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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 multi-variable 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)

Image: 18.02 Multivariable Calculus


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.)

References
18.02 Multivariable Calculus
Instructors: Prof. Denis Auroux. Lecture Notes. Exams and Solutions. Subtitles/Transcript. Assignments (no Solutions). This course covers vector and multi-variable calculus.