MA 2314 - Calculus III

• 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

• 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

• 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