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Reflecting Cengage Learning's commitment to offering flexible teaching solutions and value for students and instructors, this new hybrid edition features the instructional presentation found in the printed text while delivering end-of-section exercises online in Enhanced WebAssign. The result—a briefer printed text that engages students online! Full of relevant, diverse, and current real-world applications, Stefan Waner and Steven Costenoble's APPLIED CALCULUS, Sixth Edition helps your students relate to mathematics. A large number of the applications are based on real, referenced data from business, economics, the life sciences, and the social sciences. Thorough, clearly delineated spreadsheet and TI Graphing Calculator instruction appears throughout the text. The Technology Notes and Technology Guides are optional, allowing you to include any amount of technology instruction in your courses. Acclaimed for accuracy and readability, APPLIED CALCULUS appeals to, and is appropriate for, all types of teaching and learning styles. Resources, such as the accompanying author website, allow the text to support a range of course formats, from traditional lectures to strictly online courses.
- Current Applications: Many examples and exercises based on dated information have been replaced by updated versions; those based on unique or historically interesting data have been kept. New and updated real data applications reflect topics that are of intense current interest or of general interest to contemporary students, such as Facebook, XBoxes, iPhones, Androids, iPads, foreclosure rates, the housing crisis, subprime mortgages, the BP 2011 Gulf oil spill, and the U.S. stock market "flash crash" in May 2010. The inside back cover lists corporations referenced in the applications.
- More Flexible Technology Guides: End-of-chapter Technology Guides now discuss the use of spreadsheets in general rather than focusing exclusively on Microsoft® Excel. This enables readers to use any of the several alternatives now available, such as Google's online Google Sheets®, Open Office®, and Apple's Numbers®.
- Connection Between Functions and Equations: Chapter 1 now discusses the common practice of representing functions as equations and vice versa; for instance, a cost equation like C = 10x + 50 can be thought of as defining a cost function C(x) = 10x + 50. The authors encourage students to see this connection and equip them to be able to switch from one interpretation to the other.
- Discussion of Functions in Context: Coverage of functions and models in Section 1.2 now includes a discussion of the algebra of functions presented through the context of important applications rather than as an abstract concept. This allows students to see from the outset why it's important to learn about sums, products, etc. of functions rather than simply how to manipulate them.
- Chapter 3: The material on limits now includes extensive discussions of when, and why, substitution can be used to obtain a limit. The book now also follows the usual convention of allowing only one-sided limits at endpoints of domains. This approach also applies to derivatives, where the text now disallows derivatives at endpoints of domains, as is the normal convention.
- Chapter 4: The closed-form formula for the derivative of
- , introduced in Section 4.1, is now more fully integrated into the text, as is that for its antiderivative (in Chapter 6).
- Chapter 6: The sections on antiderivatives and substitution have been reorganized and streamlined, and now include discussion of the closed-form antiderivative of
- as well as new exercises featuring absolute values. The definite integral is now introduced in the realistic context of the volume of oil released in an oil spill comparable in size to the BP 2011 Gulf oil spill.
- Chapter 8: The discussion of level curves in Section 8.1 is now more extensive, and includes added examples and exercises.
- Case Studies: A number of the Case Studies at the ends of the chapters have been extensively revised with updated real data, and continue to reflect topics of current interest, such as spending on housing construction, modeling tax revenues, and pollution control.
- Chapter Review Exercises: Chapter review exercise sets have been expanded to be more representative of the material within the chapter. Students will appreciate the applications in these exercises, all of which revolve around the fictitious online bookseller, OHaganBooks.com, and the various (and often amusing) travails of company CEO John O'Hagan and his business associate Marjory Duffin. In addition, numerous new conceptual Communication and Reasoning exercises include many dealing with common student errors and misconceptions.
- Case Studies: Each chapter ends with a Case Study, an extended application that uses and illustrates the central ideas of the chapter, focusing on the development of mathematical models appropriate to the topics. Ideal for assignment as projects, these applications conclude with groups of exercises.
- Before We Go On: Most examples are followed by supplementary discussions, which may include a check on the answer, a discussion of the feasibility and significance of a solution, or an in-depth look at what the solution means.
- Quick Examples: Most definition boxes include quick, straightforward examples that students can use to solidify their understanding of each new concept.
- Question-and-Answer Dialogues: The text frequently uses informal question-and-answer dialogues that anticipate the kinds of questions that may occur to students, and guide students through the development of new concepts.
