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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