Multivariable Calculus

Course Description

Parametric equations and polar coordinates. Vectors in 2- and 3-dimensional Euclidean spaces. Partial derivatives. Multiple integrals. Vector calculus. Theorems of Green, Gauss, and Stokes.

Lectures

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   Lecture 1 - Areas and Lengths in Polar Coordinates

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   Lecture 2 - Vectors, Dot Product

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   Lecture 3 - Cross Product, Determinant

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   Lecture 4 - Lines and Planes

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   Lecture 5 - Cylinders and Quadric Surfaces

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   Lecture 6 - Vector-Valued Functions and Space Curves

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   Lecture 7 - Functions of Several Variables

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   Lecture 8 - Limits and Continuity

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   Lecture 9 - Partial Derivatives

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    Lecture 10 - Tangent Planes and Linear Approximations

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    Lecture 11 - The Chain Rule

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    Lecture 12 - Directional Derivatives and the Gradient Vector

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    Lecture 13 - Maxima and Minima

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    Lecture 14 - More Maxima and Minima; Lagrange Multipliers

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    Lecture 15 - Midterm Review

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    Lecture 16 - More Lagrange Multipliers

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    Lecture 17 - Double Integrals Over Rectangles

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    Lecture 18 - Double Integrals over General Regions

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    Lecture 19 - Double Integrals in Polar Coordinates

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    Lecture 20 - Applications of Double Integrals

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    Lecture 21 - Triple Integrals

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    Lecture 22 - Triple Integrals in Cylindrical Coordinates

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    Lecture 23 - Triple Integrals in Spherical Coordinates

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    Lecture 24 - Change of Variables, Jacobians

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    Lecture 25 - More change of variables and Jacobians

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    Lecture 26 - Vector Fields

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    Lecture 27 - Line Integrals

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    Lecture 28 - Green's Theorem I

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    Lecture 29 - Green's Theorem II

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    Lecture 30 - Curl and Divergence

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    Lecture 31 - Parametric Surfaces

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    Lecture 32 - More Parametric Surfaces; Surface Integrals, part I

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    Lecture 33 - Surface Integrals, part II

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    Lecture 34 - Surface Integrals, part III

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    Lecture 35 - Stokes' Theorem I

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    Lecture 36 - Stokes' theorem II

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    Lecture 37 - Divergence Theorem I

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    Lecture 38 - Divergence theorem II

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    Lecture 39 - Review I

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    Lecture 40 - Review II