## Fall 2019 lectures with steve Butler

Calculus review; Cartesian coordinates; distance; spheres. Notes (filled)

Cylindrical and spherical coordinates. Notes (filled)

Vectors; magnitude; unit vectors; midpoint. Notes (filled)

Dot product; angle between vectors; projection; work. Notes (filled)

Cross product; areas; volume. Notes (filled)

Lines; planes; normal vectors; distances. Notes (filled)

Parametric curves; motion; derivatives of vector valued functions; tangent lines. Notes (filled)

Integrals of vector functions. Notes (filled)

Arc length; cumulative arc length. Notes (filled)

Decomposing motion; unit tangent; unit normal; unit binormal; osculating plane. Notes (filled)

Curvature. Notes (filled)

Review for Exam 1. Problems (solutions)

Q&A for Exam 1. Notes

Functions of several variables; level curves; level surfaces; contour diagrams. Notes (filled)

Limits; continuity. Notes (filled)

Partial derivatives; higher order partial derivatives. Notes (filled)

Differentiability; tangent plane; chain rule; implicit differentiation. Notes (filled)

Tangent planes; properties of gradient; linear approximation. Notes (filled)

Taylor polynomials for multi-variable functions. Notes (filled)

Optimization; critical points; classification with second partials test. Notes (filled)

Optimization for a closed and bounded region. Notes (filled)

Optimization using method of Lagrange multipliers. Notes (filled)

Review for Exam 2. Problems (solutions)

Q&A for Exam 2. Notes

Multivariable integration; iterated integrals over rectangles and regions. Notes (filled)

Changing order of integration. Notes (filled)

Integration in polar coordinates. Notes (filled)

Triple integration in Cartesian coordinates; changing order of integration. Notes (filled)

Geometrical applications of multivariable integration. Notes (filled)

Physics applications of multivariable integration. Notes (filled)

Integration in cylindrical and spherical. Notes (filled)

Jacobian; substitution in multiple integrals. Notes (filled)

Vector fields; curl; divergence. Notes (filled)

Line integrals; work. Notes (filled)

Line integrals of conservative functions. Notes (filled)

Green's Theorem. Notes (filled)

Surface integrals. Notes (filled)

Review for Exam 3. Problems (solutions)

Q&A for Exam 3. Notes

Stokes' Theorem. Notes (filled)

Gauss's Divergence Theorem. Notes (filled)

Practice recognizing Stokes and Divergence. Notes (filled)

Review for Final Exam. Problems (solutions)

Final unboxing