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Course 30189: Maths21A Summer 2008
Multivariable Calculus
Supplements
Office: SciCtr 434


We post here some summaries and some complements to the lecture topics. These notes have been evolved since a few years. They are quite densely written and do not replace the book of course. If you find typos, please email them or talk to me about it. Errata found after the notes being distributed are acknowledged to the right. The files found here are already the latest version.


Week 1 Lecture 1. Coordinates
Week 1 Lecture 2. Vectors
Week 1 Lecture 3. Cross product
Week 1 Lecture 3. Lines
Week 2 Lecture 1. Lines planes
Week 2 Lecture 1. Distance
Week 2 Lecture 2. Contours
Week 2 Lecture 2. Functions
Week 3 Lecture 3 Implicit surfaces
Week 2 Lecture 3 Other coordinates
Week 2 Lecture 3 Parametric surfaces
Week 3 Lecture 1 Curves
Week 3 Lecture 2 Arc length
Week 3 Lecture 2 Partial derivatives
Week 4 Linearization
Week 4 Tangent spaces
Week 4 Extrema
Week 4 Constrained extrema
Week 5 2dintegral
Week 5 Type I and II regions
Week 5 Polar integration
Week 5 Polar integration
Week 5 3D integrals
week 5 Integration in cylindrical coordinates
Week 5 Integration in spherical coordinates
Week 6 Vector fields
Week 6 Line integrals
Week 6 Fundamental theorem of line integrals
Week 7 Greens theorem
Week 7 Stokes theorem
Week 7 Divergence theorem
Week 7 Overview
Please send questions and comments to maths21a@fas.harvard.edu
Maths21A | Oliver Knill | Summer 2008 | Summer school | Department of Mathematics | Faculty of Art and Sciences | Harvard University