MATHEMATICS For Economics, Business and The Social Sciences

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PREFACE
Mathematics is necessary for the understanding of the study economics, business and social sciences. The aim of teaching mathematics to students in the above mentioned disciplines is not to mystify the subjects but to give them the necessary background to be able to cope in a world which is becoming more and more
quantitatively and computer oriented. As future decision makers,
students of economies, business and the social sciences must be well equipped to be able to make rational decisions through the use of logical thought processes and quantitative methods.

This book is an applied mathematical text for students of economics, business and the social sciences. However, student in the natural sciences may find some of the topics useful. It is intended for students at the first three levels of tertiary education. Having thought mathematics to economies and social science students for over fifteen years, the authors intention of writing the book is borne out of the need to help students out of foundational problems in mathematics and then lead them to higher levels of learning of the subject.

Chapter one introduces the different branches of mathematics and the need for mathematics in the social sciences. Chapter two reviews basic mathematical process, coefficients, monomials and
polynomials while chapter three deals with the real number system. Chapter four treats complex numbers while chapter five introduces the theory offset. In chapter six we review the concepts of indices and logarithms. Chapter seven, eight and nine treat equations and formula. simultaneous equations and quadratic equations respectively. In chapter ten, series, sequences and progressions are treated while chapter eleven undertakes an extensive treatment of matrices. Chapter twelve discusses basic trigonometry while chapter thirteen deals with mathematics of finance.

Chapters fourteen to nineteen cover the mathematics of change.
These include differential calculus, maxima and minima, partial and total differentiation, integral calculus, differential equations and
difference equations. The economic and business applications of
matrices, mathematics of change are comprehensively handed in thisbook.

At the end of the book, answers to all the exercises are given for
different chapters.

We are grateful to various generations of students in economies and social sciences at the University of Uyo whose responsiveness and questions have assisted us in the determinations of the depth and contents of this book. We are also indebted to colleagues in our departments and the current Dean of the Faulty of Social Sciences, Professor Imoh Ukpong for their encouragement, as well as Dr. U. B. Uwatt who read the work and wrote the foreword. We are thankful to our Vice Chancellor, Professor Akpan H. Ekpo for his inspiration. He taught us to be hardworking. Finally, we are indebted to Mr. Samuel Antai of Ubique Ventures, Uyo who painstakingly typeset the book for publication. However we take responsibility for all the shortcomings that may be inherent in this book.

University of Uyo Okon J. Umoh
November2004 Emmanuel P. Udofia

Sold By Dr. Okon Umoh
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CONTENTS
Chapter 1: The different branches of mathematics and the need for mathematics in the social
Chapter 2: Basic mathematical processes, coefficients, monomials and polynomials
Chapter 3: The real number system
Chapter 4: Complex numbers
Chapter 5: Introduction to the theory of set
Chapter 6: Indices and logarithms
Chapter 7: Equations and formulae
Chapter 8: Simultaneous equations
Chapter 9: Quadratic equations
Chapter 10: Series, sequences and progressions
Chapter 11: Matrix algebra
Chapter 12: Basic trigonometry
Chapter 13: Mathematics 0f Finance
Chapter 14 Differential Calculus
Chapter 15 Maxima and minima
Chapter 16 Partial and total differentiation
Chapter 17 Integral calculus
Chapter 18 Differential equations
Chapter 19 Difference equations

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