# Calculus Early Transcendental Functions

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

4th

### 9780618606245

0618606246

Paperback

1/3/2006

Cengage Learning

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## 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 | |

Table of Contents provided by Publisher. All Rights Reserved. |