Multivariable Calculus

Course Description

This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space.

Lectures

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   Lecture 1 - Dot Product

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   Lecture 2 - Determinants; Cross Product

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   Lecture 3 - Matrices; Inverse Matrices

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   Lecture 4 - Square Systems; Equations of Planes

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   Lecture 5 - Parametric Equations for Lines and Curves

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   Lecture 6 - Velocity, Acceleration - Kepler's Second Law

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   Lecture 7 - Review: Vectors and Matrices

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   Lecture 8 - Level Curves; Partial Derivatives; Tangent Plane Approximation

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   Lecture 9 - Max-Min Problems; Least Squares

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    Lecture 10 - Second Derivative Test; Boundaries and Infinity

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    Lecture 11 - Differentials; Chain Rule

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    Lecture 12 - Gradient; Directional Derivative; Tangent Plane

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    Lecture 13 - Lagrange Multipliers

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    Lecture 14 - Non-Independent Variables

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    Lecture 15 - Partial Differential Equations; Review

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    Lecture 16 - Double Integrals

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    Lecture 17 - Double Integrals in Polar Coordinates; Applications

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    Lecture 18 - Change of Variables

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    Lecture 19 - Vector Fields and Line Integrals in the Plane

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    Lecture 20 - Path Independence and Conservative Fields

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    Lecture 21 - Gradient Fields and Potential Functions

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    Lecture 22 - Green's Theorem

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    Lecture 23 - Flux; Normal Form of Green's Theorem

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    Lecture 24 - Simply Connected Regions; Review

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    Lecture 25 - Triple Integrals in Rectangular and Cylindrical Coordinates

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    Lecture 26 - Spherical Coordinates; Surface Area

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    Lecture 27 - Vector Fields in 3D; Surface Integrals and Flux

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    Lecture 28 - Divergence Theorem

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    Lecture 29 - Divergence Theorem (continued): Applications and Proof

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    Lecture 30 - Line Integrals in Space, Curl, Exactness and Potentials

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    Lecture 31 - Stokes' Theorem

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    Lecture 32 - Stokes' Theorem (continued); Review

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    Lecture 33 - Topological Considerations - Maxwell's Equations

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    Lecture 34 - Multivariable Calculus Final Review

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    Lecture 35 - Multivariable Calculus Final Review (continued)