Mathematics for Economists

Syllabus

1. Linear algebra. Arithmetic vectors (linear combination, dependence and independence). Economic interpretation of vector algebra. Matrix (transposed, unit, upper (lower) triangular, stepped, reduced stepped). Matrix operations (sum, difference, multiplication). Equivalent row adjustments to the matrix. 2. Matrix rank (equivalent adjustments). Matrix determinant. Inverse matrix (equivalent adjustments). Matrix equations. Economic interpretation of matrix algebra. 3. System of linear equations. Frobeni's theorem. Gaussian elimination method (homogeneous and inhomogeneous system). Use of software in solving problems from linear algebra. 4. Definition of a function of one real variable. (graphs of elementary functions, functional rule transformations, inverse function, domains), function of total cost (revenue, profit) and average costs (revenue, profit). Demand function. 5. Definition of function limits. Limit of a function in one's own and in one's own point. Unilateral limits. Continuity of function. Asymptotes of a function graph. 6. Differential ratio and derivation of a function of one real variable. Derivatives of elementary functions. Derivation of sum, difference, product, proportion and derivation of a compound function. Higher order derivatives. L'Hospital's rule. 7. Economic interpretation of derivation and differential. Marginal quantity, elasticity and economic interpretation. 8. Monotonicity of the function. Local extremes of function. Optimization tasks: Maximizing profit and minimizing average cost. 9. Convexity and concavity of a function. Inflection point. The concept of a function of two or more variables. Economic analysis functions (function of total cost, revenue, profit, demand function). Homogeneous function and economic interpretation (production function). 10. Partial derivatives. Higher partial derivatives. Marginal quantity, total differential and economic interpretation. 11. Partial elasticity of demand and economic interpretation. Definition of local extreme. Necessary and sufficient condition for the existence of a local extreme. Economic applications. 12. Bound extremes and economic applications. 13. Introduction to integral calculus.