Harvard University,FAS

Summer 2006

Mathematics Maths21a
Summer 2006

Multivariable Calculus

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

Harvard Summer school

Supplements

1. Week: Syllabus Day to Day Lectures First lecture: coordinates Second lecture: vectors Third lecture: cross product Third lecture: lines and planes Third lecture: distance formulas	2. Week: First lecture: contest First lecture: functions of three variables First lecture: functions of two variables Second lecture: Other coordinates Second lecture: implicit surfaces Second lecture: Parametric surfaces
3. Week: First lecture: curves Second lecture: arc length and curvature Second lecture: partial derivatives	4. Week: First lecture: linearization First lecture: tangent spaces and chain rule First lecture: gradient directional derivatives Second lecture: critical points Second lecture: the pendulum Third lecture: constrained extrema
5. Week: First lecture: 2D integrals First lecture: general regions Second lecture: polar integrals Second lecture: surface area	6. Week: First lecture: 3D integrals First lecture: Examples in cylindrical coordinates Second lecture: Integration in Spherical coorindates Second lecture: Three cylinders Second lecture: Sphere and Torus Second lecture: Vector fields Third lecture: Line integrals Third lecture: Fundamental theorem of line integrals
7. Week: First lecture: Greens theorem Second lecture: Stokes theorem Second lecture: Curl and Div Second lecture: Flux Third lecture: Divergence theorem Third lecture: Applications of Div theorem Third lecture: Overview over integral theorems	Review:

Please send comments to maths21a@fas.harvard.edu

Maths21a, Multivariable Calculus, Summer 2006, Department of Mathematics, Faculty of Art and Sciences, Harvard University

Fri Aug 18 10:21:21 EDT 2006