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18.02 Multivariable Calculus

18.02 Multivariable Calculus (Fall 2007, MIT OCW). This consists of 35 video lectures given by Professor Denis Auroux, covering vector and multivariable calculus. Topics covered in this course include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space. (from ocw.mit.edu)

Lecture 12 - Gradient; Directional Derivative; Tangent Plane

Go to the Course Home or watch other lectures:

Lecture 01 - Dot Product

Lecture 02 - Determinants; Cross Product

Lecture 03 - Matrices; Inverse Matrices

Lecture 04 - Square Systems; Equations of Planes

Lecture 05 - Parametric Equations for Lines and Curves

Lecture 06 - Velocity, Acceleration; Kepler's Second Law

Lecture 07 - Exam Review

Lecture 08 - Level Curves; Partial Derivatives; Tangent Plane Approximation

Lecture 09 - Max-Min Problems; Least Squares

Lecture 10 - Second Derivative Test; Boundaries and Infinity

Lecture 11 - Differentials; Chain Rule

Lecture 12 - Gradient; Directional Derivative; Tangent Plane

Lecture 13 - Lagrange Multipliers

Lecture 14 - Non-Independent Variables

Lecture 15 - Partial Differential Equations

Lecture 16 - Double Integrals

Lecture 17 - Double Integrals in Polar Coordinates

Lecture 18 - Change of Variables

Lecture 19 - Vector Fields and Line Integrals in the Plane

Lecture 20 - Path Independence and Conservative Fields

Lecture 21 - Gradient Fields and Potential Functions

Lecture 22 - Green's Theorem

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

Lecture 24 - Simply Connected Regions

Lecture 25 - Triple Integrals in Rectangular and Cylindrical Coordinates

Lecture 26 - Spherical Coordinates; Surface Area

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

Lecture 28 - Divergence Theorem

Lecture 29 - Divergence Theorem (cont.): Applications and Proof

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

Lecture 31 - Stokes' Theorem

Lecture 32 - Stokes' Theorem (cont.)

Lecture 33 - Topological Considerations - Maxwell's Equations

Lecture 34 - Final Review

Lecture 35 - Final Review (cont.)