Contact Information

Phone: 218-726-8747 / 218-726-8254
Fax: 218-726-8399
umdmathstat_dus@d.umn.edu
umdmathstat_dgs@d.umn.edu
140 Solon Campus Center (map)
1117 University Drive
Duluth, MN 55812-3000
mathstat@d.umn.edu

Credits : 5

Prerequisites : 1290, 1296 or 1596

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, 8E Early Transcendentals, James Stewart, 2016.

Course Content

 Chapter Section 7 Integration Techniques 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 8 Applications of Integration 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** 10 Parametric Equations 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 11 Sequences and Series 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 Maclaurin Series 11.11 Applications of Taylor Polynomials 14 Partial Derivatives 14.1 Functions of Several Variables 14.2 Limits and Continuity 14.3 Partial Derivatives 14.5 The Chain Rule

** Included as time permits

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