Multivariable Calculus

MIT Course , Fall 2007 , Prof. Denis Auroux

Lecture 16: Double integrals

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Course Description :

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

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