Topic Outline for Math Calculus with Analytic Geometry II by katiebelonga

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									        Topic Outline for Math 141, Calculus with Analytic Geometry II

I.     Inverse Functions
       a. Inverse Functions- One-to-one functions, horizontal line test, finding
          inverse functions, finding the derivative of an inverse function at a point.
       b. Exponential Functions and Their Derivatives- Graphing exponential
          functions, derivatives and integrals involving the natural exponential
          function.
       c. Logarithmic Functions- Graphing logarithmic functions, properties of
          logarithms.
       d. Derivatives of Logarithmic Functions- Derivatives and integrals involving
          logarithmic functions, logarithmic differentiation.
       e. Inverse Trigonometric Functions- Definition of the inverse trig functions,
          derivatives and integrals involving inverse trig functions.
       f. Indeterminate Forms and L’Hospital’s Rule- Discussion of limits that are
          in indeterminate forms and how to evaluate them using L’Hospital’s Rule
          or other methods.

II.    Techniques of Integration
       a. Integration by Parts
       b. Trigonometric Integrals- Use trigonometric identities to evaluate certain
          combinations of trigonometric integrals.
       c. Trigonometric Substitution- Evaluating certain types of algebraic
          integrals using trigonometric substitutions.
       d. Integration of Rational Functions by Partial Fractions- (Including repeated
          linear and/or irreducible quadratic factors.)
       e. Improper Integrals- Discussion of integrals involving infinite limits and/or
          discontinuities.

III.   Infinite Sequences and Series
       a. Sequences- Definition of a sequence, determining whether a sequence is
           convergent or divergent, increasing/decreasing sequences.
       b. Series- Definition of an infinite series, partial sums, geometric series,
           telescoping series, the Test for Divergence.
       c. The Integral Test- Using the integral test to determine whether a series is
           convergent/divergent, p-series.
       d. The Comparison Tests- Using the Direct Comparison Test and the Limit
           Comparison Test to determine whether a series is convergent/divergent.
       e. Alternating Series- Using the alternating series test to determine whether a
           series is convergent/divergent, Alternating Series Estimation Theorem.
       f. Absolute Convergence and the Ratio and Root Tests- Determining
           whether a series is absolutely or conditionally convergent, The Ratio and
           Root Tests.
       g. Power Series- Finding the radius and interval of convergence for power
           series.
          h. Representations of Functions as Power Series- Finding the power series
             representation of a function, differentiation and integration of power
             series, using power series to approximate definite integrals.
          i. Taylor and Maclaurin Series- Finding the Taylor Series/Maclaurin Series
             representation for a function, multiplication and division of power series.
          j. Applications of Taylor Polynomials- Approximating functions by Taylor
             polynomials, using Taylor’s Inequality to estimate the accuracy of a given
             approximation.

   IV.    Parametric Equations and Polar Coordinates
          a. Curves defined by Parametric Equations- Graphing parametric equations,
             eliminating the parameter to find the Cartesian equation.
          b. Calculus with Parametric Curves- Derivatives of parametric functions.
          c. Polar Coordinates- Discussion of the polar coordinate system, graphing
             polar curves, Derivatives of polar functions.
          d. Areas in Polar Coordinates- Finding the area enclosed by polar curves.


Note: Those items in italics are covered in Math 141 but may/may not have been covered
in AP Calculus.

								
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