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Calculus Lectures
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
Divergence theorem (cont.): applications and proof
Line integrals in space, curl, exactness and potentials
Stokes theorem
Stokes theorem (cont.) review
Topological considerations Maxwells equations
Final review
Final review (cont.)
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