Topical Outline with Specific Course Objectives
- Integration
- Apply antidifferentiation techniques, such as integration by parts, partial fractions, trigonometric substitution, and the use of a table of integrals.
- Develop an organized approach for classifying a given integrand and determining the appropriate technique of antidifferentiation.
- Model applied problems of area, volume, arc length, and work using integrals.
- Apply a variety of numerical methods for approximating definite integrals.
- Estimate and compare the errors associated with each approximation method for definite integrals.
- Recognize an improper integral and determine whether it is convergent or divergent.
- Find the value of a convergent improper integral symbolically when possible, otherwise estimate the value numerically.
- Infinite Sequences and Series
- Verify the convergence or divergence of a sequence by employing appropriate tools and find or estimate the limit of a convergent sequence.
- Define the sequence of partial sums for an infinite series and relate the convergence of this sequence to the convergence of the series. Then find or estimate the sum.
- Exhibit knowledge of convergence tests, their usefulness, conditions, and limitations, and apply the tests to determine the convergence or divergence of a series.
- Develop and apply an organized approach for proving the convergence or divergence of a series.
- Find the interval and radius of convergence for a given power series.
- Find the Taylor and Maclaurin series representations of a function and determine the interval of convergence.
- Relate differentiation/integration of a given function to differentiation/integration of the corresponding power series representation.
- Use the sequence of partial sums of a power series, in its interval of convergence, as a useful approximation for a function.
- Calculate error terms for Alternating Series and Taylor Series.
- Parametric Equations
- Represent a plane curve parametrically and determine its orientation.
- Use parametric equations to model and analyze physical processes such as curvilinear motion.
- Apply the techniques of Calculus to analyze parametric equations.
- Polar Coordinates
- Apply calculus to examine the properties of curves represented in polar coordinates, e.g. area, tangent lines, and arc length.
- Convert between rectangular and polar coordinates.
Department Policies
- Graphing Calculator not allowed on proctored tests or final exam
- Comprehensive Final