Oct 04, 2023  
2020-2021 Undergraduate Academic Catalog 
2020-2021 Undergraduate Academic Catalog [ARCHIVED CATALOG]

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MA 2314 - Calculus III

4 lecture hours 0 lab hours 4 credits
Course Description
This course is a continuation of MA 137. Topics include L’Hȏpital’s rule, improper integrals, parametric equations, polar coordinates, vector algebra, infinite series with tests for convergence, power series, Taylor and Maclaurin series, and operations with series. (prereq: MA 137 )
Course Learning Outcomes
Upon successful completion of this course, the student will be able to:
  • Use L’Hȏpital’s rule to evaluate a limit
  • Evaluate improper integrals
  • Find the length of the arc of a curve
  • Eliminate the parameter from parametric equations
  • Draw graphs of parametric equations and determine the direction of travel for an increasing parameter
  • Find first and second derivatives of parametric functions
  • Find the arc length for parametric curves
  • Convert between rectangular and polar coordinates
  • Draw graphs of polar curves
  • Find area and arc length in polar coordinates
  • Perform operations using vector algebra
  • Find dot products, cross products, and equations of lines and planes in three dimensions
  • Test sequences for convergence and divergence
  • Test infinite series for convergence and divergence
  • Find the interval of convergence for a power series
  • Perform algebraic and calculus operations on power series
  • Use Taylor and Maclaurin series to approximate functions

Prerequisites by Topic
  • The basic principles of algebra
  • The basic principles of trigonometry
  • Differentiation and integration of algebraic and transcendental functions
  • Limits
  • Understanding of the definition of the definite integral

Course Topics
  • L’Hȏpital’s rule 
  • Improper integrals
  • Arc length
  • Parametric equations 
  • Polar coordinates and graphs 
  • Vectors, lines, and planes 
  • Sequences
  • Infinite series and tests for convergence
  • Power series and intervals of convergence
  • Taylor and Maclaurin series                               

Dr. Chunping Xie

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