Math 13 - Winter 2009

Dartmouth College

home          general information       syllabus               homework            office hours          professor

This syllabus has been approved by the undergraduate program committee and you should expect that we will cover all of this material this term; however, due to time constraints some of the material will not be covered at great length. The sections in parenthesis refer to sections in your book.

Lecture Topics Some Standard Examples/Concepts
Day 1 Review of algebra and geometry in Euclidean space (1.1-1.5) Vector notation, dot and cross products, lines, planes
Day 2 Matrices; polar and cylindrical coordinates (1.6 -1.7) Basic matrix operations, determinant and area, cartesian and polar coordiantes
Day 3 Functions in several variables (2.1 - 2.3) Graphing surfaces, review of limits, continuity and partial derivatives
Day 4 Derivatives (2.3-2.5) properties of partial derivatives, the chain rule
Day 5 Directional derivatives and the gradient (2.6)
Day 6 Parametrized curves (3.1)
Day 7 Arclength (no curvature) (3.2)
Day 8 Vector fields (3.2)
Day 9 Gradient, divergence, curl, and the Del operator (3.4)
Day 10 Double integrals (5.1)
Day 11 Double integrals (5.2)
Day 12 Changing the order of integration (5.3)
Day 13 Triple integrals (5.4)
Day 14 Change of variables (5.5) linear transformations, the Jacobian
Day 15 Applications of Integration (5.6) average value, center of mass
Day 16 Scalar and vector line integrals (6.1)
Day 17 Scalar and vector line integrals (6.1)
Day 18 Green's Theorem (6.2)
Day 19 Conservative vector fields (6.3) path independence, potential functions, "partial integration"
Day 20 Parametrized surfaces (7.1)
Day 21 Areas of surfaces (7.1)
Day 22 Surface integrals (7.2)
Day 23 Surface integrasl (7.2)
Day 24 Stokes's theorem (7.3)
Day 25 Stokes's theorem (7.3)
Day 26 Gauss's Theorem (7.3)
Day 27 Gauss' theorem (7.3)
Day 28 Path Independence and the Fundamental Theorem of Calculus

Last Updated March 15, 2010 by R. Orellana