- Marginal Technology Notes: Brief marginal technology notes outline the use of graphing calculator, spreadsheet, and website technology in appropriate examples. When necessary, the reader is referred to more detailed discussion in the end-of-chapter Technology Guides.
- End-of-Chapter Technology Guides: Detailed TI-83/84 Plus and Spreadsheet Guides at the end of each chapter are referenced liberally in marginal technology notes at appropriate points in the chapter, so instructors and students can easily use this material or not, as they prefer. Groups of exercises for which the use of technology is suggested or required appear throughout the exercise sets.
- Communication and Reasoning Exercises for Writing and Discussion: These exercises, which often have no single correct answer, are designed to broaden students' grasp of the mathematical concepts and develop modeling skills. They include exercises in which the student is asked to provide his or her own examples to illustrate a point or design an application with a given solution. They also include "fill-in-the-blank" type exercises, exercises that invite discussion and debate, and exercises in which the student must identify common errors.
- Author Website: The authors' website has been evolving for more than a decade and provides students with a personalized study resource that includes interactive tutorials, games, detailed chapter summaries, Excel tutorials, online utilities, chapter true-false quizzes, and supplemental topics. In addition, chapter summaries and many of the tutorials, game tutorials, and utilities are available in Spanish.
Real Numbers. Exponents and Radicals. Multiplying and Factoring Algebraic Equations. Rational Expressions. Solving Polynomial Equations. Solving Miscellaneous Equations. The Coordinate Plane.
1. FUNCTIONS AND APPLICATIONS.
Functions from the Numerical, Algebraic, and Graphical Viewpoints. Functions and Models. Linear Functions and Models. Linear Regression.
2. NONLINEAR FUNCTIONS AND MODELS.
Quadratic Functions and Models. Exponential Functions and Models. Logarithmic Functions and Models. Logistic Functions and Models.
3. INTRODUCTION TO THE DERIVATIVE.
Limits: Numerical and Graphical Approaches. Limits and Continuity. Limits: Algebraic Approach. Average Rate of Change. Derivatives: Numerical and Graphical Viewpoints. Derivatives: Algebraic Viewpoint.
4. TECHNIQUES OF DIFFERENTIATION.
Derivatives of Powers, Sums, and Constant Multiples. A First Application: Marginal Analysis. The Product and Quotient Rules. The Chain Rule. Derivatives of Logarithmic and Exponential Functions. Implicit Differentiation.
5. APPLICATIONS OF THE DERIVATIVE.
Maxima and Minima. Applications of Maxima and Minima. Higher Order Derivatives: Acceleration and Concavity. Analyzing Graphs. Related Rates. Elasticity.
6. THE INTEGRAL.
The Indefinite Integral. Substitution. The Definite Integral: Numerical and Graphical Approaches. The Definite Integral: Algebraic Approach and the Fundamental Theorem of Calculus.
7. FURTHER INTEGRATION TECHNIQUES AND APPLICATIONS OF THE INTEGRAL.
Integration by Parts. Area Between Two Curves and Applications. Averages and Moving Averages. Applications to Business and Economics: Consumers' and Producers' Surplus and Continuous Income Streams. Improper Integrals and Applications. Differential Equations and Applications.
8. FUNCTIONS OF SEVERAL VARIABLES.
Functions of Several Variables from the Numerical, Algebraic, and Graphical Viewpoints. Partial Derivatives. Maxima and Minima. Constrained Maxima and Minima and Applications. Double Integrals and Applications.
9. TRIGONOMETRIC MODELS.
Trigonometric Functions, Models, and Regression. Derivatives of Trigonometric Functions and Applications. Integrals of Trigonometric Functions and Applications.
Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.
Instructor's Website with Complete Solutions Manual
Complete solutions to all the problems in the text. Available as a downloadable pdf on the instructor companion site.
Instructor's Website with PowerPoint®, Image Library
Available via the instructor companion site, the PowerPoint®, Image Library for Waner/Costenoble's Applied Calculus helps you make your lectures more engaging while effectively reaching your visually oriented students.
Cengage Learning Testing, powered by Cognero® Instant Access
Cognero® is a flexible, online system that allows you to author, edit, and manage test bank content; create multiple test versions in an instant; and deliver tests from your LMS, your classroom, or wherever you want. This is available online via www.cengage.com/login.
Student Solutions Manual
The manual contains complete solutions for all odd-numbered exercises in the text, plus additional algebra steps and review for selected problems.
Student Solutions Manual
Check your work and reinforce your understanding with this manual, which contains complete solutions for all odd-numbered exercises in the text. You will also find problem-solving strategies plus additional algebra steps and review for selected problems.