Software for Multivariable Calculus
Spring 2006
MATH 312.01 (1 credit), Distance Education via BlackBoard


A grade of C- or better in MATH 211 (Calculus II).


Dr. Buchanan
Office: Chester 103, Phone: 872-3659, FAX: 871-2320
Office Hours: 10:00AM-10:50AM (MTuWThF), or by appointment
Course URL:


The material for this course will be delivered on-line. No textbook is required for this course though the following book is a good general reference for people beginning to learn the software.

The Students' Introduction to Mathematica: A Handbook for Precalculus, Calculus, and Linear Algebra, Bruce F. Torrence and Eve A. Torrence, Cambridge University Press, 1999, ISBN 0-521-59461-8.


The objectives of this course include introducing students to a computer algebra system and programming environment.

Students who achieve these objectives will be able to effectively use a CAS to enhance their learning in MATH 311 Calculus III as well as in other upper level mathematics and science courses such as MATH 365 Ordinary Differential Equations and MATH 375 Numerical Analysis. These students will gain experience with a software tool that will enable them to create professional-looking computer-based presentations and printed output. They will also begin working with one of the most commonly used mathematical research tools among professional mathematicians, scientists, and engineers.

Course Outline:
Week 1
Introduction to a computer algebra system: expression evaluation, the front-end vs. the kernel, case sensitivity, built-in constants, some common commands, integer arithmetic, rational arithmetic, floating point arithmetic, saving, opening, and printing notebooks.
Week 2
Vectors: defining vectors, performing vector operations such as scalar multiplication, inner product and cross product, displaying vectors.
Week 3
Plotting functions (Part I): plotting, multiple curves or surfaces on the same axes, generating curves with specified plotting styles, useful options for plotting.
Week 4
Functions: defining and naming functions, the syntax for variables, evaluating user-defined functions.
Week 5
Unit tangent and normal vectors: calculating and plotting the unit tangent, unit normal, and binormal vectors for vector-valued functions in two and three dimensions. The topic of curvature is also covered.
Week 6
Plotting functions (Part II): parametric plots in two and three dimensions, plotting traces and level sets.
Week 7
Calculus: symbolic differentiation and integration, numerical integration, solving systems of equations, series.
Week 8
Elementary programming and animation: controlling iteration, conditional evaluation, use of local variables inside of functions.
Week 9
Optimization: finding the extreme values of multivariable functions including the Second Derivative Test and Lagrange Multipliers. Plotting objective functions on constraint curves or surfaces, solving the necessary simultaneous equations.
Week 10
Plotting functions (Part III): contour plots in two and three dimensions, density plots, generating wireframe graphics
Week 11
Animation of particle motion described by a vector-valued function including the principle unit tangent and normal vectors, plotting the tangential and normal components of acceleration.
Week 12
Multiple integrals: rectangular, polar, cylindrical, and spherical coordinates.
Week 13
Vector Fields: defining and plotting vector fields in two and three dimensions.
Week 14
Vector Calculus: exploration of topics in vector calculus including curl, divergence, Stokes', Green's, and the Divergence Theorems.

If time permits other topics may be covered as well.


Students are expected to attend all class meetings. If you must be absent from class on the day an assignment is due, you must complete and hand in the assignment prior to the absence. No final examination exemptions.


Students are expected to do their homework and participate in class. Students should expect to spend several hours outside of class on homework and review for every hour spent in class. Each week homework problems will be assigned for collection and grading. Students should submit all homework by the date due. Late homework will not be accepted without valid excuse. In no cases will late homework be accepted after an assignment has been graded and returned to the students. Homework submitted for grading should be your own work.


There will be three tests and a comprehensive final examination. So as not to crowd class time with the tests, all tests and the final examination will be distributed via the web for students to complete outside of class. The material submitted for grading on tests should be the student's own, individual work. Students who work together on tests or homework assignments will be considered to be in violation of the Code of Academic Honesty (see and ).

  1. Wednesday, February 8, 2006
  2. Wednesday, March 8, 2006
  3. Wednesday, April 19, 2006
The final exam will be made available by 9:00AM on Monday, May 8, 2006 and will be due by Friday, May 12, 2006 at 4:00PM. I will not ``curve'' test, homework, or exam grades.


Course grade will be calculated as follows.

Tests 10% each
Homework 50%
Exam 20%

Tests and the final examination will be graded individually on a 100-point scale. Homework sets will vary in the number of problems assigned, but generally each homework problem will be worth ten points. For example on a homework assignment of five problems, the maximum numerical grade would be 50 points. To ensure that all homework assignments are weighted equally, each student's score will be normalized by the maximum score for that assignment. Again for example, on a five problem homework assignment grades will be among the set of scores $\{ 0/50, 1/50, \ldots, 49/50, 50/50 \}$. I keep a record of students' test, homework, and exam scores. Students should also keep a record of graded assignments, tests, and other materials. As an example of the calculation of the numerical course grade, suppose a student's three test grades were 87, 86, and 70 (out of a maximum of 100 points on each test), the student's final examination grade was 81 (again, out of a maximum of 100), and the student's ten homework grades were $\{ 25/30, 20/40, 40/50, 37/40, 40/40, 20/30, 0/40, 15/20, 45/50, 30/30 \}$. This student's homework average is $0.7375$. The student's numerical course grade is then

(87 + 86 + 70)(0.10) + (81)*(0.20) + (0.7375)(50) = 77.375 \approx 78 .

The course letter grades will be calculated as follows. I will not ``curve'' course grades.

90-92 A$-$ 93-100 A    
80-82 B$-$ 83-86 B 87-89 B$+$
70-72 C$-$ 73-76 C 77-79 C$+$
60-62 D$-$ 63-66 D 67-69 D$+$
    0-59 F    

Course Repeat Policy

An undergraduate student may not take an undergraduate course of record more than three times. A course of record is defined as a course in which a student receives a grade of A, B, C, D, (including $+$ and $-$) F, U, Z or W. The academic department offering a course may drop a student from a course if the student attempts to take a course more than three times.1

Inclement Weather Policy:

If we should miss a class day due to a school closing because of weather, any activities planned for that missed day will take place the next time the class meets. For example, if a test is scheduled for a day that class is canceled on account of snow, the test will be given the next time the class meets.

Final Word:

Math is not a spectator sport. What you learn from this course and your final grade depend mainly on the amount of work you put forth. Daily contact with the material through homework assignments and review of notes taken during lectures is extremely important. Organizing and conducting regular study sessions with other students in this class will help you to understand the material better.

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