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

Lecture Videos

Problem Sets

Exams with Solutions

Lecture Notes

Download Course

Readings

CV. Changing Variables in Multiple Integrals

D. Determinants

G. Gravitational Attraction

I. Limits in Iterated Integrals

K. Kepler's Second Law

LS. Least Squares Interpolation

M. Matrices and Linear Algebra

Matlab Instructions

N. Non-independent Variables

P. Partial Differential Equations

SD. Second Derivative Test

TA. The Tangent Approximation

1. Vectors and Matrices

1. Vectors and Matrices

V1. Plane Vector Fields

2. Partial Differentiation

2. Partial Differentiation

V2. Gradient Fields and Exact Differentials

3. Double Integrals

3. Double Integrals

V3. Two-dimensional Flux

4. Line Integrals in the Plane

4. Line Integrals in the Plane

V4. Green's Theorem in Normal Form

5. Triple Integrals

5. Triple Integrals

V5. Simply-Connected Regions

6. Vector Integral Calculus in Space

6. Vector Integral Calculus in Space

V6. Multiply-connected Regions; Topology

V7. Laplace's Equation and Harmonic Functions

V8. Vector Fields in Space

V9. Surface Integrals

V10. The Divergence Theorem

V11. Line Integrals in Space

V12. Gradient Fields in Space

V13. Stokes' Theorem

V14. Some Topological Questions

V15. Relation to Physics

Course Info

Instructor

Prof. Denis Auroux

Departments

Mathematics

As Taught In

Fall 2007

Level

Undergraduate

Topics

Mathematics

Learning Resource Types

Lecture Videos

Problem Sets

Exams with Solutions

Lecture Notes

Download Course

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