Multivariable Calculus, Fall 2011

MWF9 Carney 106; Tu11 Carney 303

Prof. Dan Chambers   
365 Carney Hall
617-552-3769 (best method)

Office Hours: M2-3, W10-11, F3-4 or by appointment


Multivariable calculus has a rich history, interesting mathematics, and many applications. In this class we will explore all of these. Topics include vectors and vector valued functions, functions of several variables, multiple integrals, and vector calculus.

The text we'll use is Multivariable Calculus, 2nd edition, by Brian Blank and Steven Krantz; Wiley ISBN: 978-0-470-45359-9. We'll cover most of the first five chapters. Here is the syllabus.

Note the exam dates below are tentative, subject to perturbation. This is a work in progress; check back later.

week Monday
Sep. 5-9

9.1 Vectors in R^2
9.1 finished
9.2 Vectors in R^3
9.3 The dot product
Sep. 12-16
9.3 The dot product finished; projections begun
9.3 Projections finished
9.4 The cross product
9.4 Properties of the cross product
HW1 due; HW1 solns
9.5 Planes
Sep. 19-23
9.5 Lines
HW2 due
HW2 solns
9.5 Problems with lines and planes
10.1 Vector valued functions
10.2 Velocity and acceleration
HW3 due; HW3 solns
Sep. 26-30
10.3 Parameterization
10.3 Arc length
HW4 due; HW4 solns
Exam 1
11.1 2- and 3-variable functions
Oct. 3-7
11.1 Level sets/surfaces 11.2 Quadric surfaces 11.3 Limits of a function of several variables 11.3 more limits
11.4 Partial derivatives
HW5 due; HW5 solns
Oct. 10-14
Columbus Day
no class
11.4 Partial derivatives
11.5 Differentiability
Oct. 17-21
11.5 Chain rule
11.6 Directional derivatives and gradient of f(x,y)
11.6 directional derivatives, gradient examples
11.7 Tangent planes to surfaces
11.6 More on gradients
11.7 Justification of gradient as normal vector; tangent plane approximation to f(x,y)
HW6 due; HW6 solns
11.7 concluded
Oct. 24-28
11.8 Optimization
11.8 Optimization
HW7 due; HW7 solns
Exam 2

Oct. 31-Nov. 4
11.9 Lagrange multipliers
More Lagrange multipliers
12.1 Multiple integrals over rectangles
12.2 Integrals over general regions
Nov. 7-11
12.2 ct'd
12.3: Double integrals: volumes
12.3 ct'd
HW8 due
HW8 solns
12.4: Polar coordinates
12.5: Double integrals in polar coordinates
Nov. 14-18
12.5 ct'd
12.6 Triple integrals
HW9 due
HW9 solns
12.6 ct'd
12.8: Other coordinate systems
Nov. 21-25
13.1 Vector fields
13.1 ct'd
13.2 Line integrals
HW10 due
HW10 solns
Nov. 28-Dec. 2
13.2 Line integrals
Exam 3 13.3 Conservative vector fields
13.3 Path independence
Dec. 5-8
13.5 Green's theorem
13.5 Green's theorem
HW11 due
HW11 solns
13.4 Div, grad, curl
final class
13.5 problems
Dec. 11-15

Dec. 17
Final 12:30 pm