18.02 Multivariable Calculus

Video Lectures

Displaying all 35 video lectures.
I. Vectors and Matrices
Lecture 1
Dot Product
Play Video		 Dot Product
Lecture 2
Determinants and Cross Product
Play Video		 Determinants and Cross Product
Lecture 3
Matrices and Inverse Matrices
Play Video		 Matrices and Inverse Matrices
Lecture 4
Square Systems and Equations of Planes
Play Video		 Square Systems and Equations of Planes
Lecture 5
Parametric Equations for Lines and Curves
Play Video		 Parametric Equations for Lines and Curves
Lecture 6
Velocity, Acceleration and Kepler's Second Law
Play Video		 Velocity, Acceleration and Kepler's Second Law
Lecture 7
Review
Play Video		 Review
II. Partial Derivatives
Lecture 8
Level Curves, Partial Derivatives and Tangent Plane Approximation
Play Video		 Level Curves, Partial Derivatives and Tangent Plane Approximation
Lecture 9
Max-min Problems and Least Squares
Play Video		 Max-min Problems and Least Squares
Lecture 10
Second Derivative Test, Boundaries and Infinity
Play Video		 Second Derivative Test, Boundaries and Infinity
Lecture 11
Differentials and Chain Rule
Play Video		 Differentials and Chain Rule
Lecture 12
Gradient, Directional Derivative and Tangent Plane
Play Video		 Gradient, Directional Derivative and Tangent Plane
Lecture 13
Lagrange Multipliers
Play Video		 Lagrange Multipliers
Lecture 14
Non-independent Variables
Play Video		 Non-independent Variables
Lecture 15
Partial Differential Equations (Review)
Play Video		 Partial Differential Equations (Review)
III. Double Integrals and Line Integrals in the Plane
Lecture 16
Double Integrals
Play Video		 Double Integrals
Lecture 17
Double Integrals in Polar Coordinates and Applications
Play Video		 Double Integrals in Polar Coordinates and Applications
Lecture 18
Change of Variables
Play Video		 Change of Variables
Lecture 19
Vector Fields and Line Integrals in the Plane
Play Video		 Vector Fields and Line Integrals in the Plane
Lecture 20
Path Independence and Conservative Fields
Play Video		 Path Independence and Conservative Fields
Lecture 21
Gradient fields and Potential Functions
Play Video		 Gradient fields and Potential Functions
Lecture 22
Green Theorem
Play Video		 Green Theorem
Lecture 23
Flux and Normal Form of Green Theorem
Play Video		 Flux and Normal Form of Green Theorem
Lecture 24
Simply Connected Regions (Review)
Play Video		 Simply Connected Regions (Review)
IV. Triple Integrals and Surface Integrals in 3-space
Lecture 25
Triple Integrals in Rectangular and Cylindrical Coordinates
Play Video		 Triple Integrals in Rectangular and Cylindrical Coordinates
Lecture 26
Spherical Coordinates and Surface Area
Play Video		 Spherical Coordinates and Surface Area
Lecture 27
Vector Fields in 3D and Surface Integrals and Flux
Play Video		 Vector Fields in 3D and Surface Integrals and Flux
Lecture 28
Divergence Theorem
Play Video		 Divergence Theorem
Lecture 29
Divergence Theorem (cont.) and Applications and Proof
Play Video		 Divergence Theorem (cont.) and Applications and Proof
Lecture 30
Line Integrals in Space, Curl, Exactness and Potentials
Play Video		 Line Integrals in Space, Curl, Exactness and Potentials
Lecture 31
Stokes' Theorem
Play Video		 Stokes' Theorem
Lecture 32
Stokes' Theorem (cont.) and Review
Play Video		 Stokes' Theorem (cont.) and Review
Lecture 33
Topological Considerations and Maxwell's Equations
Play Video		 Topological Considerations and Maxwell's Equations
Lecture 34
Final Review
Play Video		 Final Review
Lecture 35
Final Review (cont.)
Play Video		 Final Review (cont.)