33, 37, 39, 41, 45, 53, 61, 65, 67, 79, 89.


Several sources schedule exams either immediately before or after this section.


Tangent Planes and Differentials

Briggs: 12.7
Stewart [5e]: 14.4
Stewart [6e]: 15.4
Problems:
Briggs 12.7
    #3, 4, 9, 10, 11, 15, 17, 18, 21, 23, 24, 25, 42, 43, 44, 47, 52.

Stewart [6e], 15.4
    #1, 11, 17, 21, 23, 29, 35, 37.

The Chain Rule

Briggs: 12.5
Stewart [5e]: 14.5
Stewart [6e]: 15.5
Problems:

Briggs 12.5
    #7–19, 21, 27, 28, 29, 30, 45, 53, 55, 57

Stewart [6e], 15.5
    #4, 10, 16, 18, 22, 30, 32, 36, 38, 48.
    #2, 4, 8, 16, 22, 34, 36, 40, 48, 54.

Directional Derivatives and the Gradient Vector

Briggs: 12.6
Stewart [5e]: 14.6
Stewart [6e]: 15.6
Problems:

Briggs 12.6
    #6, 7, 9, 10–29, 33, 34, 35, 37, 39, 45, 47, 49, 51, 53, 56, 59, 61, 63.

Maximum and Minimum Values

Briggs: 12.8
Stewart [5e]: 14.7
Stewart [6e]: 15.7

Problems:

Briggs [1e], 12.8
    #9, 11, 13, 18, 19, 20, 21, 23, 25, 29, 31, 34, 37, 39, 40, 45, 47, 52.

Briggs [1e], 12.9:
    #4, 5, 7, 9, 10.

Stewart [6e], 15.7
    #2, 4, 6, 18, 30, 38, 44, 48, 52, 54.

Lagrange Multipliers

Briggs: 12.9
Stewart [5e]: 14.8
Stewart [6e]: 15.8

Paul's Online Notes

Problems:

Briggs [1e], 12.9:
    #11, 12, 16, 18, 20, 22, 25, 32, 42.

Stewart [6e], 15.8
    #4, 8, 16, 18, 22, 24, 32, 36.

Multiple Integrals

Corresponding Chapters 
Briggs [1e]    - Ch. 13
Stewart [5e]    - Ch. 15
Stewart [6e]    - Ch.16


Supplementary Resources:
    Khan Academy: Double and Triple Integrals

Double Integrals over Rectangles

Briggs: 13.1
Stewart [5e]: 15.1
Stewart [6e]: 16.1

Problems:

Briggs[1e], 13.1
    #3, 5, 7, 9, 10, 11, 13, 14, 15, 17, 18, 20, 21, 22, 23, 24, 35, 37, 39, 41.

Briggs [1e], 13.2:
    #5, 6, 7, 9, 13, 14.

Stewart [6e], 16.1
    #3, 5, 9, 13.

Iterated Integrals

Stewart [5e]: 15.2
Stewart [6e]: 16.2
Problems:

Stewart [6e], 16.2
    #3, 7, 17, 21, 23, 29, 33.

Double Integrals over General Regions

Briggs: 13.2
Stewart [5e]: 15.3
Stewart [6e]: 16.3

Problems:

Briggs 13.2
    #7–15, 16, 19–25, 29, 30, 31, 32, 35, 37, 39–45, 49–63, 69.

Stewart [6e], 16.3
    #3, 7, 13, 17, 19, 31, 37, 43, 49, 55.

Double Integrals in Polar Coordinates

Briggs: 13.3
Stewart [5e]: 15.4
Stewart [6e]: 16.4
Problems:

Briggs [1e], 13.3
    #11, 13, 15, 17, 19, 21, 23–29, 35, 37, 39, 40, 41, 47, 49, 53.

Stewart [6e], 16.4
    #3, 5, 7, 13, 17, 25, 29, 37.

Applications of Double Integrals

Briggs: 13.6
Stewart [5e]: 15.5
Stewart [6e]: 16.5

Problems:

Briggs [1e], 13.6
    #9, 13, 16, 19, 24, 27, 34, 37.

Stewart [6e], 16.5
    #1, 5, 15, 23.

Surface Area

Stewart [5e]: 15.6

Problems:
???

Paul's Online Notes: Surface Area

Triple Integrals

Briggs: 13.4
Stewart [5e]: 15.7
Stewart [6e]: 16.6
Problems:

Briggs [1e], 13.4
    #7–17, 20, 23, 25, 28, 29–37, 39, 47, 49, 57.

