Calculus II - Power Series

Service Description

Topics for this course include techniques and applications of integration, infinite sequences, power series, parametric equations, and an introduction to differential equations. This course uses the University of Illinois CAS-ILE course system featuring Mathematica which will be provided online. Earns 3 credit hours in Calculus from the Univeristy of Illinois. Prerequisite: Calculus I or equivalent. A brief outline of topics for this course appears below: • Growth o Linear, exponential, and trigonometric functions o Dominance in the global scale o Data modeling and analysis • Expansions in Powers of x o Approximating various functions o Differentiating and Integrating to find new expansions • Applications of Expansions o Newton’s Method o Calculating limits o Generating trigonometric identities • Taylor’s Formula o Estimating integrals o Applying Taylor’s Formula to calculate limits o Approximating solutions to differential equations • Barriers to Convergence o Examining convergence of various expansions o Convergence intervals and infinite sums • Power Series o Functions defined by power series and their plots o Convergence intervals for power series o The Ratio Test • Parametric Plotting o Plotting ellipses, curves, and surfaces o Applications including projectile motion • Integrals for Area and Volume Measurement o Properties of integrals o Approximation using trapezoidal rule o Measuring by slicing and accumulating • The Fundamental Formula of Calculus o Finding distance and velocity o Integrating the area between two curves o Applying the formula to differential equations • Techniques for Calculating Integrals o Integration by parts o Applying a complex exponential to integrate o Partial Fractions and u-substitution Format Course content is drawn from Calculus II and Calculus III written by Bill Davis, Horacio Porta and Jerry Uhl ©2006‐2010.