The focus of this course will be on the study of differentiation and integration.

Prerequisite: AP Calculus AB

Course Expectations

This course will cover:

1.) Integration Techniques and Applications

Fit an integrand to one of the basic integration rules
Find an antiderivative using substitution of variables
Find an antiderivative using integration by parts
Evaluate trigonometric integrals involving powers of sine and cosine
Evaluate trigonometric integrals involving powers of secant and tangent
Use trigonometric substitution to evaluate an integral
Use partial fraction decomposition with linear and/or quadratic factors to integrate rational functions
Apply L'Hopital's Rule to evaluate a limit
Evaluate an improper integral that has an infinite limit of integration
Evaluate an improper integral that has an infinite discontinuity
Determine the numerical solution of differential equations using Euler's method
Solve logistic differential equations and use them in modeling

2.) Parametric, Polar, and Vector-Valued Functions

Eliminate the parameter in a set of parametric equations
Find a set of parametric equations to represent a curve
Find the slope of a tangent line to a curve given by a set of parametric equations
Find the arc length of a curve given by a set of parametric equations
Analyze planar curves given in parametric form including velocity and acceleration
Write rectangular equations in polar form
Write polar equations in rectangular form
Find the slope of a tangent line to a polar graph
Find the area of a region bounded by a polar graph
Find the points of intersection of two polar graphs
Find the arc length of a polar graph
Write the component form of a vector
Perform vector operations and interpret the results geometrically
Write a vector as a linear combination of standard unit vectors
Use vectors to solve problems involving position, velocity, and acceleration
Extend the concepts of limits and continuity to vector-valued functions
Differentiate a vector-valued function
Integrate a vector-valued function
Describe the velocity and acceleration associated with a vector-valued function
Use a vector-valued function to analyze projectile motion.

3.) Infinite Series

Recognize indeterminate forms and evaluate them using L'Hopitals rule
Define an improper integral and determine its value using limits
Recognize the format of geometric series, p-series, and alternating series
Use the geometric series test for convergence and use the formula to find the sum of the series
Use the p-series test for convergence/divergence
Use the Alternating Series Test for convergence & use the value of the first neglected term to quantify the error created by calculating a partial sum
Use the Direct Comparison Test and the Limit Comparison Test to determine convergence or divergence of an unknown series
Use the Ratio Test (and the Root Test) to determine convergence or divergence of an unknown series
Find Taylor and Maclaurin polynomial approximations of elementary functions and compare them with actual values of elementary functions
Use the Lagrange Error Bound to calculate the error associated with a Taylor (or Maclaurin) Series
Calculate the radius and interval of convergence of a power series
Determine endpoint convergence of a power series
Differentiate and integrate a power series
Construct a power series using series operations
Find a Taylor or Maclaurin series for a function
Use a basic list of Taylor series to find other Taylor series.

Grading Weights are as follows

Class information can be found on Google Classroom

Cedar Creek High School

Mr. McNally