Math 222 - John Travis

MATHEMATICS 222

Calculus IV

Contour Plot Model Project

MAT 222 Textbook and other Instructional Materials: Calculus, Early Transcendental Functions , 5th edition, by Larson, Hostetler and Edwards

A number of other software packages downloaded from the internet will be utilized.

Sage (Sage documentation) - opensource mathematical environment
Webwork - online homework system
Winplot - easy graphing utility

Prerequisites: MAT 221

Projects: Several individual and group projects may be assigned during the term. These projects may involve reading and reviewing published papers, computational projects and constructions.

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 Fifteen 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 the Counseling and Career Development Center.

Grading: Assessment of the student's progress will be made through regular homework exercises and periodic examinations as well as through classroom feedback. During the term, there will be at least three exams during the semester. Homework will be assigned and graded online. Additional daily work may be assigned during the term and an average of these daily grades will count for 15% of your final grade. The remaining 85% of your final grade will be based on an average of the periodic exams.

Any daily work missed will be awarded a grade of zero. 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.

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.