Detailed Schedule -- Multivariable Calculus

Fall 2010, 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 Topic Reading (Damiano and Freije)

9/1 Course Introduction
9/3 Euclidean coordinates in R³ 1.1
9/6 Subsets of R³ 1.1
9/7 Vectors 1.2
9/8 Begin lines and planes 1.2
9/10 Dot products and orthogonality (Quiz 1) 1.3
9/13 Projections, cross products in R³ 1.3
9/14 More on lines and planes in R³ 1.4
9/15 Lab Day 1: Getting started in Maple, graphing in R³ TD> 1.4
9/17 Parametric curves (Quiz 2) 2.1
9/20 More on parametric curves 2.1
9/21 Derivatives 2.2
9/22 Lab Day 2: Parametric curves, the chain rule 2.2
9/24 Modeling with parametric curves (Quiz 3) 2.3
9/27 Vector fields and flow lines 2.4
9/28 Modeling with vector fields 2.5
9/28 Lab Day 3: Modeling with vector fields 2.5
10/1 Exam I (covers material from 9/1 through 9/27)
10/4 Graphs and contours 3.1
10/5 More on graphs and contours 3.1
10/6 Directional and Partial derivatives 3.2
10/8 Higher order partial derivatives (Quiz 4) 3.2
10/11, 12, 13, 15 No Class -- Columbus Day Break 3.3
10/18 Limits and Continuity 3.3
10/19 Definition of differentiability 3.4
10/20 Lab Day 4: Differentiability 3.4
10/22 Chain rule and gradient (Quiz 5) 3.5
10/25 Critical points for functions of several variables 4.1
10/26 More on critical points -- the gradient 4.1
10/27 Algebraic classification of critical points 4.2
10/29 The Hessian criterion (Quiz 6) 4.2
11/1 Constrained optimization and Lagrange multipliers 4.3
11/2 Lab Day 5: More on Lagrange multipliers 4.3
11/3 Optimization in space 4.4
11/5 Exam II (covers material from 9/28 through 10/29)
11/8 Riemann sums 5.1
11/9 Double integrals over rectangles 5.2
11/10 Double integrals over non-rectangular regions 5.2
11/12 Polar coordinates (Quiz 7) 5.3
11/15 Polar double integrals 5.3
11/16 Triple integrals 5.4
11/17 Cylindrical coordinates 5.5
11/19 Cylindrical triple integrals (Quiz 8) 5.5
11/22 Spherical coordinates 5.6
11/23 Integration in spherical coordinates 5.6
11/24,26 No Class -- Thanksgiving Break
11/29 Path integrals 6.1
11/30 Line integrals 6.2
12/1 Line integrals over closed curves and Green's theorem 6.3
12/3 Exam III (covers material from 11/1 through 11/23)
12/6 More on Green's theorem 6.3
12/7 Lab Day 6: Parametric surfaces 7.1
12/8 Surface integrals and Gauss's theorem 7.2
12/10 Course wrap-up (Quiz 9) 7.3

The final exam for this course will be given at the scheduled time for MWF 8:00am classes.

Last modified: August 17, 2010

Date	Class Topic	Reading (Damiano and Freije)

9/1	Course Introduction
9/3	Euclidean coordinates in R³	1.1
9/6	Subsets of R³	1.1
9/7	Vectors	1.2
9/8	Begin lines and planes	1.2
9/10	Dot products and orthogonality (Quiz 1)	1.3
9/13	Projections, cross products in R³	1.3
9/14	More on lines and planes in R³	1.4
9/15	Lab Day 1: Getting started in Maple, graphing in R³ TD> 1.4
9/17	Parametric curves (Quiz 2)	2.1
9/20	More on parametric curves	2.1
9/21	Derivatives	2.2
9/22	Lab Day 2: Parametric curves, the chain rule	2.2
9/24	Modeling with parametric curves (Quiz 3)	2.3
9/27	Vector fields and flow lines	2.4
9/28	Modeling with vector fields	2.5
9/28	Lab Day 3: Modeling with vector fields	2.5
10/1	Exam I	(covers material from 9/1 through 9/27)
10/4	Graphs and contours	3.1
10/5	More on graphs and contours	3.1
10/6	Directional and Partial derivatives	3.2
10/8	Higher order partial derivatives (Quiz 4)	3.2
10/11, 12, 13, 15	No Class -- Columbus Day Break	3.3
10/18	Limits and Continuity	3.3
10/19	Definition of differentiability	3.4
10/20	Lab Day 4: Differentiability	3.4
10/22	Chain rule and gradient (Quiz 5)	3.5
10/25	Critical points for functions of several variables	4.1
10/26	More on critical points -- the gradient	4.1
10/27	Algebraic classification of critical points	4.2
10/29	The Hessian criterion (Quiz 6)	4.2
11/1	Constrained optimization and Lagrange multipliers	4.3
11/2	Lab Day 5: More on Lagrange multipliers	4.3
11/3	Optimization in space	4.4
11/5	Exam II	(covers material from 9/28 through 10/29)
11/8	Riemann sums	5.1
11/9	Double integrals over rectangles	5.2
11/10	Double integrals over non-rectangular regions	5.2
11/12	Polar coordinates (Quiz 7)	5.3
11/15	Polar double integrals	5.3
11/16	Triple integrals	5.4
11/17	Cylindrical coordinates	5.5
11/19	Cylindrical triple integrals (Quiz 8)	5.5
11/22	Spherical coordinates	5.6
11/23	Integration in spherical coordinates	5.6
11/24,26	No Class -- Thanksgiving Break
11/29	Path integrals	6.1
11/30	Line integrals	6.2
12/1	Line integrals over closed curves and Green's theorem	6.3
12/3	Exam III	(covers material from 11/1 through 11/23)
12/6	More on Green's theorem	6.3
12/7	Lab Day 6: Parametric surfaces	7.1
12/8	Surface integrals and Gauss's theorem	7.2
12/10	Course wrap-up (Quiz 9)	7.3