Summer 2005
Mathematics Maths21a
Summer 2005
Multivariable Calculus
Course Head: Oliver knill
Office: SciCtr 434
Email:
knill@math.harvard.edu
Harvard Summer school
News
Syllabus
Calendar
Homework
Exams
Quizes
Exhibits
Handouts
Lab
Project
Faq
Links
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