Calculus Early Transcendental Functions

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  • Edition: 4th
  • Format: Paperback
  • Copyright: 1/3/2006
  • Publisher: Brooks Cole
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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
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
Antiderivatives and Indefinite Integration
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
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
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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