MA 231 - Calculus for Engineers 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 (2 classes)
• Improper integrals (3 classes)
• Arc length (1 class)
• Work (2 classes)
• Fluid pressure and force (2 classes)
• Parametric equations (2 classes)
• Polar coordinates and graphs (3 classes)
• 3-Space Vectors, lines, and planes (6 classes)
• Surfaces in three dimensions (3 classes)
• Functions of several variables (1 class)
• Partial derivatives (6 classes)
• Extrema of functions of two variables (2 classes)
• Review and exams (7 classes)