Calculus An Applied Approach

by Larson, Ron; Edwards, Bruce H.

• ISBN13: 9780618547180
• ISBN10: 0618547185
• Edition: 7th
• Format: Hardcover
• Copyright: 2005-03-14
• Publisher: Brooks Cole

Summary

Designed specifically for the non-math major who will be using calculus in business, economics, or life and social science courses, Calculus: An Applied Approach, 7/e, addresses students' weak math skills through added structure and guidance on how to study math. Special student-success-oriented sections include chapter-opening Strategies for Success; What You Should Learn--and Why You Should Learn It; Section Objectives; Chapter Summaries and Study Strategies; Try Its; Study Tips; and Warm-Up exercises. In addition the text presents Algebra Tips at point of use and Algebra Review at the end of each chapter. The Seventh Edition places a new emphasis on algebra review through Algebra Tips at point of use throughout the chapter and Algebra Review at the end of each chapter. This edition also builds on a proven emphasis on applications; updates and increases the coverage of technology at point of use; and includes sample post-graduation exam questions. A strong support package includes the HM mathSpace CD-ROM--which further emphasizes algebra review--and Instructional DVDs that allow students to review material outside of class. Approximately 6,000 exercises--progress from skill-development problems to more challenging, real-world application questions--are easily customized to the difficulty level of the instructor's choice. In addition, a number of relevant exercises from textbooks in other disciplines--such as biology, chemistry, economics, finance, geology, physics, and psychology--to show students that they will use calculus in future courses outside of the math curriculum. Algebra Review offers students algebraic support at point of use and at the end of the chapter. The end-of-chapter Algebra Review illustrate the key algebraic concepts called out in the Algebra Reviews used throughout the chapter. This feature is designed to help students who may have weak algebra skills and need help as they take a calculus course. Prerequisite Review exercises at the beginning of each exercise set help students review skills covered in previous sections. The answers are provided at the back of the text, enabling students to check their work. Review Exercises are also included at the end of each chapter and offer students the opportunity for additional practice and review. Discovery Projects expose students to concepts before the topic is covered in the text. This allows students to explore the concept on their own, making them more likely to remember the results. Take Another Look, appearing just before each section exercise set, asks students to look back at one or more concepts presented in the section. The questions in these sections are designed to enhance understanding of key ideas. Post-Graduation Exam Questions appear at the end of each chapter. They include sample questions representative of the types of questions on various standardized tests (i.e. GMAT, CPA exams, GRE, College Level Academic Skills Test). These questions challenge students and provide additional practice. Business Capsules appear at the end of numerous sections. Along with accompanying exercises, these features deal with business situations related to the mathematical concepts covered in the chapter. This feature allows students to see the relevance of what they are learning, and the importance of everyday mathematics. Ready to use and easy to integrate into your calculus course, Eduspace, powered by Blackboard, brings your students quality homework, tutorials, and testing while saving you time. Browser-based, algorithmically generated homework problems are scored for you automatically. You determine whether the grade is recorded and how much each assignment counts toward a final grade.

Table of Contents

Note: Each chapter includes an Algebra Review, Chapter Summary, Study

Strategies, Review Exercises, and Sample Post-Graduation Exam Questions

A Precalculus Review

The Real Number Line and Order

Absolute Value and Distance on the Real Number Line

Exponents and Radicals

Factoring Polynomials

Fractions and Rationalization

Functions, Graphs, and Limits

The Cartesian Plane and the Distance Formula

Graphs of Equations

Lines in the Plane and Slope

Functions

Limits

Continuity

Differentiation

The Derivative and the Slope of a Graph

Some Rules for Differentiation

Rates of Change: Velocity and Marginals

The Product and Quotient Rules

The Chain Rule

Higher-Order Derivatives

Implicit Differentiation

Related Rates

Applications of the Derivative

Increasing and Decreasing Functions

Extrema and the First-Derivative Test

Concavity and the Second-Derivative Test

Optimization Problems

Business and Economics Applications

Asymptotes

Curve Sketching: A Summary

Differentials and Marginal Analysis

Exponential and Logarithmic Functions

Exponential Functions

Natural Exponential Functions

Derivatives of Exponential Functions

Logarithmic Functions

Derivatives of Logarithmic Functions

Exponential Growth and Decay

Integration and Its Applications

Antiderivatives and Indefinite Integrals

The General Power Rule

Exponential and Logarithmic Integrals

Area and the Fundamental Theorem of Calculus

The Area of a Region Bounded by Two Graphs

The Definite Integral as the Limit of a Sum

Volumes of Solids of Revolution

Techniques of Integration

Integration by Substitution

Integration by Parts and Present Value

Partial Fractions and Logistic Growth

Integration Tables and Completing the Square

Numerical Integration

Improper Integrals

Functions of Several Variables

The Three-Dimensional Coordinate System

Surfaces in Space

Functions of Several Variables

Partial Derivatives

Extrema of Functions of Two Variables

Lagrange Multipliers

Least Squares Regression Analysis

Double Integrals and Area in the Plane

Applications of Double Integrals

Trigonometric Functions

Radian Measure of Angles

The Trigonometric Functions

Graphs of Trigonometric Functions

Derivatives of Trigonometric Functions

Integrals of Trigonometric Functions

L'Hocirc;pital's Rule

Probability and Calculus

Discrete Probability

Continuous Random Variables

Expected Value and Variance

Series and Taylor Polynomials

Sequences

Series and Convergence

p-Series and the Ratio Test

Power Series and Taylor's Theorem

Taylor Polynomials

Newton's Method

Appendices

Alternate Introduction to the Fundamental Theorem of Calculus

Formulas

Differentiation and Integration Formulas

Formulas from Business and Finance

Differential Equations

Solutions of Differential Equations

Separation of Variables

First-Order Linear Differential Equations

Applications of Differential Equations The following Appendices available at the text-specific website at college.hmco.com:

Properties of Measurement

Review of Algebra, Geometry, and Trigonometry

Units of Measurement

Graphing Utility Programs

Graphing Utility Programs

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