# Multivariable Calculus

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2 STUDENTS

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

### Course Curriculum

 Dot product Details 38:41 Determinants; cross product Details 52:51 Matrices; inverse matrices Details 51:5 Square systems; equations of planes Details 49:3 Parametric equations for lines and curves Details 50:50 Velocity, acceleration; Keplers second law Details 48:4 Review Details 49:50 Level curves; partial derivatives; tangent plane approximation Details 46:13 Max-min problems; least squares Details 49:44 Second derivative test; boundaries and infinity Details 52:18 Differentials; chain rule Details 50:9 Gradient; directional derivative; tangent plane Details 50:10 Lagrange multipliers Details 50:10 Non-independent variables Details 49:11 Partial differential equations Details 45:23 Double integrals Details 0:48 Double integrals in polar coordinates; applications Details 51:30 Change of variables Details 49:55 Vector fields and line integrals in the plane Details 51:9 Path independence and conservative fields Details 50:23 Gradient fields and potential functions Details 50:11 Greens theorem Details 46:45 Flux; normal form of Greens theorem Details 50:13 Simply connected regions Details 0:49 Triple integrals in rectangular and cylindrical coordinates Details 48:42 Spherical coordinates; surface area. Details 51:5 Vector fields in 3D; surface integrals and flux Details 50:34 Divergence theorem Details 49:16 Divergence theorem (cont.): applications and proof Details 50:13 Line integrals in space, curl, exactness and potentials Details 49:42 Stokes theorem Details 48:21 Stokes theorem (cont.); review Details 50:9 Topological considerations; Maxwells equations Details 28:39 Final review Details 43:54 Final review (cont.) Details 48:52

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