MT202
Multivariable Calculus, Fall 2011

MWF9 Carney 106; Tu11 Carney 303

Prof. Dan Chambers
365 Carney Hall
617-552-3769
chambers@bc.edu (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 Tuesday Wednesday Friday 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 Review 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 Thanksgiving Thanksgiving 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 solns Dec. 11-15 Dec. 17 Final 12:30 pm