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Math 53 - Multivariable Calculus

Math 53: Multivariable Calculus (Fall 2009, UC Berkeley). This is a collection of video lectures on Multivariable Calculus given by Edward Frenkel, Professor of Mathematics at University of California, Berkeley. This course discusses essential topics in multivariable calculus, focusing on functions of two and three variables. Topics covered in this course include parametric curves, vectors in 2- and 3-dimensional spaces, partial derivatives, multiple integrals, vector calculus, Green's theorem, Stokes' theorem, and divergence theorem.

Introduction


Lecture 01 - Introduction, Parametric Curves
Lecture 02 - Parametric Curves, Calculus with Parametric Curves
Lecture 03 - Calculus with Parametric Curves, Polar Coordinates
Lecture 04 - Coordinates and Vectors in 3 Dimensions
Lecture 05 - Dot and Cross Products, Lines and Planes in 3D Space
Lecture 06 - More Complicated Surfaces in 3D Space, Parametric Curves in 3D Space
Lecture 07 - Vector-valued Functions, Functions in Two and Three Variables
Lecture 08 - Limits, Partial Derivatives
Lecture 09 - Differentials in one and two variables, Tangent Planes and differentiability
Lecture 10 - Review
Lecture 11 - Directional Derivatives, Gradient Vector
Lecture 12 - Applications of Directional Derivatives, Local Maxima and Minima
Lecture 13 - Maxima and Minima, Lagrange multipliers
Lecture 14 - Maxima and Minima, Multiple Integrals over Rectangles
Lecture 15 - Multiple Integrals in Cylindrical & Spherical Coordinate Systems
Lecture 16 - Multiple Integrals over General Regions, Change of Variables
Lecture 17 - Review
Lecture 18 - General Domains: "Curved", Vector Fields, Line Integrals
Lecture 19 - Line Integrals
Lecture 20 - Line Integrals, Green's Theorem
Lecture 21 - Intro to Stokes' Theorem, Curl, Divergence
Lecture 22 - Surface Integrals, Parametric Surfaces
Lecture 23 - Stokes' Theorem
Lecture 24 - Divergence Theorem
Lecture 25 - Review