Hoffmann, Table of Contents

Table of Contents

Based on extensive reviewer feedback, the following changes have been made to the organization of the text.

Focused Coverage

The focus of Calculus for Business, Economics, and the Social and Life Sciences, Seventh Edition has been improved by eliminating subjects generally viewed as unnecessary to the intended audience. Using extensive reviewer feedback, the following chapters and topics from the sixth edition have been deleted or reduced to create a more streamlined and accessible text.

Chapter 8, Sequences and Series, and Chapter 9, Trigonometric Functions , of the sixth edition have been removed from the seventh edition. (For individuals who need this material, it may still be obtained from McGraw-Hill in a customized format. Please consult with your McGraw-Hill representative for more details.)

Integration by tables, numerical integration, and L'Hopital's rule no longer appear in the text. These topics were viewed by the reviewer panel as unnecessary for business calculus students, especially for those with access to computers or calculators.

The chain rule for partial derivatives has also been deleted. There is no question that this topic is of great value for economics majors, but it was the almost unanimous opinion of the reviewing panel that its inclusion, even as an optional section, tends to disrupt the focus of the chapter on functions of several variables (Chapter 7).

The method of least squares now appears as an example in the section on optimizing functions of several variables (Chapter 7, Section 3). Purely computational aspects of least-squares approximation are illustrated in a single example and appear in few exercises, but are not strongly emphasized.

Probability density functions, which is an important application of calculus, especially for life science majors, is now introduced as a subtopic in the section on improper integrals (Chapter 6, Section 4) and joint density functions is covered as an application of double integrals (Chapter 7, Section 5).

Enhanced Pedagogical Organization
Topics are now presented so that each section corresponds roughly to a single class time period. For example, Section 1 of Chapter 5 in the sixth edition dealt with both antidifferentiation and an introduction to differential equations. In the seventh edition, each of these important topics is presented in its own section (antidifferentiation in Chapter 5, Section 1 and differential equations in Chapter 5, Section 3). Definite Integration
The material on definite integration in Chapter 6 has been revised extensively. The definite integral is now defined as the limit of a sum and is evaluated using the fundamental theorem of calculus. Applications of integration to business and economics have been gathered into Chapter 6, Section 2, while those involving other areas (sociology, physiology, ecology, demography) appear in Chapter 6, Section 3. Limits Involving Infinity
In order to illustrate the practical value of limits involving infinity, it is useful for the student to know something about graphing. For this reason, limits involving infinity have been moved from Chapter 1 to Chapter 3, where they now appear as part of the development of curve-sketching techniques. With this topic placement, limits involving infinity can be applied to finding "long-term" behavior of functions of interest.

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Annotated Brief Table of Contents

Chapter	Changes in this edition
1 Functions, Graphs, and Limits	Slope criteria for parallel and perpendicular lines has been added. The development of limits has been separated from that of continuity, and a discussion of one-sided limits has been added. There is a new introduction to the concept of continuity, and the text now includes examples involving the intermediate value property of continuous functions. Limits involving infinity and asymptotic behavior have been transferred from Chapter 1 to Chapter 3.
2 Differentiation: Basic Concepts	There is a new introduction linking slope and rate of change. The coverage of techniques of integration has been split into two smaller sections, one on the sum, multiple, and power rules and the other on the product and quotient rules. There is a new example illustrating the use of marginal cost and marginal revenue. The introduction to the chain rule has been expanded. There is a new example illustrating implicit differentiation and several new practical problems involving implicit differentiation and related rates.
3 Additional Applications of the Derivative	There is a new introductory example illustrating the practical use of graphical analysis. Techniques of curve sketching include more explanation and several new examples. There is a new section featuring limits involving infinity and graphs with asymptotes. Examples of graphs with asymptotes have been added, along with several practical problems involving asymptotic behavior. Marginal analysis and other business and economics applications are now discussed throughout the chapter instead of being concentrated in a single section. The coverage of elasticity has been significantly reduced.
4 Exponential and Logarithmic Functions	The chapter begins with a new introduction featuring exponential and logistic growth. Present value and other business and economics applications now appear throughout the chapter instead of being concentrated in a single section.
5 Integration	Antidifferentiation and differential equations are now developed in separate sections. The development of integration by substitution now includes a practical example in which substitution is used to compute demand and another example illustrating when substitution fails. Integration by tables has been deleted from this edition.
6 Further Topics in Integration	The development of definite integration has been extensively revised. In particular, the definite integral is now defined as the limit of a Riemann sum and evaluated using the fundamental theorem of calculus. There is now a separate section for applications of definite integration to business and economics and another section for applications to other areas. In response to reviewer requests, this edition includes coverage of producers' surplus and Lorentz curves. Examples and practical problems involving these topics have also been added. Coverage of numerical integration has been deleted in this edition. Coverage of probability density functions has been condensed and now appears as a subsection of the section on improper integrals.
7 Functions of Several Variables	Substitute and complementary commodities are now covered in the text. The chain rule for partial derivatives has been deleted, along with tangent plane approximations. There is a new introduction to the section on optimizing a function of two variables, and a new example dealing with minimizing total distance to a warehouse The method of least squares now appears as a subsection in the section on optimization. New examples and exercises involving the method of Lagrange multipliers have been added. In response to reviewer suggestions, the discussion of double integrals has been simplified and now involves only rectangular regions of integration.

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