
MA 231  Calculus III4 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
Coordinator Kseniya Fuhrman
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