Introduction to mathematical economics, 3rd ed.

Abstract

The mathematics needed for the study of economics and business continues to grow with each passing year, placing ever more demands on students and faculty alike. Introduction to Mathematical Economics, third edition, introduces three new chapters, one on comparative statics and concave programming, one on simultaneous differential and difference equations, and one on optimal control theory. To keep the book manageable in size, some chapters and sections of the second edition had to be excised. These include three chapters on linear programming and a number of sections dealing with basic elements such as factoring and completing the square. The deleted topics were chosen in part because they can now be found in one of my more recent Schaum books designed as an easier, more detailed introduction to the mathematics needed for economics and business, namely, Mathematical Methods for Business and Economics. The objectives of the book have not changed over the 20 years since the introduction of the first edition, originally called Mathematics for Economists. Introduction to Mathematical Economics, third edition, is designed to present a thorough, easily understood introduction to the wide array of mathematical topics economists, social scientists, and business majors need to know today, such as linear algebra, differential and integral calculus, nonlinear programming, differential and difference equations, the calculus of variations, and optimal control theory. The book also offers a brief review of basic algebra for those who are rusty and provides direct, frequent, and practical applications to everyday economic problems and business situations. The theory-and-solved-problem format of each chapter provides concise explanations illustrated by examples, plus numerous problems with fully worked-out solutions. The topics and related problems range in difficulty from simpler mathematical operations to sophisticated applications. No mathematical proficiency beyond the high school level is assumed at the start. The learning-by-doing pedagogy will enable students to progress at their own rates and adapt the book to their own needs. Those in need of more time and help in getting started with some of the elementary topics may feel more comfortable beginning with or working in conjunction with my Schaum’s Outline of Mathematical Methods for Business and Economics, which offers a kinder, gentler approach to the discipline. Those who prefer more rigor and theory, on the other hand, might find it enriching to work along with my Schaum’s Outline of Calculus for Business, Economics, and the Social Sciences, which devotes more time to the theoretical and structural underpinnings. Introduction to Mathematical Economics, third edition, can be used by itself or as a supplement to other texts for undergraduate and graduate students in economics, business, and the social sciences. It is largely self-contained. Starting with a basic review of high school algebra in Chapter 1, the book consistently explains all the concepts and techniques needed for the material in subsequent chapters. Since there is no universal agreement on the order in which differential calculus and linear algebra should be presented, the book is designed so that Chapters 10 and 11 on linear algebra can be covered immediately after Chapter 2, if so desired, without loss of continuity. This book contains over 1600 problems, all solved in considerable detail. To get the most from the book, students should strive as soon as possible to work independently of the solutions. This can be done by solving problems on individual sheets of paper with the book closed. If difficulties arise, the solution can then be checked in the book.