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Appendix E Sage examples

1.1 Double integrals over rectangles

Sage example 1.1.1 Visualizing/approximating double integrals

1.2 Iterated integrals and Fubini's theorem

Sage example 1.2.1 Iterated integrals over rectangle

1.3 Double integrals over general regions

Sage example 1.3.1 Iterated integrals over elementary regions

1.5 Triple integrals

Sage example 1.5.1 Three-dimensional plots
Sage example 1.5.2 Iterated integrals over solid regions

2.1 Line integrals of scalar functions

Sage example 2.1.1 Parametrized curves
Sage example 2.1.2 Scalar line integral

2.2 Line integrals of vector fields

Sage example 2.2.1 Vector line integral

2.3 Path independence, conservative fields, potential functions

Sage example 2.3.1 Computing curl

2.5 Surfaces and their area

Sage example 2.5.1 Plane parametrization
Sage example 2.5.2 Surface parametrizations

2.6 Surface integrals

Sage example 2.6.1 Nonorientable surface: Möbius strip
Sage example 2.6.2 Surface integrals of vector fields