MATH& 153 Calculus III

• Determine if a sequence converges or diverges, and if it converges, find its limit
• Determine if an infinite series converges absolutely, converges conditionally, or diverges using an appropriate test (nth term test, integral test, comparison tests, ratio test, root test, alternating series test)
• Calculate the sum of a convergent infinite geometric series
• Find the radius and interval of convergence for a power series
• Express basic and transcendental functions as power series, and derive Maclaurin and Taylor series
• Convert between regular and parametric form for curves in a plane
• Convert points and equations between polar and rectangular form
• Recognize and sketch graphs of equations in polar coordinates
• Compute arc length of parametrically-defined functions and polar coordinate equations
• Identify conic sections from their equations in rectangular or polar form
• Perform vector calculations in two- and three-dimensions (including dot products, cross products, and projections)
• Solve problems involving distances and angles between lines using vectors
• Write equations of lines and planes using vectors, and solve problems involving their intersections
• Identify and sketch quadric surfaces
• Differentiate and integrate vector-valued functions
• Find the unit normal and binormal vectors of a curve defined by a vector-valued function
• Calculate the tangential and normal components of the acceleration vector
• Calculate the curvature of a path of motion
• Use the mathematical critical thinking skills of problem solving, pattern recognition, substitution, following structural rules, and quantitative modeling to solve problems requiring reasoning, critical thinking, and computation