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Multivariable Calculus

MIT,, Fall 2007 , Prof. Denis Auroux

Overview

Dot product - Determinants - cross product - Matrices - inverse matrices - Square systems - equations of planes - Parametric equations for lines and curves - Velocity, acceleration - Keplers second law - Review - Level curves - partial derivatives - tangent plane approximation - Max-min problems - least squares - Second derivative test; boundaries and infinity - Differentials; chain rule - Gradient; directional derivative; tangent plane - Lagrange multipliers - Non-independent variables - partial differential equations - Double integrals - Double integrals in polar coordinates - applications

Change of variables - Vector fields and line integrals in the plane - Path independence and conservative fields - Gradient fields and potential functions - Greens theorem - Flux; normal form of Greens theorem - Simply connected regions -Triple integrals in rectangular and cylindrical coordinates - Spherical coordinates; surface area - Vector fields in 3D - surface integrals and flux - Divergence theorem - Line integrals in space, curl, exactness and potentials - Stokes theorem -Topological considerations - Maxwells equations - Final review

Includes

Lecture 35: Final review (cont.)

4.1 ( 11 )

Lecture Details

Ratings

5.0


1 Ratings
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Comments
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Sam

Excellent course helped me understand topic that i couldn't while attendinfg my college.

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Dembe

Great course. Thank you very much.

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