Math 222 - John Travis

MATHEMATICS 222

Calculus IV

John Travis
MCC 315
925-3817 (voice mail)
travis@mc.edu (email)
Textbook | Course Description | Course Meetings | Grading
Symbolic Software | Sample Directional Derivative

MAT 222 Textbook and other Instructional Materials: Calculus, Early Transcendental Functions , 4th edition, by Larson, Hostetler and Edwards

A good calculator, preferably a graphing calculator such as the TI-84, is useful for this class. Further, a number of other software packages downloaded from the internet will be utilized to illustrate the concepts. Students will be able to access all classroom materials from the instructor's web site. (Winplot)

Prerequisites: MAT 221

Projects:

Writing Projects:

Useful Periodicals:

The American Mathematical Monthly, published by the Mathematical Association of America, 1529 Eighteenth Street, NW, Washington, DC 20036-1385
The College Mathematics Journal, published by the Mathematical Association of America, 1529 Eighteenth Street, NW, Washington, DC 20036-1385
Mathematics Magazine, published by the Mathematical Association of America, 1529 Eighteenth Street, NW, Washington, DC 20036-1385

Assigned Articles (Spring 2008)

Examining Continuity, Partial Derivatives and Differentiability with Cylindrical Coordinates, Thomas McMillan, CMJ, Vol 34, #1, Jan 2003

Moire Fringes and the Conic Sections, Mike Cullen, CMJ, November 1990

Partial Differentiable, Yes; Continuous, No, David Calvis, CMJ, Vol 31, #1, Jan 2000

Mixed Partial Derivatives and Fubini's Theorem, Aksoy and Martelli, CMJ, Vol 33, #2, March 2002

Each of these papers should be read and a written review prepared. In the review, the student should point out the major points of the article including how the article related to the material being studied in Calculus IV. Comments on the examples presents and on "obvious" statements given should be included. Any extensions, applications or connections to other material that the student discovers should be included.

Group Project: In groups of two or three students, take some play-doh and determine it's volume using some standard shape. Then, reshape the play-doh into some "interesting" non-canonical shape. Using dental floss, divide the mass into uniformly thick slices. Then, divide each slice into uniformly thick strips. Then, divide each strip into uniformly thick boxes. Measure the volume of a few if the boxes and use an average as the standard volume dV for approximating the volume of the original shape. Compare to the exact volume. Prepare of paper reviewing with your findings and relate to techinques for integration with respect to dz dy dx. Post the results on the facebook group for this class.

Computational Project: Using software (such as Winplot), create the graph of an interesting surface with tangent lines in x- and y-directions at various points using animated parameters. Create the gradient vector at each point as well. Use the above information to animate the tangent planes to the surface. Email your resulting file to the professor and come by the office to show that is works correctly.

Course Description: Description from the college catalog: A study of vectors in three dimensions, partial differentiation, the gradient and applications, double and triple integrals, vector fields and line and surface integrals.

This course carries 3 hours of academic credit.

The student who is prepared for a study of Calculus IV is assumed to be proficient with the following:

Limits by the rules
Continuity
Definition of Derivative
Derivatives by the Rules
Application of the Derivative
Mean Value Theorem for Derivatives
Definition of Integral
Integration Rules
Logarithms and Exponentials
Inverse Trig Functions
Integration by Parts
Partial Fractions
Polar, cylindrical and spherical coordinates
Plane curves and parametric equations
Vectors in the plane and vectors in space
Vector-Valued Functions
Velocity and Acceleration vectors in space
Curvature

Learning Objectives: The student will demonstrate a comprehensive understanding of the following:

Multivariate functions
Partial Derivatives and differentials
Chain Rule for multi-variate functions
Directional Derivatives and Gradients
Tangent Planes and Normal Lines
Exterma for multi-variate functions
Lagrange Multipliers and Constrained Optimization
Vector Fields
Double and Triple Integrals and various applications (Winplot sliced volume)
Line Integrals
Fundamental Theorem of Line Integrals
Exact Differential Equations
First Order Linear Differential Equations
Higher order constant coefficient linear differential equations

(Roughly chapters Thirteen thru Sixteen of the text.)

In aiming at these target ideas, we will use graphical calculators and computers to promote better intuition, greater understanding and increased proficiency in doing mathematics.

Meetings: This class meets as scheduled. You are expected to be in class on time. University policy states that a student cannot miss more than 25% of class meetings and receive credit for the course. Further, attendance will be necessary in order to understand the material and make a good grade. The student is responsible for work and material missed when absent. Cheating in any way will be properly rewarded according to University policy (Tomahawk; Undergraduate Bulletin; http://www.mc.edu/publications/policies/219.html).

If you need special accommodations due to learning, physical, psychological, or other disabilities, please contact Dr. Buddy Wagner in the Counseling and Career Development Center. He may be reached by phone at (601)925-3354 or by mail at P.O. Box 4013, Clinton, MS 39058.

Grading: Assessment of the student's progress will be made through daily quizzes and examinations as well as through classroom feedback. During the term, there will be at least three exams during the semester. The daily quizzes will be collected and graded. Extra credit quiz grades to replace missed or low quiz grades will be granted for students preparing a review of an approved article from the periodicals listed above. An average of the quiz grades will count as an additional exam grade. The semester grade will be based on an average of these exam grades.

Any quizzes or projects missed will be awarded a grade of zero. Your final average will be computed by taking an average of the exam grades and the quiz grade.

Near the end of the term, an out-of-class, comprehensive makeup exam will be given for any student missing one or more excused exams. There will be no makeups for quizzes.

The grading scale is

A=90-100

B=80-89

C=70-79

D=65-69

F=0-64

Aim now for the desired grade. Finally, all graded work will be returned to the student for keeping. If there were any question later about your grade, you would be expected to show these papers.