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UMass Boston, Spring 2010
Math 240: Calculus III

Last modified:
February 15, 2010

Part I

Coordinate Systems
- Cartesian Coordinates
- Polar Coordinates
- Cylindrical Coordinates
- Spherical Coordinates
Vectors
- Vectors
- Dot Product
- Cross Product
Geometry
- Lines and Planes
- Quadric Surfaces
Parametric Curves
- Parametric Curves
- Calculus of Parametric Curves
- Geometry of Parametric Curves

Part III

Double Integrals
- Double Integrals over Rectangles
- Iterated Double Integrals
- Double Integrals over General Regions
Triple Integrals
- Triple Integrals
- Iterated Triple Integrals
- Applications of Triple Integrals
Change of Variables
- Double Integrals in Polar Coordinates
- Triple Integrals in Cylindrical Coordinates
- Triple Integrals in Spherical Coordinates
- Change of Variables for Double Integrals
- Change of Variables for Triple Integrals

Part II

Functions of Several Variables
- Functions of Several Variables
- Graphical Representations
- Limits and Continuity
Partial Derivatives
- Partial Derivatives
- The Chain Rule
- Directional Derivatives
Applications of Partial Derivatives
- Linear Approximations
- Unconstrained Optimization
- Constrained Optimization

Part IV

Line Integrals
- Scalar and vectorial line integrals
- Conservative fields
- Green's Theorem
- Curl and divergence in Flatland
Surface Integrals
- Parametrized surfaces
- Scalar and vectorial surface integrals
- Divergence Theorem
- Stokes' Theorem
Fundamental Theorems of Calculus

Cite/attribute Resource. Zara, C. (Sep 03, 2010). Topics. Retrieved Nov 06, 2014, from UMass Boston OpenCourseware Web site: http://ocw.umb.edu/mathematics/math-240-calculus-iii-spring-2010/topic.

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