Applied Calculus,
7th Edition

0. PRECALCULUS REVIEW.
Real Numbers. Exponents and Radicals. Multiplying and Factoring Algebraic Equations. Rational Expressions. Solving Polynomial Equations. Solving Miscellaneous Equations. The Coordinate Plane. Logarithms.
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.

• Stefan Waner

  Stefan Waner and Steven R. Costenoble both received their Ph.D.s from the University of Chicago, having studied several years apart with the same advisor, J. Peter May. Their paths merged when Dr. Waner joined Dr. Costenoble at Hofstra University in 1987. Since then, they have coauthored 18 research papers as well as a research-level monograph in algebraic topology. By the early 1990s, they had become dissatisfied with many of the finite mathematics and applied calculus textbooks available. They wanted textbook choices that were more readable and relevant to students' interests -- texts that contained engaging examples and exercises and texts that reflected the interactive approaches and techniques they found worked well with their own students. It, therefore, seemed natural to extend their research collaboration to a joint textbook writing project that expressed these ideals. To this day, they continue to work together on textbook projects, research in algebraic topology and in their teaching.

• Steven Costenoble

  Stefan Waner and Steven R. Costenoble both received their Ph.D.s from the University of Chicago, having studied several years apart with the same advisor, J. Peter May. Their paths merged when Dr. Waner joined Dr. Costenoble at Hofstra University in 1987. Since then, they have coauthored 18 research papers as well as a research-level monograph in algebraic topology. By the early 1990s, they had become dissatisfied with many of the finite mathematics and applied calculus textbooks available. They wanted textbook choices that were more readable and relevant to students' interests -- texts that contained engaging examples and exercises and texts that reflected the interactive approaches and techniques they found worked well with their own students. It, therefore, seemed natural to extend their research collaboration to a joint textbook writing project that expressed these ideals. To this day, they continue to work together on textbook projects, research in algebraic topology and in their teaching.

• Numerous real data exercises and examples have been updated or added based on real, referenced data on topics that students will relate to, including data on numerous well-known corporations, social media, on the 2009–2016 economic recovery, and on the 2014 Ebola epidemic, while retaining those of important historical interest, such as the 2008 economic crisis, the SARS outbreak of 2003, the 2010 stock market “flash crash” and many others. The inside back cover lists over 50 corporations referenced in the applications.

• Many new conceptual Communication and Reasoning exercises, including many dealing with common student errors and misconceptions have been added.

• Logarithms are now discussed in the Precalculus Review chapter, up through solving for unknowns in the exponent. Students who need additional preparation in the basis of logarithms can now be assigned this material before studying the section on logarithmic functions and models in Chapter 2.

• Chapter 1 now downplays the algebra sophistication somewhat so as not to present artificial barriers to the mastery of the important new concepts we discuss.

• Rather than follow other books that avoid discussing the important distinction between discontinuities and domain singularities (for instance, the fact that 1/x is continuous on its domain but singular at zero), we discuss this distinction carefully, providing lots of practice and figures.

• ENHANCED WEBASSIGN: APPLIED CALCULUS, 7th Edition, is fully supported by Enhanced WebAssign (EWA), the powerful online homework and course management system that engages students in learning the math. EWA includes new end-of-chapter exercises and pre-built assignments vetted by trusted subject matter experts along with robust course, section, assignment, and question settings and online testing to help instructors foster a deeper understanding of course concepts.

• Exercises: The end-of-section exercises have been carefully curated and ordered to move from straightforward basic exercises and exercises that are similar to examples in the text to more interesting and advanced ones, marked as “more advanced” for easy reference. There are also several much more difficult exercises, designated as “challenging.” We have also included, in virtually every section of every chapter, exercises ideal for the use of technology.

• Innovative Pedagogy: Question-and-Answer Dialogues: End-of-Section FAQs, and Before We Go On: The text frequently uses informal question-and-answer dialogues that anticipate the kinds of questions that may occur to students, thereby guiding students through the development of new concepts. Most examples are followed by supplementary “Before We Go On” 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.

• 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.

• Marginal Technology Notes and End-of-Chapter Technology Guides: 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, which provide detailed TI-83/84 Plus and Spreadsheet Guides at the end of each chapter. 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.

• Examples: Many of the scenarios used in application examples and exercises are revisited several times throughout the book. In this way, students will find themselves using a variety of techniques to analyze the same application providing unifying threads that show the complex nature of real-life problems. Complete solutions are provided with every example. Most definition boxes also include quick, straightforward examples that students can use to solidify their understanding of each new concept.

• Author Website: The authors' website at www.wanermath.com has been evolving for more than a decade and provides instructors with a variety of resources -- including powerful online utilities that can be used in the classroom to do everything from graphing and evaluating functions to displaying and computing integrals and Riemann sums. In addition, instructors often use the online interactive tutorials as interactive teaching tools that invite class participation, and can use the randomized “game tutorials” for in-class quizzes that teach as they test. Online interactive text and exercises are also provided for a variety of topics not in the printed book.

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.

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