Calculus of a Single Variable : Early Transcendental Functions

by Larson, Ron

Edition:

4th

ISBN13:

9780618606252

ISBN10:

0618606254

Format:

Hardcover

Pub. Date:

1/3/2006

Publisher(s):

Cengage Learning

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Summary

This volume covers chapters P–9 of Larson et al., Calculus: Early Transcendental Functions, 3/e. For a complete description, see the entry for that text.

Note: Each chapter concludes with Review Exercises and P.S. Problem Solving
Preparation for Calculus
Graphs and Models
Linear Models and Rates of Change
Functions and Their Graphs
Fitting Models to Data
Inverse Functions
Exponential and Logarithmic Functions
Limits and Their Properties
A Preview of Calculus
Finding Limits Graphically and Numerically
Evaluating Limits Analytically
Continuity and One–Sided Limits
Infinite Limits
Section Project: Graphs and Limits of Trigonometric Functions
Differentiation
The Derivative and the Tangent Line Problem
Basic Differentiation Rules and Rates of Change
The Product and Quotient Rules and Higher–Order Derivatives
The Chain Rule
Implicit Differentiation
Section Project: Optical Illusions
Derivatives of Inverse Functions
Related Rates
Newton's Method
Applications of Differentiation
Extrema on an Interval
Rolle's Theorem and the Mean Value Theorem
Increasing and Decreasing Functions and the First Derivative Test
Section Project: Rainbows
Concavity and the Second Derivative Test
Limits at Infinity
A Summary of Curve Sketching
Optimization Problems
Section Project: Connecticut River
Differentials
Integration
Antiderivatives and Indefinite Integration
Area
Riemann Sums and Definite Integrals
The Fundamental Theorem of Calculus
Section Project: Demonstrating the Fundamental Theorem
Integration by Substitution
Numerical Integration
The Natural Logarithmic Function: Integration
Inverse Trigonometric Functions: Integration
Hyperbolic Functions
Section Project: St. Louis Arch
Differential Equations
Slope Fields and Euler's Method
Differential Equations: Growth and Decay
Differential Equations: Separation of Variables
The Logistic Equation
First–Order Linear Differential Equations
Section Project: Weight Loss
Predator–Prey Differential Equations
Applications of Integration
Area of a Region Between Two Curves
Volume: The Disk Method
Volume: The Shell Method
Section Project: Saturn
Arc Length and Surfaces of Revolution
Work
Section Project: Tidal Energy
Moments, Centers of Mass, and Centroids
Fluid Pressure and Fluid Force
Integration Techniques, L'Hopital's Rule, and Improper Integrals
Basic Integration Rules
Integration by Parts
Trigonometric Integrals
Section Project: Power Lines
Trigonometric Substitution
Partial Fractions
Integration by Tables and Other Integration Techniques
Indeterminate Forms and L'Hopital's Rule
Improper Integrals
Infinite Series
Sequences
Series and Convergence
Section Project: Cantor's Disappearing Table
The Integral Test andp–Series
Section Project: The Harmonic Series
Comparisons of Series
Section Project: Solera Method
Alternating Series
The Ratio and Root Tests
Taylor Polynomials and Approximations
Power Series
Representation of Functions by Power Series
Taylor and Maclaurin Series
Conics, Parametric Equations, and Polar Coordinates
Conics and Calculus
Plane Curves and Parametric Equations
Section Project: Cycloids
Parametric Equations and Calculus
Polar Coordinates and Polar Graphs
Section Project: Anamorphic Art
Area and Arc Length in Polar Coordinates
Polar Equations of Conics and Kepler's Laws
Appendices
Appendix
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