CONTENIDO: FUNCTIONS
Functions and Graphs
Combining Functions
Polynomial and Rational Functions
Transcendental Functions
Inverse Functions
Exponential and Logarithmic Functions
From Words to Functions
LIMIT OF A FUNCTION
Limits ¿ An Informal Approach
Limit Theorems
Continuity
Trigonometric Limits
Limits that Involve Infinity
Limits ¿ A Formal Approach
The Tangent Line Problem
THE DERIVATIVE
The Derivative
Power and Sum Rules
Product and Quotient Rules
Trigonometric Functions
Chain Rule
Implicit Differentiation
Derivatives of Inverse Functions
Exponential Functions
Logarithmic Functions
yperbolic Functions
APPLICATIONS OF THE DERIVATIVE
Rectilinear Motion
Related Rates
Extrema of Function
Mean Value Theorem
Limits Revisited - L¿Hôpital¿s Rule
Graphing and the First Derivative
Graphing and the Second Derivative
Optimization
Linearization and Differentials
Newton¿s Method
INTEGRALS
The Indefinite Integral
Integration by the u-Substitution
The Area Problem
The Definite Integral
Fundamental Theorem of Calculus
APPLICATIONS OF THE INTEGRAL
Rectilinear Motion Revisited
Area Revisited
Volumes of Solids: Slicing Method
Volumes of Solids: Shell Method
Length of a Graph
Area of a Surface of Revolution
Average Value of a Function
Work
Liquid Pressure and Force
Centers of Mass and Centroids
TECHNIQUES OF INTEGRATION
Integration ¿ Three Resources
Integration by Substitution
Integration by Parts
Powers of Trigonometric Functions
Trigonometric Substitutions
Partial Fractions
Improper Integrals
Approximate Integration
FIRST-ORDER DIFFERENTIAL EQUATIONS
Separable Equations
Linear Equations
Mathematical Models
Solution Curves without a Solution
Euler¿s Method
SEQUENCES AND SERIES
Sequences
Monotonic Sequences
Series
Integral Test
Comparison Tests
Ratio and Root Tests
Alternating Series
Power Series
Representing Functions by Power Series
Taylor Series
Binomial Series CONICS AND POLAR COORDINATES
Conic Sections
Parametric Equations
Calculus and Parametric Equations
Polar Coordinate System
Graphs of Polar Equations
Calculus in Polar Coordinates
Conic Sections in Polar Coordinates
APPENDIX
Proofs of Selected Theorems
Answers to Test Yourself
Answers to Selected Odd-Numbered Problems
Resource Pages
Review of Algebra
Formulas from Geometry
Graphs and Functions
Review of Trigonometry
Exponential and Logarithmic Functions
Differentiation
Integration Formulas
Index
