MIT Course , Fall 2007 , Prof. Denis Auroux

**105**students enrolled

MIT Course , Fall 2007 , Prof. Denis Auroux

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

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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5.0 (1 Ratings)

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- 1.Dot product
- 2.Determinants; cross product
- 3.Matrices; inverse matrices
- 4.Square systems; equations of planes
- 5.Parametric equations for lines and curves
- 6.Velocity, acceleration; Keplers second law
- 7.Review
- 8.Level curves; partial derivatives; tangent plane approximation
- 9.Max-min problems; least squares
- 10.Second derivative test; boundaries and infinity
- 11.Differentials; chain rule
- 12.Gradient; directional derivative; tangent plane
- 13.Lagrange multipliers
- 14.Non-independent variables
- 15.Partial differential equations
- 16.Double integrals
- 17.Double integrals in polar coordinates; applications
- 18.Change of variables
- 19.Vector fields and line integrals in the plane
- 20.Path independence and conservative fields
- 21.Gradient fields and potential functions
- 22.Greens theorem
- 23.Flux; normal form of Greens theorem
- 24.Simply connected regions
- 25.Triple integrals in rectangular and cylindrical coordinates
- 26.Spherical coordinates; surface area.
- 27.Vector fields in 3D; surface integrals and flux
- 28.Divergence theorem
- 29.Divergence theorem (cont.) applications and proof
- 30.Line integrals in space, curl, exactness and potentials
- 31.Stokes theorem
- 32.Stokes theorem (cont.); review
- 33.Topological considerations; Maxwells equations
- 34.Final review
- 35.Final review (cont.)

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