Mathematics for Economics

System of Linear equations: examples. General form, Matrix and Vector representation, basic techniques for solving linear system. Rank of matrix and Rouché-Capelli Theorem. Matrix algebra: basic operations, scalar and matrix multiplication. Transpose Matrix. Square Matrix. Determinant. Inverse Matrix. Special kind of matrices. Quadratic Form. Eigenvalues and Eigenvector. Real vector spaces. Linear combination, dependence and linear independence. Basis and dimension in R^n. Algebra of vectors, inner product and Norm. Linear Transformation and Linear subspaces. Basic Calculus functions of one variable. Functions of several variables: graphs of functions of Two Variables, Level Curves. Special Kinds of functions: linear functions, quadratic functions. Domain, continuity and partial derivatives. Differentiability. Directional derivatives. Gradients. Second order Derivatives. Hessian matrix. Concave and convex functions. Optimization problems: Definition of local and global minimum/maximum. First and Second order conditions for unconstrained problems. Constrained optimization: equality constraints and Lagrange Multipliers. Inequality constraints and Kuhn Tucker conditions. Linear programming (Basic)