Topics
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Math 240: Calculus III
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Topics
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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
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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
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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
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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
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