MA 231 - Calculus III

• 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

• 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 
• 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