S. Tan – Applied Mathematics for the Managerial Life and Social Sciences (5th edition, 2010)

Автор: S. Tan
Название книги: Applied Mathematics for the Managerial Life and Social Sciences (5th edition)
Формат: PDF
Жанр: Математика
Страницы: 952
Качество: Изначально компьютерное, E-book

Math is an integral part of our increasingly complex daily life. Applied Mathematics
for the Managerial, Life, and Social Sciences, Fifth Edition, attempts to illustrate this point
with its applied approach to mathematics. Our objective for this Fifth Edition is threefold:
(1) to write an applied text that motivates students while providing the background in the
quantitative techniques necessary to better understand and appreciate the courses normally
taken in undergraduate training, (2) to lay the foundation for more advanced courses, such
as statistics and operations research, and (3) to make the text a useful tool for instructors.
Since the book contains more than enough material for the usual two-semester or
three-semester course, the instructor may be flexible in choosing the topics most suitable
for his or her course. The following chart on chapter dependency is provided to help the
instructor design a course that is most suitable for the intended audience.

Level of Presentation
My approach is intuitive, and I state the results informally. However, I have taken special care
to ensure that this approach does not compromise the mathematical content and accuracy.
Problem-Solving Approach
A problem-solving approach is stressed throughout the book. Numerous examples and
applications illustrate each new concept and result. Special emphasis is placed on helping
students formulate, solve, and interpret the results of the problems involving applications.
Because students often have difficulty setting up and solving word problems, extra care
has been taken to help students master these skills:
■ Very early on in the text students are given practice in solving word problems (see
Example 7, Section 1.8).
■ Guidelines are given to help students formulate and solve word problems (see Section
2.7).
■ One entire section is devoted to modeling and setting up linear programming problems
(see Section 6.2).
■ Optimization problems are covered in two sections. In Section 10.4 students are asked
to solve problems in which the objective function to be optimized is given, and in Section
10.5 students are asked to solve problems in which the optimization problems must
first be formulated.
Intuitive Introduction to Concepts
Mathematical concepts are introduced with concrete, real-life examples wherever appropriate.
An illustrative list of some of the topics introduced in this manner follows:
■ The algebra of functions: The U.S. Budget Deficit
■ Mathematical modeling: Social Security Trust Fund Assets
■ Limits: The Motion of a Maglev
■ The chain rule: The Population of Americans Age 55 and Older
■ Increasing and decreasing functions: The Fuel Economy of a Car
■ Concavity: U.S. and World Population Growth
■ Inflection points: The Point of Diminishing Returns
■ Curve sketching: The Dow Jones Industrial Average on “Black Monday”
■ Exponential functions: Income Distribution of American Families
■ Area between two curves: Petroleum Saved with Conservation Measures
Connections
One example (the maglev) is used as a common thread throughout the development of calculus—
from limits through integration. The goal here is to show students the connections
between the concepts presented—limits, continuity, rates of change, the derivative, the
definite integral, and so on.
Motivation
Illustrating the practical value of mathematics in applied areas is an important objective of
my approach. Many of the applications are based on mathematical models (functions) that
I have constructed using data drawn from various sources, including current newspapers,
magazines, and the Internet. Sources are given in the text for these applied problems

Modeling
I believe that one of the important skills that a student should acquire is the ability to translate
a real problem into a mathematical model that can provide insight into the problem.
In Section 2.7, the modeling process is discussed, and students are asked to use models
(functions) constructed from real-life data to answer questions. Students get hands-on
experience constructing these models in the Using Technology sections