Harvard University,FAS

Summer 2005

Mathematics Maths21a
Summer 2005

Multivariable Calculus

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

Harvard Summer school

Supplements

1. Week: Essential things Extended hour to hour syllabus Lecture 1: coordinates Lecture 1: ICE completion Lecture 2: vectors and dot product Lecture 3: cross product Lecture 3: lines Lecture 3: ICE cross product	2. Week: Lecture 4: Lines and Planes Lecture 4: Distance formulas Lecture 4: Tranquility ICE Lecture 5: Functions and quadrics Lecture 5: Functions and contour lines Lecture 5: Contest Lecture 6: Parametric surfaces Lecture 6: Implicit surfaces
3. Week: Lecture 7: Curves Lecture 7: Knot Lecture 7: Scate Lecture 8: Arc length Lecture 8: Partial derivatives Lecture 8: Partial differential equations	4. Week: Lecture 9: Chain rule, directonal derivative, tangent line, linearization Lecture 10: critical points Lecture 10: the island theorem Lecture 10: double pendulum Lecture 11: constrained extrema Lecture 11: Cobb-Douglas
5. Week: Lecture 12: double integrals Lecture 12: ICE on double integrals Lecture 12: the Gauss problem Lecture 13: Polar coordinates Lecture 13: ICE Roses Lecture 13: Applications of 2D integrals Lecture 13: Gabriels trumpet	6. Week: Lecture 14: 3D integrals Lecture 14: cylindrical coordinates Lecture 14: volume of sphere and torus Lecture 15: spherical coordinates Lecture 15: vector fields Lecture 15: quiz (pictures) Lecture 15: quiz (formulas) Lecture 16: Perpetuum motion machines Lecture 16: Carnot Process Lecture 16: Line integrals (I) Lecture 16: Line integrals (II) Lecture 16: Fundamental thm of line integrals
7. Week: Lecture 17: Greens theorem Lecture 17: More on Greens theorem (optional) Lecture 18: Flux integrals Lecture 18: Stokes theorem Lecture 18: Stokes ICE Lecture 19: Curl and Divergence Lecture 19: Divergence theorem	Review: Review beyond integrals Review material

Please send comments to maths21a@fas.harvard.edu

Maths21a, Multivariable Calculus, Summer 2005, Department of Mathematics, Faculty of Art and Sciences, Harvard University

Fri Aug 19 20:56:00 EDT 2005