Calculus of a Single Variable : Early Transcendental Functions

by Larson, Ron

• ISBN13: 9780618606252
• ISBN10: 0618606254
• Edition: 4th
• Format: Hardcover
• Copyright: 2006-01-03
• Publisher: Cengage Learning

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.

Table of Contents

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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