Summer 2006
Mathematics Maths21a
Summer 2006
Multivariable Calculus
Course Head:
Oliver knill
Office: SciCtr 434
Email:
knill@math.harvard.edu
Harvard Summer school
News
Syllabus
Calendar
Homework
Exams
Handouts
Exhibits
Lab
Faq
Links
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