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MIT OpenCourseWare

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 )

Instructor

2009

Mathematics

Dot Product

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.)

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