MAT 235 - Calculus III
Spring 2006
Class Message Area:
5-05 Final Exam answers are here. Grades are available by email (pmacdonald@qcc.mass.edu).
Not everyone turned in Problem 3 so, in fairness to those who did not visit this site to see the note below, Problem 3 became optional. Therefore the exam was based on 110 points with 10 points additional as extra credit for Problem 3.
By and large the class did quite well on the exam; as a result it was not necessary to curve the grades.
As I've said, this course is the most interesting math course in the Calculus sequence. I certainly enjoyed teaching it. Hopefully it has prepared you for the remaining math courses.
4-29 Somehow Problem 3 did not make it to the printed copy of the exam. Here it is. Please print it, complete the problem and attach it to your exam when you hand it in. Also note that the points for Problem 1 are: a - 4 pts, b - 6 pts.
4-27 Quiz answers available below.
Final Exam due back no later than May 4th at 6:00 pm. Class will follow.
4-21 Quiz answers available below. Homework for next week has been updated.
The Take-Home Final exam will be distributed at next week's class and due back May 4th at 6:00 pm.
4-16 Exam III solution posted below
4-13 Next week's quiz will be on material from 13.5-6,8 and 14.1. Homework for next week has been updated.
4-06 The exam next week will cover 12.4 - 12.8 and 13.1 - 13.4. Homework for next week has been updated.
3-30 Quiz VII answers available below. Homework for next week has been updated.
Exam II average was 85.
Project I solution is here - html and mw
As promised here is the solution to problem 21 from section 13.1
3-25 Exam solution posted below
3-23 Exams not turned in tonight will receive a zero. Homework for next week has been updated.
3-09 There will be a quiz on 12.4 - 12.7 on 3/23 when you come back from break. Homework has been updated to reflect what we covered tonite.
3-03 Quiz V answers available below. Homework for next week changed to reflect what was covered in class this week.
2-27 Just a reminder that Exam II will be a take-home exam. It will be given out on 3/9 and expected back on 3/23 (3/16 is Spring Break).
2-24 Quiz IV answers available below. Homework for next week changed to reflect what has been covered. As promised here is Example 3 on page 813 of the text.
2-22 Added an extra-credit Maple Project here.
2-19 Added a couple of problems to homework for next week.
2-17 Quiz III answers available below. Homework for next week changed to reflect what was covered in class this week.
The equation θ = c describes different surfaces in cylindrical and spherical coordinates. We can discuss. But in spherical coordinates, ρ ≥ 0 and 0 ≤ φ ≤ π whereas in cylindrical coordinates, r = ± √ x2 + y2
2-11 Exam solutions available. See below.
2-10 Homework for next week changed to reflect what was covered in class this week. Exam I solution will be posted sometime before the next class.
2-03 Quiz II answers available below. Homework for next week changed to reflect what was covered in class this week.
Exam I next week (2/9) covering 10.1 thru 10.7. I'll be around for questions before class - at around 5:20 or so.
1-27 Quiz I answers available below. Homework for next week changed to reflect what was covered in class this week.
1-20 Familiarize yourself with the html version of Chapter 10 Vectors. There are a couple of items in there which we didn't cover this past Thursday. The html version is the output from Maple for the corresponding worksheet (mw).
Catalog Description:
This course covers conic sections, rotation of axis, plane curves, parametric equations, vectors; polar, cylindrical, and spherical coordinates and graphs; vector-valued functions, differentiation, and integration; functions of several variables, partial derivatives, gradients; applications of extrema of functions, Lagrange multipliers; multiple integration; area, volume, center of mass, moment of inertia, change of variables, Jacobians; Green's divergence and Stoke's theorems. Students learn to use calculus to solve engineering and scientific problems. The course may conclude (time permitting) with some elementary differential equations.
It encompasses (essentially) Chapters 9 through 14 of the text.
My Description:
This is the most interesting calculus course of the sequence. You are going to analyze curves and surfaces in space. Everything you've learned (math-wise that is…) will be used in the course.
