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Math 230-2:
Kursobjekt
Aaron Greicius
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Contents
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Front Matter
Colophon
0
Foundations
Sets and functions
Logic
1
Multiple integrals
Double integrals over rectangles
Iterated integrals and Fubini's theorem
Double integrals over general regions
Area of planar regions and average value
Triple integrals
Substitution: general
Substitution: polar and cylindrical coordinates
Substitution: spherical coordinates
Applications of multiple integrals
2
Integrals and Vector Fields
Line integrals of scalar functions
Line integrals of vector fields
Path independence, conservative fields, potential functions
Green's theorem in the plane
Surfaces and their area
Surface integrals
Stokes's theorem
Divergence theorem
Back Matter
A
Notation
B
Definitions
C
Theory and procedures
D
Examples
E
Sage examples
Index
Authored in PreTeXt
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Chapter
1
Multiple integrals
1.1
Double integrals over rectangles
1.2
Iterated integrals and Fubini's theorem
1.3
Double integrals over general regions
1.4
Area of planar regions and average value
1.5
Triple integrals
1.6
Substitution: general
1.7
Substitution: polar and cylindrical coordinates
1.8
Substitution: spherical coordinates
1.9
Applications of multiple integrals
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