Math 141: Calculus with Analytic Geometry II	Fall 2012
Penn State University	Sections 4, 18, 21

Instructor: David Little Office: 403 McAllister Office Hours: MWRF 1:00-2:00, T 2:00-4:00 and by appointment/walk-in	Phone: (814) 865-3329 Fax: (814) 865-3735 E-mail:dlittle@psu.edu
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Course Topics CHAPTER 6 Inverse Functions 6.1 Inverse Functions One-to-one functions, horizontal line test, how to find the inverse of a one-to-one function, derivative of an inverse function 6.2* The Natural Logarithm Function The natural logarithm function defined as a definite integral, derivative of ln(x), laws of logarithms, the definition of e, logarithmic differentiation 6.3* The Natural Exponential Function The relationship between ex and ln(x), properties of ex, laws of exponents, derivative and integral of ex 6.4* General Logarithmic and Exponential Functions derivatives and integrals of exponential functions, change of base formula for logarithms, e as a limit 6.6 Inverse Trigonometric Functions Inverse trigonometric functions, derivatives and their corresponding integral formulae Section 6.8 Indeterminate Forms and L'Hospital's Rule Indeterminate products, differences and powers. CHAPTER 7 Techniques of Integration Section 7.1 Integration by Parts Integrating products and inverse functions using integration by parts Section 7.2 Trigonometric Integrals Integrating functions of the form sinn(x)cosm(x), tann(x)secm(x) and sin(nx)cos(mx) Section 7.3 Trigonometric Substitution Integrating functions involving (a2 - x2)1/2, (a2 + x2)1/2, or (x2 - a2)1/2 Section 7.4 Integration of Rational Functions by Partial Fractions Integrating rational functions (i.e., functions of the form p(x)/q(x) where p(x) and q(x) are polynomials) Section 7.5 Strategy for Integration Table of integrals, simplifying integrand, substitution, integration by parts, classify integrand (trig. integral, trig. substitution, partial fractions, radicals) Section 7.8 Improper Integrals Integrating functions over unbounded intervals, integrating over an interval where the integrand is not continuous CHAPTER 10 Parametric Equations and Polar Coordinates Section 10.1 Curves Defined by Parametric Equations Understanding and interpreting curves defined parametrically by x=x(t) and y=y(t) Section 10.2 Calculus with Parametric Equations How to calculate the derivative of a function define parametrically. Section 10.3 Polar Coordinates Converting between Cartesian and polar coordinates. How to draw a polar curves. Section 10.4 Areas and Lengths in Polar Coordinates Finding the area of a region bound by a Polar curve. CHAPTER 11 Infinite Sequences and Series Section 11.1 Sequences Calculating limits of an infinite ordered list of numbers. Section 11.2 Series Geometric series, telescoping sums and the harmonic series. Section 11.3 The Integral Test and Estimates of Sums Using improper integrals to test the convergence of infinite series. Section 11.4 The Comparison Tests Use the convergence/divergence of p-series and geometric series to determine the convergence/divergence of a given series. Section 11.5 Alternating Series Convergence and error estimates of alternating series. Section 11.6 Absolute Convergence and the Ratio and Root Tests Absolute and conditional convergence of series. Section 11.7 Strategy for Testing Series Series Convergence/Divergence Flow Chart. Section 11.8 Power Series Finding radius and interval of convergence of power series using the Ratio and Root Tests Section 11.9 Representations of Functions as Power Series Obtaining power series representations of functions by differentiating, integrating or substitution involving known power series. Section 11.10 Taylor and Maclaurin Series General techniques for computing power series expansions for a given function. Section 11.11 Applications of Taylor Polynomials Using Taylor series to approximate the value of functions like sin(x), cos(x), ex, ln(1+x), and atan(x)