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    Milwaukee School of Engineering
  Oct 19, 2017
2017-2018 Undergraduate Academic Catalog
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MA 231 - Calculus III

4 lecture hours 0 lab hours 4 credits
Course Description
This course is a continuation of MA 137  and an introduction to multivariable calculus. Topics include L’Hȏpital’s rule, improper integrals, applications of integrals to physics, parametric equations, polar coordinates, vector algebra, surfaces in three dimensions, and partial derivatives with applications. (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
  • Find work, fluid pressure, and force
  • 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
  • Sketch surfaces in three dimensions
  • Find first and second partial derivatives
  • Find the total differential of a function of more than one variable and use it to approximate error
  • Use chain rules to find derivatives and partial derivatives
  • Find implicit partial derivatives
  • Determine the maximum, minimum, and saddle points on a surface

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 
  • Work 
  • Fluid pressure and force 
  • Parametric equations 
  • Polar coordinates and graphs 
  • Vectors, lines, and planes 
  • Surfaces in three dimensions 
  • Functions of several variables 
  • Partial derivatives 
  • Extrema of functions of two variables 

Kseniya Fuhrman

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