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ROCHESTER
COMMUNITY & TECHNICAL COLLEGE
COMMON COURSE OUTLINE: Math 2237 - Multivariable Calculus
A.
Catalog Description
1. Math
2237
2. Multivariable Calculus
3. 5 credits
4. 5 hours of instruction per week
5. Offered Fall Semester
6. Prerequisites:
a. Math 1128
b. College reading level
7. MNTC:
a. Critical Thinking (CT)
b. Mathematics/Symbolic Systems (MA)
8. First
in a sequence which is a continuation of the first year of calculus.
Topics are selected from the following: coordinate and vector geometry,
vector valued functions, velocity, acceleration and curvature, cylindrical
and spherical coordinate systems, partial differentiation and applications,
double and triple integrals, Green’s – Stokes Divergence Theorems, Frenet
Formulas.
B.
Revised 6/6/2000
C.
Recommended entry skills/knowledge - Above average first year
calculus skills in differentiation and integration, understanding basic
proofs, and be able to work with transcendental functions, trigonometric
and hyperbolic functions involving derivatives, integrals and applications,
L’Hopital’s Rule, Improper Integrals, Infinite Series, Taylor Polynomials
and Series, Conic Sections, Polar Coordinate Systems and Parametric
Equations.
D.
Major Content Areas:
Infinite Sequences and Series, Taylor and Maclaurin Series
Representation of Functions as Power Series, Binomial Series
Vectors and the Geometry of Space, Dot and Cross Product
Equations of Lines, Planes, Surfaces, Cylindrical and Spherical Coordinates
Vector Functions and Space Curves, Derivatives and Integrals of Vector
Functions
Arc Length and Curvature, Motion in Space, and Parametric Surfaces
Partial Derivatives, Tangent Planes, Linear Approximations
Directional Derivative and Gradient Vector, Maximums and Minimums
Lagrange Multipliers
Multiple Integrals, Iterated Integrals
Double Integrals over Rectangles, General Regions and in Polar Coordinates
Applications of Double Integrals, Surface Area
Applications of Triple Integrals in Cylindrical and Spherical Coordinates
Change of Variables in Multiple Integrals
Vector Calculus, Vector fields, Line Integrals, Green’s Theorem
Curl and Divergence, Surface Integrals, Stoke’s Theorem, The Divergence
Theorem
OPTIONAL
TOPICS:
Additional applications in any of the Major Content Areas in Part D
Introduction to the beginning topics of Differential Equations
E.
Learning Outcomes
1. Mathematical/Logical
Reasoning from MN Transfer Curriculum (MTC)
a. Illustrate
historical and contemporary applications of mathematical/logical reasoning.
b. Clearly express mathematical/logical ideas in writing.
c. Explain what constitutes a valid mathematical/logical argument (proof).
d. Recognize higher order problem-solving and/or modeling strategies.
2. Critical Thinking from MN transfer curriculum
a. Gather
factual information and apply it to a given problem in a manner that
is relevant, clear, comprehensive, and conscious of possible bias in
the information selected.
b. Imagine and seek out a variety of possible goals, assumptions, interpretations,
or perspectives which can give alternative meanings or solutions to
given situations or problems.
c. Analyze the logical connections among the facts, goals, and implicit
assumptions relevant to a problem or claim; generate and evaluate implications
that follow from them.
d. Recognize and articulate the value assumptions, which underlie and
affect decisions, interpretations, analyses, and evaluations, made by
ourselves and others.
Other Competencies:
Need to
have skilled use of the graphics calculator.
Must acquire some skills in a computer software application, e.g. Mathematica.
Must have college reading level for reading the text and interpreting
the problems.
Should have above average skills in first year calculus integration,
differentiation.
Be able to learn and use precise thinking and writing methods for structuring
problems.
a. Mastery
of Major Content Areas in Part D.
b. Introduction
of Applications of these concepts to the degree that time allows.
F.
Methods used for Evaluation
1. Test over the covered topics for each chapter
2. Quizzes and Extra Credit Opportunities
3. Homework
4. Group Assignments
5. Final Exam - comprehensive over untested material, using skills and
methods mastered in this class.
G.
Graphing Calculators needed and used in this class.
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