It's hard to appreciate the analysis without being able to see what is going on. With the help of Maple software you'll be able to visualize the functions we encounter. Maple will be used to graph 3-dimensional functions, solve equations and perform the mechanics of differentiation and integration.
We cover quite a bit of material. The catalog description above doesn't quite do justice to what you will encounter. Parametric equations provide an alternate way of describing functions, especially those that cannot be put into the form y = f(x). We spend time learning the basics of vectors, which leads to vector-valued functions. Vector-valued functions are used to describe curves in space such as the path traced out by a roller coaster or a projectile. Tangent and normal (perpendicular) vectors to the curve along with arc length let you investigate the curvature of these paths. Vector functions are used heavily in physics and engineering.
We look at functions of several variables which describe surfaces in space and generalize the ideas of limits, continuity, differentiability and integration that we learned in Calculus I. A new concept is an operator, similar to a function but acting on functions instead of real numbers. The Gradient operator is based on partial differentiation and allows you to find the direction of maximum increase of a surface. You will look at tangent planes as an extension of the tangent lines of Calculus I. Multiple integration will let you find volumes, Center of Mass and Moments of Inertia. Integration will also allow you to compute surface area. Next you will learn to apply change of variables to make certain integrations easier (recall from Calculus II how integration can be quite difficult).
Lastly we introduce Vector Analysis by looking at vector fields and defining new properties such as Divergence and Curl. Vector fields are applicable to physical phenomena such as gravitational and electromagnetic fields and velocity fields that model air or fluid flow. We develop the theory of line and surface integrals and use the results to investigate work and fluid flow through a surface. Finally we use theorems that relate the various integrals we now know. Green's Theorem relates line integrals to double integrals. The Divergence Theorem relates surface integrals to triple integrals and finally Stokes Theorem relates line and surface integrals.
That's a lot of math to cover. The course is going to take effort on your part. You'll need to keep up with the homework and use Maple to help you visualize the concepts. It's a fun course as we extend previously learned concepts and investigate new ones.Syllabus (pdf)
Where: 254 Administration Building (Was 367)
When: Thursday evening - 6:00 - 9:40 pm
Contact: pmacdonald@qcc.mass.edu
Textbook: Calculus with Analytic Geometry, 7th Edition.
Authors: Larson, Hostetler & Edwards
Publisher: Houghton Mifflin
Homework.
Do the homework. No one has successfully passed this course without doing it. Trust me on this one. You're not about to become the first.
Remember, mathematics cannot be learned vicariously or through osmosis. It takes active problem solving to understand and apply the mathematical theories. You cannot take a passive approach to this course.
Projects.
The first extra-credit Maple project is described here.
General Maple Resources
Maple will be used extensively in this course and will be available in class. The student version is available at a reduced rate. Click here for purchase information (after getting the promotion code from me). Although not required that you purchase your own copy of Maple it is highly recommended as it is a wonderful tool for this course as well as other math, physics and engineering courses.
Maple Tutorials - Maplesoft Student Center
Getting Started with Maple An Introduction to Maple produced by the Stat/Math Center at Indiana University
A Short Introduction to the Maple Language An Introduction to Maple produced at the University of Kentucky
Maple Basics - Videos, Worksheets and Tutorial North Carolina State University
Select 'Guest Access' to login)
Maple for Math Majors Excellent Reference Purdue University
Calculus III Resources
Textbook Website
Topics in Calculus - Relevant material (Lee Lady, possibly from the University of Hawaii)
Maple Resources - By Chapter
Surfaces In Space (html) (worksheet is too large)
11 Curves In Space (html) (mw)
Tangent and Normal Vectors (html) (mw)
12 Surfaces, Level Curves and Level Surfaces (html) (mw)
Gradients and Skiers (html) (mw)
13 Double Integration (html) (mw)
Quizzes (hyperlinks to answers - after the quiz has been given)
I II III IV V VI VII VIII IX X
Remember that quiz questions come directly from the homework.
Exams (same as for quizzes)
Exam I (2/9) Exam II (3/9) Exam III (4/13) Final Exam (5/4)
Extra Credit
(html) (mw)
