(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.

CEU Budapest, Hungary

Modified: May, 1996

Teg_Mathemat.F93Econ.v3

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