Routledge, 2006. — 536 p. — ISBN: 0415332818, 978-0415332811.
For all students who wish to understand current economic and business literature, knowledge of mathematical methods has become a prerequisite. Clear and concise, with precise definitions and theorems, Werner and Sotskov cover all the major topics required to gain a firm grounding in this subject including sequences, series, applications in finance, functions, differentiations, differentials and difference equations, optimizations with and without constraints, integrations and much more.
Containing exercises and worked examples, precise definitions and theorems as well as economic applications, this book provides the reader with a comprehensive understanding of the mathematical models and tools used in both economics and business.Contents:
Preface.
List of abbreviations.
List of notations.
Introduction.
Logic and propositional calculus.
Sets and operations on sets.
Combinatorics.
Real numbers and complex numbers.
Sequences; series; finance.
Sequences.
Series.
Finance.
Relations; mappings; functions of a real variable.
Relations.
Mappings.
Functions of a real variable.
Differentiation.
Limit and continuity.
Difference quotient and the derivative.
Derivatives of elementary functions; differentiation rules.
Differential; rate of change and elasticity.
Graphing functions.
Mean-value theorem.
Taylor polynomials.
Approximate determination of zeroes.
Integration.
Indefinite integrals.
Integration formulas and methods.
The definite integral.
Approximation of definite integrals.
Improper integrals.
Some applications of integration.
Vectors.
Preliminaries.
Operations on vectors.
Linear dependence and independence.
Vector spaces.
Matrices and determinants.
Matrices.
Matrix operations.
Determinants.
Linear mappings.
The inverse matrix.
An economic application: input–output model.
Linear equations and inequalities.
Systems of linear equations.
Systems of linear inequalities.
Linear programming.
Preliminaries.
Graphical solution.
Properties of a linear programming problem; standard form.
Simplex algorithm.
Two-phase simplex algorithm.
Duality; complementary slackness.
Dual simplex algorithm.
Eigenvalue problems and quadratic forms.
Eigenvalues and eigenvectors.
Quadratic forms and their sign.
Functions of several variables.
Preliminaries.
Partial derivatives; gradient.
Total differential.
Generalized chain rule; directional derivatives.
Partial rate of change and elasticity; homogeneous functions.
Implicit functions.
Unconstrained optimization.
Constrained optimization.
Double integrals.
Differential equations and difference equations.
Differential equations of the first order.
Linear differential equations of order n.
Systems of linear differential equations of the first order.
Linear difference equations.
Selected solutions.
Literature.
Index.
