Mathematics For Economics

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This uptodate, comprehensive and student- friendly book provides a thorough treatment of the mathematical concepts most frequently used in analyzing economic problems. Besides acquiring mathematical skills, the student is equipped to gain some knowledge of the main economic models and their properties. Divided into five parts, the text begins with a review of the fundamentals concerned primarily with sets, numbers and functions, and logically develops the ideas of limit and continuity. Then it moves on to the calculus of functions of one variable, linear algebra, multivariable calculus and, finally, dynamics. Further, the text focuses on simple game theory, L'Hopital's rule, Leibniz's rule, and the development of the Hamiltonian function. To develop the student's problem-solving skills, the text gives a large number of worked-out examples and economic applications. Senior undergraduate and postgraduate students of economics will find this text extremely useful and invaluable. Table of Contents Preface Part One: Introduction and Fundamentals 1. Introduction 2. Review of Fundamentals 3. Sequences, Series, and Limits Part Two: Univariate Calculus and Optimization 4. Continuity of Functions 5. The Derivative and Differential for Functions of One Variable 6. Optimization of Functions of One Variable Part Three: Linear Algebra 7. Systems of Linear Equations 8. Matrices 9. Determinants and the Inverse Matrix 10. Some Advanced Topics in Linear Algebra Part Four: Multivariate Calculus 11. Calculus for Functions of n-Variables 12. Optimization of Functions of n-Variables 13. Constrained Optimization 14. Comparative Statics 15. Concave Programming and the Kuhn-Tucker Conditions Part Five: Integration and Dynamic Methods 16. Integration 17. An Introduction to Mathematics for Economic Dynamics 18. Linear, First-Order Difference Equations 19. Nonlinear, First-Order Difference Equations 20. Linear, Second-Order Difference Equations 21. Linear, First-Order Differential Equations 22. Nonlinear, First-Order Differential Equations 23. Linear, Second-Order Differential Equations 24. Simultaneous Systems of Differential and Difference Equations 25. Optimal Control Theory Appendix: Complex Numbers and Circular Functions Answers Index