Applied Calculus (5th Edition) by Deborah Hughes-Hallett
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About this book :-
Applied Calculus (5th Edition) written by
Deborah Hughes-Hallett .
This book is praised for the creative and varied conceptual and modeling problems which motivate and challenge students. The 5th Edition of this market leading text exhibits the same strengths from earlier editions including the "Rule of Four," an emphasis on concepts and modeling, exposition that students can read and understand and a flexible approach to technology. Updated data and fresh applications throughout the book are designed to build student confidence with basic concepts and to reinforce skills. As in the previous edition, a Pre-test is included for students whose skills may need a refresher prior to taking the course.
Book Detail :-
Title: Applied Calculus
Author(s): Deborah Hughes-Hallett
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About Author :-
The author Deborah J. Hughes Hallett is a mathematician who works as a professor of mathematics at the University of Arizona. Her expertise is in the undergraduate teaching of mathematics. She has also taught as Professor of the Practice in the Teaching of Mathematics at Harvard University, and continues to hold an affiliation with Harvard as Adjunct Professor of Public Policy in the John F. Kennedy School of Government.
Hughes Hallett earned a bachelor's degree in mathematics from the University of Cambridge in 1966, and a master's degree from Harvard in 1976. She worked as a preceptor and senior preceptor at Harvard from 1975 to 1991, as an instructor at the Middle East Technical University in Ankara, Turkey from 1981 to 1984, and as a faculty member at Harvard from 1986 to 1998. She served as Professor of the Practice in the Teaching of Mathematics at Harvard from 1991 to 1998. She moved to Arizona in 1998, and took on her adjunct position at the Kennedy School in 2001.
With Andrew M. Gleason at Harvard she was a founder of the Calculus Consortium, a project for the reform of undergraduate teaching in calculus. Through the consortium, she is an author of a successful and influential sequence of high school and college mathematics textbooks. However, the project has also been criticized for omitting topics such as the mean value theorem, and for its perceived lack of mathematical rigor.
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Book Contents :-
Applied Calculus (5th Edition) written by
cover the following topics.
1. Functions and Change
Introduces the concept of a function and the idea of change, including the distinction between total change, rate of change, and relative change. All elementary functions are introduced here. Although the functions are probably familiar, the graphical, numerical, verbal, and modeling approach to them is likely to be new. We introduce exponential functions early, since they are fundamental to the understanding of real-world processes. The trigonometric functions are optional. A brief introduction to elasticity has been added to Section 1.3.
2. Rate of Change: The Derivative
Presents the key concept of the derivative according to the Rule of Four. The purpose of this chapter is to give the student a practical understanding of the meaning of the derivative and its interpretation as an instantaneous rate of change. Students will learn how the derivative can be used to represent relative rates of change. After finishing this chapter, a student will be able to approximate derivatives numerically by taking difference quotients, visualize derivatives graphically as the slope of the graph, and interpret the meaning of first and second derivatives in various applications. The student will also understand the concept of marginality and recognize the derivative as a function in its own right. Focus on Theory: This section discusses limits and continuity and presents the symbolic definition of the derivative.
3. Short-Cuts to Differentiation
The derivatives of all the functions in Chapter 1 are introduced, as well as the rules for differentiating products, quotients, and composite functions. Students learn how to find relative rates of change using logarithms. Focus on Theory: This section uses the definition of the derivative to obtain the differentiation rules. Focus on Practice: This section provides a collection of differentiation problems for skill-building.
4. Using the Derivative
The aim of this chapter is to enable the student to use the derivative in solving problems, including optimization and graphing. It is not necessary to cover all the sections.
5. Accumulated Change: The Definite Integral
Presents the key concept of the definite integral, in the same spirit as Chapter 2. The purpose of this chapter is to give the student a practical understanding of the definite integral as a limit of Riemann sums, and to bring out the connection between the derivative and the definite integral in the Fundamental Theorem of Calculus. We use the same method as in Chapter 2, introducing the fundamental concept in depth without going into technique. The student will finish the chapter with a good grasp of the definite integral as a limit of Riemann sums, and the ability to approximate a definite integral numerically and interpret it graphically. The chapter includes applications of definite integrals in a variety of contexts, including the average value of a function. Chapter 5 can be covered immediately after Chapter 2 without difficulty. The introduction to the definite integral has been streamlined. Average values, formerly in Section 6.1, are now in Section 5.6. Focus on Theory: This section pre
sents the Second Fundamental Theorem of Calculus and the properties of the definite integral.
6. Antiderivatives and Applications
This chapter combines the former Chapter 6 and 7. It covers antiderivatives from a graphical, numerical, and algebraic point of view. The Fundamental Theorem of Calculus is used to evaluate definite integrals. Optional application sections are included on consumer and producer surplus and on present and future value; the integrals in these sections can be evaluated numerically or using the Fundamental Theorem. The chapter concludes with optional sctions on integration by substitution and integration by parts. Section 6.1, on graphical and numerical antiderivatives, is based on the former Section 7.5. Section 6.2, on symbolic antiderivatives, is based on the former Section 7.1. Using the Fundamental Theorem to find definite integrals is in Section 6.3, formerly Section 7.3. Sections 6.4 and 6.5 are the former Sections 6.2 and 6.3. Sections 6.6 and 6.7 are the former Sections 7.2 and 7.4. Focus on Practice: This section provides a collection of integration problems for skill-building.
This chapter covers probability density functions, cumulative distribution functions, the median and the mean. Chapter 7 is the former Chapter 8.
8. Functions of Several Variables
This chapter introduces functions of two variables from several points of view, using contour diagrams, formulas, and tables. It gives students the skills to read contour diagrams and think graphically, to read tables and think numerically, and to apply these skills, along with their algebraic skills, to modeling. The idea of the partial derivative is introduced from graphical, numerical, and symbolic viewpoints. Partial derivatives are then applied to optimization problems, ending with a discussion of constrained optimization using Lagrange multipliers. Chapter 8 is the former Chapter 9. Focus on Theory: This section uses optimization to derive the formula for the regression line.
9. Mathematical Modeling Using Differential Equations
10. Geometric Series
This chapter covers geometric series and their applications to business, economics, and the life sciences. Chpater 10 is the former Chapter 11.
The first appendix introduces the student to fitting formulas to data; the second appendix provides further discussion of compound interest and the definition of the number e. The third appendix contains a selection of spreadsheet projects.
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