MATHEMATICS
(Introductory course)

Miron Tegze and Vladimir Rogalewicz
Fall, 1993
Department of Economics
CENTRAL EUROPEAN UNIVERSITY



Main reference:

Alpha C. Chiang, "Fundamental Methods of Mathematical Economics", Third Edition, McGraw-Hill, 1984

Also recommended:
M.J. Brennan and T.M. Carroll, "Preface to Quantitative Economics and Econometrics", Forth Edition, SW Publishing company.

Content of the Lecture

A. Basic Notions

Sets, Relations, Functions. Transitivity and the choice problem.

B. Linear Algebra (Chapters 4,5)

Linear functions, solution of linear systems, degeneration, Gauss elimination procedure. Linear space, dimension, basis, linear transformations, matrixes, determinants. Particular solution and general solution of a linear equation.

C. Calculus (Chapters 6,7,E,10)

Implicit and explicit formulation and conversion between them. Basic functions and their properties. Exponential and logarithmic function.

Limits. Derivation of a real function. Rules for differentiation. Mac Laurin series. Looking for extremes. Chain rule and it's consequences. Inversion function rule.

Functions of more variables. Cuts, partial derivations, examples.

D. Unconstrained Optimization (Chapters 9,10,11)

Gradient of f. Total differential as a linear approximation of a function. First order necessary conditions. Second order conditions and Hessian.

E. Constrained Optimization (Chapters 12,21)

Level sets, geometrical intuition. Implicit function theorem. First order necessary conditions for extremes - Lagrange multipliers. Second order conditions, Bordered Hessian. Introduction to Kuhn-Tucker conditions.

F. Integral Calculus & Differential Equations (Chapters 13,14)

Short introduction to Integral calcus. Introduction to Differential equations.



CRC-Curriculum Resource Center
CEU Budapest, Hungary
Modified: May, 1996

Teg_Mathemat.F93Econ.v3

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