Math 12 - Calculus Plus - Fall 2010

Dartmouth College

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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 reading assignment should be read before the lecture, so that you are already prepared and can come with questions; the assignments refer either to sections in your textbook or to handouts available at the course Blackboard site.

Lecture Date Section in Text Brief Description
Day 1 Wed. Sept. 22 13.1-13.3 Three-dimensional coordinate systems, vectors, dot product
Day 2 Fri. Sept. 24 13.4, handout on matrices Cross Products in three dimensions; matrices
Day 3 Mon. Sept. 27 13.5 Equations of planes and lines
Day 4 Wed. Sept. 29 14.1 - 14.2 Curves, vector functions, their derivatives and integrals
Day 5 Fri. Oct. 1 14.3 - 14.4 Arc length, velocity and acceleration
Day 6 Mon. Oct. 4 15.1 - 15.2 Fuctions of several variables, their limits and continuity
Day 7 Wed. Oct. 6 15.3 -15.4 Partial derivatives, tangent planes and linear approximations
Day 8 Fri. Oct. 8 Handout on linear transformations Linear transformations
Day 9 Mon. Oct. 11 Handout on representing matrices Representing linear transformations by matrices
Day 10 Wed. Oct. 13 Handout on derivative The derivative as a matrix (Jacobian)
Day 11 Fri. Oct. 15 15.5 Chain Rule
Day 12 Mon. Oct. 18 15.6 Directional derivative and gradient
Day 13 Wed. Oct. 20 15.7 Maxima and minima
Day 14 Fri. Oct. 22 16.1 - 16.2 Double integrals over rectangles, iterated integrals
Day 15 Mon. Oct. 25 16.3 Double integrals over general regions
Day 16 Wed. Oct. 27 16.4 Triple Integrals
Day 17 Fri. Oct. 29 16.6 and class notes Change of Variables formula, examples using linear transformations and polar coordinates
Day 18 Mon. Nov. 1 16.7, 16.8 and 16.9 and class notes Change of variables formula for triple integrals, examples using cylindrical and spherical coordinates
Day 19 Wed. Nov. 3 17.1 - 17.2 Line integrals and vector fields
Day 20 Fri. Nov. 5 17.3 The fundamental theorem for line integrals
Day 21 Mon. Nov. 8 17.3 The fundamental theorem of line integrals
Day 22 Wed. Nov. 10 17.4 Green's Theorem
Day 23 Fri. Nov. 12 17.5 Curl and divergence
Day 24 Mon. Nov. 15 17.6 Parametric surfaces and their area
Day 25 Wed. Nov. 17 17.7 Surface integrals
Day 26 Fri. Nov. 19 17.8 Gauss Divergence Theorem
Day 27 Mon. Nov. 22 17.8 Stokes Theorem
Day 28 Mon. Nov. 29 No section in book Wrap up
Day 29 Wed. Dec. 1 No section in book Wrap up

Last Updated Sept 16, 2010 by R. Orellana