MAC2312 - Calculus 2 with Analytic Geometry

Topical Outline with Specific Course Objectives

  1. Integration
    1. Apply antidifferentiation techniques, such as integration by parts, partial fractions, trigonometric substitution, and the use of a table of integrals.
    2. Develop an organized approach for classifying a given integrand and determining the appropriate technique of antidifferentiation.
    3. Model applied problems of area, volume, arc length, and work using integrals.
    4. Apply a variety of numerical methods for approximating definite integrals.
    5. Estimate and compare the errors associated with each approximation method for definite integrals.
    6. Recognize an improper integral and determine whether it is convergent or divergent.
    7. Find the value of a convergent improper integral symbolically when possible, otherwise estimate the value numerically.
  2.  Infinite Sequences and Series
    1. Verify the convergence or divergence of a sequence by employing appropriate tools and find or estimate the limit of a convergent sequence.
    2. 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.
    3. Exhibit knowledge of convergence tests, their usefulness, conditions, and limitations, and apply the tests to determine the convergence or divergence of a series.
    4. Develop and apply an organized approach for proving the convergence or divergence of a series.
    5. Find the interval and radius of convergence for a given power series.
    6. Find the Taylor and Maclaurin series representations of a function and determine the interval of convergence.
    7. Relate differentiation/integration of a given function to differentiation/integration of the corresponding power series representation.
    8. Use the sequence of partial sums of a power series, in its interval of convergence, as a useful approximation for a function.
    9. Calculate error terms for Alternating Series and Taylor Series.
  3. Parametric Equations
    1. Represent a plane curve parametrically and determine its orientation.
    2. Use parametric equations to model and analyze physical processes such as curvilinear motion.
    3. Apply the techniques of Calculus to analyze parametric equations.
  4. Polar Coordinates
    1. Apply calculus to examine the properties of curves represented in polar coordinates, e.g. area, tangent lines, and arc length.
    2. Convert between rectangular and polar coordinates.

Department Policies

  • Graphing Calculator not allowed on proctored tests or final exam 
  • Comprehensive Final
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