Detailed Schedule -- Multivariable Calculus

Detailed Schedule -- Multivariable Calculus, section 1

Fall 2013, Prof. Little

This is a tentative, evolving schedule. 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)

8/28 Course Introduction
8/30 Cartesian coordinates in R³ 1.1
9/2 Subsets of R³ 1.1
9/3 Vectors 1.2
9/4 Begin lines and planes 1.2
9/6 Dot products and orthogonality (Quiz 1) 1.3
9/9 Projections, cross products in R³ 1.3
9/10 More on lines and planes in R³ 1.4
9/11 Lab Day 1: Getting started in Maple, graphing in R³ 1.4
9/13 Parametric curves (Quiz 2) 2.1
9/16 More on parametric curves 2.1
9/17 Derivatives 2.2
9/18 Parametric curves, the chain rule 2.2
9/20 Modeling with parametric curves (Quiz 3) 2.3
9/23 Vector fields and flow lines 2.4
9/24 Modeling with vector fields 2.5
9/25 Lab Day 2: Modeling with vector fields 2.5
9/27 Exam I (covers material from 8/28 through 9/23)
9/30 Graphs and contours 3.1
10/1 More on graphs and contours 3.1
10/2 Directional and Partial derivatives 3.2
10/4 Higher order partial derivatives (Quiz 4) 3.2
10/7 More on partial derivatives 3.2
10/8 Open and closed sets, limits 3.3
10/9 Continuity 3.4
10/11 Differentiability (Quiz 5) 3.5

10/14, 15, 16, 18 No Class -- Columbus Day Break 3.5

10/21 Chain Rule and gradient 4.1
10/22 Critical points for functions of several variables 4.1
10/23 Lab Day 3: More on critical points and the gradient 4.2
10/25 Algebraic classification of critical points (Quiz 6) 4.2
10/28 The Hessian Criterion 4.2
10/29 Constrained optimization and Lagrange multipliers 4.3
10/30 Lab Day 4: More on Lagrange multipliers 4.3
11/1 Exam II (cover material from 9/24 through 10/28)
11/4 Riemann sums 5.1
11/5 Double integrals over rectangles 5.2
11/6 Double integrals over non-rectangular regions 5.2
11/8 Polar coordinates (Quiz 7) 5.3
11/11 Polar double integrals 5.3
11/12 Triple integrals 5.4
11/13 Cylindrical coordinates 5.5
11/15 Cylindrical triple integrals (Quiz 8) 5.5
11/18 Spherical coordinates 5.6
11/19 Integration in spherical coordinates 5.6
11/20 Path integrals 6.1
11/22 Line integrals (Quiz 9) 6.2
11/25 Line integrals over closed curves and Green's theorem 6.3
11/26 Exam III (covers material from 11/1 through 11/22)

11/27,29 No Class -- Thanksgiving Break

12/2 More on Green's theorem 6.3
12/3 Lab Day 5: Parametric surfaces 7.1
12/4 Surface integrals and Gauss's theorem 7.2
12/6 Course wrap-up 7.3

The final exam for this course will be given 11:30am - 2:00pm on Saturday, December 14, 2013.

Last modified: October 8, 2013

Date	Class Topic	Reading (Damiano and Freije)

8/28	Course Introduction
8/30	Cartesian coordinates in R³	1.1
9/2	Subsets of R³	1.1
9/3	Vectors	1.2
9/4	Begin lines and planes	1.2
9/6	Dot products and orthogonality (Quiz 1)	1.3
9/9	Projections, cross products in R³	1.3
9/10	More on lines and planes in R³	1.4
9/11	Lab Day 1: Getting started in Maple, graphing in R³	1.4
9/13	Parametric curves (Quiz 2)	2.1
9/16	More on parametric curves	2.1
9/17	Derivatives	2.2
9/18	Parametric curves, the chain rule	2.2
9/20	Modeling with parametric curves (Quiz 3)	2.3
9/23	Vector fields and flow lines	2.4
9/24	Modeling with vector fields	2.5
9/25	Lab Day 2: Modeling with vector fields	2.5
9/27	Exam I	(covers material from 8/28 through 9/23)
9/30	Graphs and contours	3.1
10/1	More on graphs and contours	3.1
10/2	Directional and Partial derivatives	3.2
10/4	Higher order partial derivatives (Quiz 4)	3.2
10/7	More on partial derivatives	3.2
10/8	Open and closed sets, limits	3.3
10/9	Continuity	3.4
10/11	Differentiability (Quiz 5)	3.5

10/14, 15, 16, 18	No Class -- Columbus Day Break	3.5

10/21	Chain Rule and gradient	4.1
10/22	Critical points for functions of several variables	4.1
10/23	Lab Day 3: More on critical points and the gradient	4.2
10/25	Algebraic classification of critical points (Quiz 6)	4.2
10/28	The Hessian Criterion	4.2
10/29	Constrained optimization and Lagrange multipliers	4.3
10/30	Lab Day 4: More on Lagrange multipliers	4.3
11/1	Exam II	(cover material from 9/24 through 10/28)
11/4	Riemann sums	5.1
11/5	Double integrals over rectangles	5.2
11/6	Double integrals over non-rectangular regions	5.2
11/8	Polar coordinates (Quiz 7)	5.3
11/11	Polar double integrals	5.3
11/12	Triple integrals	5.4
11/13	Cylindrical coordinates	5.5
11/15	Cylindrical triple integrals (Quiz 8)	5.5
11/18	Spherical coordinates	5.6
11/19	Integration in spherical coordinates	5.6
11/20	Path integrals	6.1
11/22	Line integrals (Quiz 9)	6.2
11/25	Line integrals over closed curves and Green's theorem	6.3
11/26	Exam III	(covers material from 11/1 through 11/22)

11/27,29	No Class -- Thanksgiving Break

12/2	More on Green's theorem	6.3
12/3	Lab Day 5: Parametric surfaces	7.1
12/4	Surface integrals and Gauss's theorem	7.2
12/6	Course wrap-up	7.3