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


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.)