Detailed Schedule -- Multivariable Calculus

Fall 2007, Prof. Little

This is a tentative, evolving schedule. As always, topics may be added, deleted, or rearranged during the course of the semester. Any changes will be announced in class and here.

Date Class TopicReading (Colley)
8/29 Vectors in R2 and R3 1.1
8/31 Parametrizing lines and curves 1.2
9/3 Dot products and projections 1.3
9/4 Cross products in R3 1.4
9/5 Planes in R3 1.5
9/7 Generalizing to Rn (Quiz 1) 1.6
9/10 Polar, cylindrical, spherical coordinates 1.7
9/11 Lab Day 1: More on coordinate systems 1.7
9/12 Lab, continued 1.7
9/14 Scalar functions of several variables (Quiz 2) 2.1
9/17 Limits for f : Rm -> Rn 2.2
9/18 Lab Day 2: More on limits 2.2
9/19 Partial derivatives 2.3
9/21 Definition of differentiability (Quiz 3) 2.3
9/24 Higher order partial derivatives 2.4
9/25 Chain rule 2.5
9/26 More on the chain rule 2.5
9/28 Exam I (covers material from 8/29 through 9/21)
10/1 Directional derivatives and the gradient 2.6
10/2 Spare day 2.6
10/3 Lab Day 3: More on parametric curves 3.1
10/5 Arclength of curves (Quiz 4) 3.2
10/8, 9 No Class -- Columbus Day Break 3.2
10/10 Curvature and torsion of space curves 3.2
10/12 Frenet-Serret equations for space curves 3.2
10/15 Vector fields 3.3
10/16 Lab Day 4: More on vector fields 3.3
10/17 Div, grad, curl 3.4
10/19 Spare day (Quiz 5) 4.1
10/22 Taylor's theorem 4.1
10/23 Extrema for functions of several variables 4.2
10/24 Hessian criterion 4.2
10/26 Exam II (covers material from 9/24 through 10/19)
10/29 Global extrema on compact sets 4.2
10/30 Constrained optimization and Lagrange multipliers 4.3
10/31 Lab Day 5: More on Lagrange multipliers 4.3
11/2 Applications of optimization (Quiz 6) 4.4
11/5 Areas and volumes 5.1
11/6 Double integrals over rectangles 5.2
11/7 Double integrals over non-rectangular regions 5.2
11/9 Changing order of integration (Quiz 7) 5.3
11/12 Triple integrals 5.4
11/13 Change of variables 5.5
11/14 More on change of variables 5.5
11/16 Applications: average value, center of mass (Quiz 8) 5.6
11/19 Line integrals 6.1
11/20 Green's theorem 6.2
11/21,23 No Class -- Thanksgiving Break
11/26 Conservative vector fields 6.3
11/27 Lab Day 6: Parametric surfaces 7.1
11/28 Surface integrals 7.2
11/30 Exam III (covers material from 10/2 through 11/16)
12/3 Theorems of Gauss and Stokes 7.3
12/4 Course wrap-up 7.3

The final exam for this course will be given at 8:30 am on Tuesday, December 11.

Last modified: August 16, 2007