MATHEMATICS 2210-90 Calculus III (Multivariable Calculus)

Spring 2007

Do not neglect to read the page "Course Information"; there you will be told what the materials for this course is are, how you will be graded, and you will find references to important dates.

The schedule link gives an approximate guide to how you should progress through the textbook, at a one section per regular class period rate. The exam dates on the schedule are just approximate, indicating when the material for that exam should be covered. The actual dates on Thursdays and Saturdays when UOnline does proctoring are listed below. New practice exams with detailed solutions will be posted (i.e., the are links emailed to you through the webwork system) shortly before the exam dates and are the best guide to what you may expect to be covered on the current actual exams. I recommend doing the practice problems before consulting the solutions to get the best idea of what you feel solid on and what you most need to review. We usually receive the completed exams from UOnline in the middle of the week after they are taken, due to out of area exams and campus mail times. After they are graded, your scores will be mailed and solutions posted through the webwork system around the following weekend.

For each topic to be covered, there are also supplementary notes and practice problems with detailed solutions from Prof. Hugo Rossi who originated these courses. It is strongly recommended to do these problems, checking your work against the answers, before going on to the webwork assignments. The practice problem sets loosely correspond to the webwork sets of the same number. There is also a list of suggested problems for each section from the textbook. Answers for odd-numbered textbook problems are in the back of the book, and complete worked solution manuals for all problems are available on reserve in the math library. The purpose of the practice problem sets is to compensate for the classroom experience; these are written so as to reproduce, as well as possible, the act of watching the instructor work through a problem.

The Webwork assignments form the core of this course; Assignments must be completed by 10:59 p.m. on the date shown, usually Mondays. Do assignment 0 ("Demo", non-credit) first in order to understand the protocols for submitting answers on Webwork.

Do your webwork assignments by first printing out the assignment, then doing the problems on paper, referring to the sources as needed. After the problem is done, submit your answer. If it is correct, proceed to the next problem; if not, try to find your error. It could just as well be arithmetic, a syntactical error in submission, or a conceptual error. In the latter case, reread the appropriate text and try again (there is no penalty for incorrect tries), or finally, send an email to the instructor for assistance for guidance by clicking the Feedback button from that problem - this gives us a link directly to your specific version of the problem, and allows you to describe to us what you have tried and what is or isn't working. You can avoid roundoff errors by entering your answer symbolically rather than numerically and let webwork do the calculations (e.g., sqrt(2) may work where 1.41 may not.) The help button on each problem page has useful information for using webwork.

A summary of webwork formats, conventions, and available mathematical functions is available here.

Plan to complete your assignment two days before the closing time. If the system goes before then, you still have time to submit answers. If you wait until the last night, you will not have that time. I will sometimes extend a due date collectively or individually if there are significant technical difficulties or other pressing reasons, but once a set closes, reopening it wipes out your previous work and you would have to repeat your work on different versions of each problem.

Finally, you should note the page "Practice and Past Examinations", which contains typical and actual problems from past semesters. The exams starting from Fall 2004 are a bit closer to current exams than earlier ones.

Register for all exams at least two weeks before the exam through the Uonline webpage. Direct all questions concerning scheduling of exams to their office.

Past and Practice Examinations

Recent Exams, Practice Exams, and Detailed Solutions

Recommended Textbook Problems



January 8 Classes Begin
January 15 Martin Luther King Jr. Day Holiday
February 19 Fall Break Presidents Day Holiday
March 19-23 Spring Break
April 25 Classes End


Jan. 17 Webwork Assignment 0 (Demo), Introduction to Webwork. (Non-credit, for practicing formats.)
Jan. 22 Webwork Assignment 1, Vectors and Lines in Two Dimensions (13.1-13.4) is due
Jan. 29 Webwork Assignment 2, Vectors, Lines, and Planes in Three Dimensions (13.5-14.2) is due
Feb. 5 Webwork Assignment 3, Curves, Tangents, and Normals (14.3-14.5) is due
Feb 12 Webwork Assignment 4, Surfaces, Cylindrical and Spherical Coordinates (14.6-14.7) is due
Feb. 26 Webwork Assignment 5, Partial & Directional Derivatives, The Gradient, Chain Rule, Implicit Differentiation, Differentials (15.1-15.6) is due
Mar. 5 Webwork Assignment 6, Maxima, Minima, LagrangeÕs Method (15.7-15.9) is due
Mar. 26 Webwork Assignment 7, Double Integrals and Applications (16.1-16.5) is due
Apr. 2 Webwork Assignment 8, Surface Area, Triple Integrals (16.6-16.8) is due
Apr. 9 Webwork Assignment 9, Vector Fields and Line Integrals (17.1-17.2) is due
Apr. 16 Webwork Assignment 10, Independence of Path, GreenÕs Theorem (17.3-17.4) is due
Apr. 23 Webwork Assignment 11, Surface Integrals, Divergence and StokesÕ Theorem (17.5-17.7) is due


