Licence:
Course Description:
This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space.
Lectures:
Lecture 1 - Dot Product
Lecture 2 - Determinants; Cross Product
Lecture 3 - Matrices; Inverse Matrices
Lecture 4 - Square Systems; Equations of Planes
Lecture 5 - Parametric Equations for Lines and Curves
Lecture 6 - Velocity, Acceleration - Kepler's Second Law
Lecture 7 - Review: Vectors and Matrices
Lecture 8 - Level Curves; Partial Derivatives; Tangent Plane Approximation
Lecture 9 - 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; Review
Lecture 16 - Double Integrals
Lecture 17 - Double Integrals in Polar Coordinates; Applications
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; Review
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 (continued): Applications and Proof
Lecture 30 - Line Integrals in Space, Curl, Exactness and Potentials
Lecture 31 - Stokes' Theorem
Lecture 32 - Stokes' Theorem (continued); Review
Lecture 33 - Topological Considerations - Maxwell's Equations
Lecture 34 - Multivariable Calculus Final Review
Lecture 35 - Multivariable Calculus Final Review (continued)
Source: http://academicearth.org/courses/multivariable-calculus-1
