Lecture 19: Triple Integrals with Cyclindrical Coordinates and Spherical Coordinates, Double Integrals for Surface Area, Vector Fields, and Line Integrals.

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Presentation transcript:

Lecture 19: Triple Integrals with Cyclindrical Coordinates and Spherical Coordinates, Double Integrals for Surface Area, Vector Fields, and Line Integrals

Part I: Triple Integrals with Cylindrical and Spherical Coordinates

Changing variables for Triple Integrals

Triple Integrals with Cylindrical Coordinates

Example: Volume of a cone

Triple Integrals with Spherical Coordinates

Example: Volume of a Sphere

Part II: Double Integrals for Surface Area

Surface Area

Part III: Vector Fields and Line Integrals

Objectives Be familiar with vector fields and how to compute line integrals. Know how to compute the work done on an object by a given force. Corresponding Section of Simmons: 21.1

Vector Fields

Line Integrals

Line Integrals with Parametric Equations

Kinetic Energy and Acceleration

Work

Examples

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