Spring 2003

Mathematics Math21a
Spring 2003

Multivariable Calculus

Course Head: Oliver knill
Office: SciCtr 434
Email: knill@math.harvard.edu

Supplements

You only are required to check out handouts marked with a star (*). They will be distributed course wide. Other supplements or material is complementary.

Week 1: Hour 1: Coordinates Hour 2: Vectors and dot product Hour 3: Cross product	Week 2: Distance formulas (*) Hour 1: Lines and Planes Hour 2: Functions Hour 3: Quadrics 3D Applet of surfaces in the book Applets to quadrics and spherical coordinates.
Week 3: Hour 1: Presidents day Hour 1: Curves Hour 2: Curvature	Week 4: Hour 1: Other coordinates Hour 2: Parametric Surfaces Hour 3: Contour lines
Week 5: PDE's (*) Hour 1: Partial derivatives Hour 2: Linear approximation Hour 3: Review Hourly 1	Week 6: Hour 1: Chain rule Hour 2: D_v, gradient ICE: Van der Waals' law Hour 3: Summary ICE: Relief of impact crater
Week 7: Hour 1: Critial Points Hour 2: Constrained Extrema Hour 3: Combined ICE: Cobb Douglas Formula	Week 8: Hour 1: 2D Integrals Hour 2: Polar Integration Hour 3: Surface area ICE: Area of Roses ICE: Gabriel's Trumpet
Week 9: Hour 1: 3D Integrals Hour 2: Spherical/Cylindrical Coordinates Hour 3: Change of coordinates Volume of Sphere and Torus Objects in Multivariable calculus (*) ICE: Vector field matching	Week 10: Hour 1: Vector fields Hour 2: Line integrals ICE: Carnot Process Hour 3: Fundamental theorem of lineintegrals Perpetuum motion machines
Week 11: Hour 1: Review for midterm (see Exam page) Hour 2: Greens theorem Hour 3: Div/Curl Green's theorem and the Planimeter (CCP at Duke) with applet.	Week 12: Hour 1: Flux integrals Hour 2: Stokes theorem Hour 3: Divergence theorem Overview Integral theorems Nash ICE

Probability in multivariable calculus (PDF)

Please send comments to math21a@fas.harvard.edu

Wed May 21 22:22:42 EDT 2003

Mathematics Math21a Spring 2003

Multivariable Calculus

Supplements

Mathematics Math21a
Spring 2003