Introductory Mathematical Analysis: for Business, Economics, and the Life and Social Sciences Eleventh Edition Ernest F. Haeussler, Jr., Richard S. Paul, Richard Wood
The eleventh edition of Introductory Mathematical Analysis continues to provide a mathematical foundation for students in business, economics, and the life and social sciences. It begins with noncalculus topics such as equations, functions, matrix algebra, linear programming, mathematics of finance, and probability. Then it progresses through both single-variable and multivariable calculus, including continuous random variables. Technical proofs, conditions, and the like are sufficiently described but are not overdone. Our guiding philosophy led us to include those proofs and general calculations that shed light on how the corresponding calculations are done in applied problems. At times, informal intuitive arguments are given to preserve clarity.
Applications An abundance and variety of applications for the intended audience appear through the book; students continually see how the mathematics they are learning can be used. These applications cover such diverse areas as business, economics, biology, medicine sociology, psychology, ecology, statistics, earth science, and archeology. Many of these real-world situations are drawn from literature and are documented by references. In some, the background and context are given in order to stimulate interest. However, the text is virtually self-contained, in the sense that it assumes no prior exposure to the concepts on which the applications are based. Organization Changes to the Eleventh Edition The material from earlier editions has been rearranged to reflect what we understand to be the usage patterns of adoptees. Chapter 0 (Algebra Refresher) has been expanded and subsumes what was formerly Chapter 1 (Equations). It seems useful to us to teach the Mathematics of Finance, now Chapter 5, immediately after students have become acquainted (or reacquainted) with the Exponential and Logarithmic Functions in Chapter 4. The chapters on differentiation have been rearranged to provide more unified themes. For example, the section on Elasticity of Demand has been moved to Chapter 12 (Additional Differentiation Topics) where it is placed immediately before Implicit Differentiation, which in turn followed by Logarithmic Differentiation. All three of these topics have a similar flavour. Since Applications are stressed throughout it was decided to move the topics that formerly appeared in a Chapter titled Applications of Differentiations so as to reinforce the applicability of those topics to which they are mathematically related. In particular, Applied Maxima and Minima now provides the conclusion to Chapter 13 (Curse Sketching). Chapter 14 (Integration) and Chapter 15 (Methods and Applications of Integration) have also been rearranged as a unit, beginning with the section on Differentials. Approximate Integration (14.9) now follows the definition of the Definite Integral as a limit of sums (14.7), sooner than in earlier editions. While the Fundamental Theorem of Calculus (14.8) provides the preferred method of evaluating a define integral when the requisite antiderivative can be found, it is important for an applied text such as this to stress that the definite integral is a number that can be computed as accurately as one requires using only elementary arithmetic.