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Math 1297 Calculus II
Credits: 5
Prerequisites: 1290 or 1296
Grading: A-F only
Liberal Education Category:
Category Satisfied: CATEGORY TWO: Math, Logic and Critical Thinking
Liberal Education Goals and Objectives: By the end of the term, the
successful student will understand the important role that calculus plays in
modeling real-world phenomena and how to apply calculus to problems in
his/her discipline. Business, economics, biology, geology, chemistry,
physics, engineering and numerous other disciplines make heavy use of
calculus. Whenever numerical quantities change with respect to time or with
respect to other variables, calculus is probably involved. The incredible
success of the physical sciences and engineering in today's world is largely
due to "the unreasonable effectiveness of mathematics," and
calculus plays a major role in that effectiveness! The biological social and
managerial scientists today also make tremendous use of calculus to solve
their problems.
Course Description:
This course covers the second part of a standard introduction to calculus. It
in includes discussion of parametric equations and polar coordinates,
applications of integrals, series, and partial derivatives.
Text: Calculus, 6E Early Transendentals,
James Stewart, 2008.
Course Content:
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Chapter
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Section
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7 Integration Techniques
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7.1 Integration by Parts (review only)
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution
7.4 Integration of Rational Functions by Partial Fractions
7.5 Strategy for Integration
7.6 Integration Using Tables
7.7 Approximate Integration
7.8 Improper Integrals
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8 Applications of Integration
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8.1 Arc
Length
8.2 Area of a Surface of Revolution
8.3 Applications to Physics and Engineering
8.4 Applications to Economics and Biology
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10 Parametric Equations
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10.1 Curves Defined by Parametric Equations
10.2 Calculus with Parametric Curves
10.3 Polar Coordinates
10.4 Areas and Lengths in Polar Coordinates
10.5 Conic Sections
10.6 Conic Sections in Polar Coordinates
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11 Sequences and Series
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11.1 Sequences
11.2 Series
11.3 The Integral Test and Estimates of Sums
11.4 Comparison Tests
11.5 Alternating Series
11.6 Absolute Convergence and the Ratio and Root Tests
11.7 Strategy for Testing Series
11.8 Power Series
11.9 Representations of Functions as Power Series
11.10 Taylor and Maclaurin
Series
11.11 Applications of Taylor
Polynomials
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14 Partial Derivatives
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14.1 Functions of Several Variables**
14.3 Partial Derivatives
14.5 The Chain Rule
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** Included as time permit
Copyright 2008, University of Minnesota, Duluth.
The University
of Minnesota
is an equal opportunity educator and employer.
This web page is maintained by the Department of Mathematics and Statistics,
and was last updated November 18, 2008. Send comments to math@d.umn.edu.
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