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sisvu:description ELEMENTS OF LINEAR ALGEBRA Matrices. Matrix addition, multiplication of matrix by a scalar, matrix multiplication. Invers of matrix, transpose of matrix. Vector spaces. Scalar product, ortogonality of vectors, norms of vectors, distance between vectors. Subspace, linear combination, linear dependence and independence. Basis of vector space, dimension. Rank of matrix, rank and regularity (nonsingularity). Linear systems of equations. Solution and its existence. Structure of the solution set. Gauss-Jordan's algorithm. Matrix inversion. Determinants. Basic rules for determinants. Determinant and regularity. Cramer's system of equations. Systems of linear inequalities. Solution set. Convex sets, basic properties, extreme points. Linear economic models. Linear programming problem. Input-output model. Sufficient conditions for existence and nonnegativity of inverse of the technological matrix. DIFFERENTIAL CALCULUS AND APPLICATIONS Derivatives of functions of one variable. Real numbers, real functions of one real variable, limit of function, rules for limits, continuity of function. Derivative and its interpretations. Derivatives of elementary functions, derivative of invrese function and of composite function. Differential. Higher-order derivatives. Mean-value 159 theorems, Taylor's formula. Derivatives of functions of several variables. Real functions of several real variables, limit and continuity. Homogeneous functions, convex functions. Partial derivatives, total differential. Euler's theorem. Implicit functions. Partial derivatives and differentials of higherorder, Hessian matrix. Comparative static analysis. Economic models, equilibrium, comparative static analysis of states at equilibrium. Total, marginal and average functions. Elasticities and partial elasticities. Optimization problems. Global and local extrem points. Extrem points of functions of one variable, necessary and sufficient conditions. Unconstrained extrem points of functions of several variables, necessary and sufficient conditions. Extreme point (en)
sisvu:description Elementi linearne algebre. Diferencijalni računi i primjene. Integralni računi i dinamička analiza. Financijska matematika. Diskretna kapitalizacija. Neprekidna kapitalizacija. (hr)
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