Briggs [1e], 13.5:
    #12, 15, 16, 18, 21.

Stewart [6e], 16.6
    #3, 9, 11, 17, 25, 31, 37, 43.

Triple Integrals in Cylindrical and Spherical Coordinates

Briggs: 13.5
Stewart [5e]: 15.8
Stewart [6e]:
16.7 (Cylindrical),
16.8 (Spherical)

Paul's Notes - Cylindrical Coordinates
Paul's Notes - Spherical Coordinates

PatrickJMT - Evaluating a Triple Integral in Spherical Coordinates

Problems:

Briggs [1e], 13.5
    #11–21, 23, 25–31, 35–43, 42, 44, 46, 47, 49, 51, 55, 57, 63, 65, 67.

    Cylindrical
    Stewart [6e], 16.7 
        #1, 3, 7, 11, 13.

    Spherical
    Stewart [6e], 16.8
        #1, 4, 7, 9, 13, 15.


Several sources schedule exams either immediately before or after this section.


Change of Variable in Multiple Integrals

Briggs: 13.7
Stewart [5e]: 15.9
Stewart [6e]: 16.9


Problems:

Briggs [1e], 13.7
    #5, 7, 11, 13, 24, 27, 29, 31, 33, 34, 42.

Stewart [6e], 16.9
    #3, 5, 7, 9, 11, 19, 23.

Vector Calculus

Corresponding Chapters
Briggs [1e]    - Ch. 14
Stewart [5e]    - Ch. 16
Stewart [6e]    - Ch. 17

Vector Fields

Briggs: 14.1
Stewart [5e]: 16.1
Stewart [6e]: 17.1


Problems:

Briggs 14.1
    #2, 6, 7, 8, 11, 13, 16, 17, 18, 19, 25–35, 41, 43.

Stewart [6e], 17.1
    #1, 11, 17, 23, 25, 33.

Line Integrals

Briggs: 14.2
Stewart [5e]: 16.2
Stewart [6e]: 17.2

Problems:

Briggs [1e], 14.2
    #11–19, 25–29, 33–39, 43, 47, 49, 54, 55.

Stewart [6e], 17.2
    #1, 15, 17, 21, 33, 37, 39, 43, 47.

Fundamental Theorem for Line Integrals

Stewart [5e]: 16.3
Stewart [6e]: 17.3

Paul's Notes
PatrickJMT

Problems:

Stewart [6e], 17.3
    #1, 3, 15, 19, 23, 33.

Greens' Theorem

Briggs: 14.4
Stewart [5e]: 16.4
Stewart [6e]: 17.4
Problems:

Briggs 14.4
    #11, 13, 17, 19, 23, 25, 29, 30, 32, 35, 37, 41

Stewart [6e], 17.4
    #1, 5, 13, 17, 21, 23.

Curl and Divergence

Briggs: 14.5
Stewart [5e]: 16.5
Stewart [6e]: 17.5


Problems:

Briggs 14.5
    #9–15, 16, 17, 19, 21, 23–33, 38, 47.

Stewart [6e], 17.5
    #1, 5, 11, 12, 15, 19, 25, 37.

Parametric Surfaces and Their Areas

Stewart [5e]: 16.6
Stewart [6e]: 17.6

Problems:

Stewart [6e], 17.6
    #1, 3, 5, 15, 21, 25, 35, 45, 59.

Surface Integrals

Briggs: 14.6
Stewart [5e]: 16.7
Stewart [6e]: 17.7


Problems:

Briggs 14.6
    #11–29, 30, 32, 35, 41, 43, 45, 47, 61.

Briggs [1e], 14.7:
    #5, 8, 11, 15, 18, 22.

Stewart [6e], 17.7
    #3, 7, 11, 15, 21, 23, 41, 47.

Stokes' Theorem

Briggs: 14.7
Stewart [5e]: 16.8
Stewart [6e]: 17.8


Problems:

Briggs [1e], 14.7
    #7, 11–19, 27, 29, 39.

Stewart [6e], 17.8
    #3, 7, 15, 17, 19.

The Divergence Theorem

Briggs: 14.8
Stewart [5e]: 16.9
Stewart [6e]: 17.9


Problems:

Briggs [1e], 14.8
    #9, 13–25, 33, 35, 39.

Stewart [6e], 17.9
    #1, 7, 11, 13, 17, 19, 23, 31, 32.
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