Calculus Early Transcendental Functions

by Larson, Ron; Hostetler, Robert P.; Edwards, Bruce H.

• ISBN13: 9780618606245
• ISBN10: 0618606246
• Edition: 4th
• Format: Paperback
• Copyright: 2006-01-03
• Publisher: Brooks Cole

Summary

Designed for the three-semester engineering calculus course,Calculus: Early Transcendental Functions,4/e, continues to offer instructors and students innovative teaching and learning resources. Two primary objectives guided the authors in the revision of this book: to develop precise, readable materials for students that clearly define and demonstrate concepts and rules of calculus; and to design comprehensive teaching resources for instructors that employ proven pedagogical techniques and save time. The Larson/Hostetler/EdwardsCalculusprogram offers a solution to address the needs of any calculus course and any level of calculus student. Every edition from the first to the fourth ofCalculus: Early Transcendental Functions,4/e has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas. Now, the Fourth Edition is part of the first calculus program to offer algorithmic homework and testing created in Maple so that answers can be evaluated with complete mathematical accuracy. Exercise sets have been carefully examined and revised to ensure they cover all calculus topics appropriately. Many new exercises have been added. A variety of exercise types are included in each exercise set. Questions involving skills, writing, critical thinking, problem-solving, applications, and real-data applications are included throughout the text. Exercises are presented in a variety of question formats, including matching, free response, true/false, modeling, and fill-in the blank. Putnam Exam Questions--taken from the William Lowell Putnam Mathematical Competition--offer challenging problems that often require students to look for creative solutions;Graphical Analysisexercises offer the opportunity to analyze graphs;Think About Itexercises require students to use critical reasoning skills to explore the intricacies of calculus. Explanations, theorems, and definitions in the text have been thoroughly reviewed to ensure the text is mathematically precise and easily comprehensible. Clear, multi-step examples with worked-out solutionshelp students learn difficult mathematical concepts. Examples correspond to the exercises, serving as a supportive reference for students. This is the only text on the market whereevery example, proof, and explanation begins and ends on the same page. Explorationshelp students develop their intuitive understanding of calculus concepts. These optional activities are short enough to integrate into class, but they can also be omitted without loss of continuity. Theorem boxesclearly explain important mathematical concepts. TheIntegrated Learning Systemresources are available in print, CD-ROM, and online formats. Eduspace, powered by Blackboard,Houghton Mifflin's online learning tool, offers your students quality online homework, tutorials, multimedia, and testing that correspond to theCalculus: Early Transcendental Functionstext. This content is paired with the course management tools of Blackboard. In addition,eSolutions,the complete solutions to the odd-numbered text exercises, provides students with a convenient and comprehensive way to do homework and view the course materials. SMARTHINKING online tutoring brings students real-time, online tutorial support when they need it most.

Table of Contents

Note: Each chapter includes 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

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

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'Hocirc;pital'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'Hocirc;pital'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 Projects: 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

Vectors and the Geometry of S

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