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.
| Lecture 04 - Coordinates and Vectors in 3 Dimensions |
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Go to the Course Home or watch other lectures:
| 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 and 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 |