# 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
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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