Feb. 15, 17

Exam 1, Textbook Chapters 13, 14: Vectors, Curves, and Surfaces

Mar. 8, 10

Exam 2, Textbook Chapter 15: Differential Calculus of Several Variables

Apr. 5, 7

Exam 3, Textbook Chapter 16: Multivariable Integration

May. 1

FINAL EXAMINATION



Supplementary Notes and Problems(Rossi)
Problems correspond to webwork assignments with the same number

Topics
Supplementary Notes (Rossi), Chapter 13, Postscript, PDF
Vector Algebra, Supplementary Notes (Rossi), Ch. 13.1
Planar vectors, distance and dot product, Supplementary Notes (Rossi), Sections 13.2,3
Practice Problems 1, Postscript, PDF
Answers to Practice Problems 1, Postscript, PDF

Supplementary Notes (Rossi), Chapter 14, Vector Calculus Postscript, PDF
Vector Algebra, Supplementary Notes (Rossi), Ch. 13.3,4,14.1
Vectors in Space, Lines and Planes, Vector Functions, Supplementary Notes (Rossi), Sections 13.4,14.1
Practice Problems 2, Postscript, PDF
Answers to Practice Problems 2, Postscript, PDF

Vector Calculus, Geometry of Space Curves, Supplementary Notes (Rossi), Sections 14.2-3
Practice Problems 3, Postscript, PDF
Answers to Practice Problems 3, Postscript, PDF

Coordinates and Surfaces, Supplementary Notes (Rossi), Chapter 15 Postscript, PDF
Graphs, Quadric Surfaces, Other coordinates, Supplementary Notes (Rossi), Sections 15.1-2
Practice Problems 4, Postscript, PDF
Answers to Practice Problems 4, Postscript, PDF
Supplementary Notes (Rossi), Sections 15.3,4

Differentiation in Several Variables, Supplementary Notes (Rossi), Chapter 16 Postscript, PDF
Chain Rule, Differentials, Tangent Plane, Gradients, Supplementary Notes (Rossi), Sections 16.1-2
Practice Problems 5, Postscript, PDF
Answers to Practice Problems 5, Postscript, PDF

Differentiation in Several Variables
Optimization, Lagrange Multipliers, Supplementary Notes (Rossi), Sections 16.3-4
Practice Problems 6, Postscript, PDF
Answers to Practice Problems 6, Postscript, PDF

Double Integrals, Supplementary Notes (Rossi), Chapter 17 Postscript, PDF
Double and Iterated Integrals, Supplementary Notes (Rossi), Chapter 17.1,2
Practice Problems 7, Postscript, PDF
Answers to Practice Problems 7, Postscript, PDF

Change of Variables
Polar Coordinates, Change of Variables, Applications, Supplementary Notes (Rossi), Section 17.3,4
Practice Problems 8, Postscript, PDF
Answers to Practice Problems 8, Postscript, PDF

Triple and Surface Integrals, Supplementary Notes (Rossi), Chapter 17.5 Postscript, PDF
Iterated Integrals, Mass and Moment in 3D, Supplementary Notes (Rossi), Section 17.5
Practice Problems 9, Postscript, PDF
Answers to Practice Problems 9, Postscript, PDF

Line Integrals, Supplementary Notes (Rossi), Chapter 18 Postscript, PDF
Vector Fields, Div and Curl, Exact Differentials, Line Integrals, Independence of path
Supplementary Notes (Rossi), Section 18.1,2,3
Practice Problems 10, Postscript , PDF
Answers to Practice Problems 10, Postscript, PDF

Independence of Path, Green's Theorem
Supplementary Notes (Rossi), Section 18.3,4
Practice Problems 11, Postscript , PDF
Answers to Practice Problems 11, Postscript, PDF

Stokes' and Gauss' Divergence Theorems, Vector Calculus in 3D
Supplementary Notes (Rossi), Section 18.5
Practice Problems 12, Postscript , PDF
Answers to Practice Problems 12, Postscript, PDF