Brief Applied Calculus

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  • Edition: 4th
  • Format: Hardcover
  • Copyright: 2006-02-01
  • Publisher: Brooks Cole
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This brief edition ofApplied Calculuscomprises Chapters 1-7 of the complete text plus two sections on differential equations. Designed for the one- or two-semester applied or business calculus course, this text uses intriguing real-world applications to engage students' interest and show them the practical side of calculus. Many applications are financial or business related, but many applications in this text cover general-interest topics as well, including the growing population of Africa, the composition of the Supreme Court, water shortage, the fastest pitch in baseball, and pollution and the depletion of natural resources. The Fourth Edition maintains the hallmark features that have madeBrief Applied Calculusso popular: contemporary and interesting applications; careful and effective use of technology, including integrated calculator coverage that is optional; constant pedagogical reinforcement through section summaries, chapter summaries, carefully annotated examples, and extra practice problems; and a variety of exercises and assignment options including exercise sets, projects, and essays. Contemporary and Interesting Applicationsoften use real, sourced data from a wide range of fields including: athletics, biomedical sciences, environmental sciences, management science and business, personal finance and management, social and behavioral sciences, and topics of general interest. Real-world examples are identified by a globe icon. Optional Graphing Calculator Explorations and Exercisesexplore new topics, carry out otherwise messy calculations, or show the limitations and pitfalls of technology. To allow for optional use of the graphing calculator, the Calculator Explorations are boxed and exercises that require a graphing calculator are identified by icon. Spreadsheet Explorationsare included in the first seven chapters of the text for those who prefer Excel or other spreadsheet technology. The spreadsheets referenced in the text can also be downloaded from the text's web site. Unique Section Summariesbriefly state essential formulas and key concepts and help students prepare for tests and quizzes. Chapter Summary with Hints and Suggestionsreview key concepts of a chapter with references to specific review exercises. This feature is included at the end of each chapter. The Hints and Suggestions features unify the concepts of the chapter, give specific reminders, and reference problems in the review exercises suitable for a practice test. Extra Practice Problemsare provided after selected worked-out examples, where students can use a little extra practice. Students are given the full solution to these problems at the end of the section. Exercise setsprovide numerous assignment options for instructors, allowing them to customize homework to their course and student population. The exercise set begins with basic practice and increases in difficulty. Application exercises are clearly labeled with general and specific titles to make it easier for instructors to select relevant exercises for assignments. New!Conceptual Exercises and Explorations and Excursionshave been added at reviewers' requests, to offer a more rounded view into the student's understanding of a topic. The Conceptual Exercises will encourage students to think 'outside the box,' expanding on and examining, their grasp of the mathematics behind the drill and application exercises. The underlying concepts of calculus become the focus. Projects and Essaysare now included on the textbook website and CD-ROM to provide opportunities for collaborative work, as well as critical thinking and writing exercises. Cumulative Review Exercisesat the end of selected chapters give students an easy way to review and reinforce previously learned conce

Table of Contents

Note: Each chapter concludes with a Chapter Summary with Hints and Suggestions and Review Exercises
Preface A User's Guide to Features Integrating Excel Graphing Calculator Terminology
Real Numbers, Inequalities, and Lines
Functions, Continued
Derivatives and Their Uses
Limits and Continuity
Rates of Change, Slopes, and Derivatives
Some Differentiation Formulas
The Product and Quotient Rules
Higher–Order Derivatives
The Chain Rule and the Generalized Power Rule
Nondifferentiable Functions
Further Applications of Derivatives
Graphing Using the First Derivative
Graphing Using the First and Second Derivatives
Further Applications of Optimization
Optimizing Lot Size and Harvest Size
Implicit Differentiation and Related Rates
Cumulative Review for Chapters 1–3
Exponential and Logarithmic Functions
Exponential Functions
Logarithmic Functions
Differentiation of Logarithmic and Exponential Functions
Two Applications to Economics: Relative Rates and Elasticity of Demand
Integration and Its Applications
Antiderivatives and Indefinite Integrals
Integration Using Logarithmic and Exponential Functions
Definite Integrals and Areas
Further Applications of Definite Integrals: Average Value and Area Between Curves
Two Applications to Economics: Consumers' Surplus and Income Distribution
Integration by Substitution
Integration Techniques
Integration by Parts
Integration Using Tables
Improper Integrals
Numerical Integration
Calculus of Several Variables
Functions of Several Variables
Partial Derivatives
Optimizing Functions of Several Variables
Least Squares
Lagrange Multipliers and Constrained Optimization
Total Differentials and Approximate Changes
Multiple Integrals
Cumulative Review for Chapters 1–7
Trigonometric Functions
Triangles, Angles, and Radian Measure
Sine and Cosine Functions
Derivatives of Sine and Cosine Functions
Integrals of Sine and Cosine Functions
Other Trigonometric Functions
Differential Equations
Separation of Variables
Further Applications of Differential Equations: Three Models of Growth
First–Order Linear Differential Equations
Approximate Solutions of Differential Equations: Euler's Method
Sequences and Series
Geometric Series
Taylor Polynomials
Taylor Series
Newton's Method
Discrete Probability
Continuous Probability
Uniform and Exponential Random Variables
Normal Random Variables
Cumulative Review for Chapters 1–11
Answers to Selected Exercises
Table of Contents provided by Publisher. All Rights Reserved.

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