Multivariable Calculus | Mathematics | MIT OpenCourseWare

Course Info

Instructor

Prof. Denis Auroux

Departments

Mathematics

As Taught In

Fall 2007

Level

Undergraduate

Topics

Mathematics

Learning Resource Types

Exam Solutions

Exams

Lecture Notes

Lecture Videos

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Lecture Videos

Lecture 1: Dot Product

Lecture 2: Determinants

Lecture 3: Matrices

Lecture 4: Square Systems

Lecture 5: Parametric Equations

Lecture 6: Kepler's Second Law

Lecture 7: Exam Review

Lecture 8: Partial Derivatives

Lecture 9: Max-Min and Least Squares

Lecture 10: Second Derivative Test

Lecture 11: Chain Rule

Lecture 12: Gradient

Lecture 13: Lagrange Multipliers

Lecture 14: Non-Independent Variables

Lecture 15: Partial Differential Equations

Lecture 16: Double Integrals

Lecture 17: Polar Coordinates

Lecture 18: Change of Variables

Lecture 19: Vector Fields

Lecture 20: Path Independence

Lecture 21: Gradient Fields

Lecture 22: Green's Theorem

Lecture 23: Flux

Lecture 24: Simply Connected Regions

Lecture 25: Triple Integrals

Lecture 26: Spherical Coordinates

Lecture 27: Vector Fields in 3D

Lecture 28: Divergence Theorem

Lecture 29: Divergence Theorem (cont.)

Lecture 30: Line Integrals

Lecture 31: Stokes' Theorem

Lecture 32: Stokes' Theorem (cont.)

Lecture 33: Maxwell's Equations

Lecture 34: Final Review

Lecture 35: Final Review (cont.)

Course Info

Instructor

Prof. Denis Auroux

Departments

Mathematics

As Taught In

Fall 2007

Level

Undergraduate

Topics

Mathematics

Learning Resource Types

Exam Solutions

Exams

Lecture Notes

Lecture Videos

Problem Sets

Download Course

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