The goal of the course is to teach students advanced topics in mathematics for Business & Economics. The course is designed to provide both intuition and deep understanding of concepts in Linear Algebra, Calculus of multiple variable functions Implicit functions, Differential Equations, Difference Equations and Constrained Optimization Methods for multiple variable functions. The first semester mathematics on Differential and Integral Calculus is a prerequisite. The course helps students familiarize real life applications that illustrate the use of mathematical concepts in business economics and technology as well as in decision sciences. During the course, students are encouraged to computer usage via modern computational platforms such as MATHEMATICA, MATLAB, and EXCEL. Specific tutorials for the Mathematica are offered during the course.
Vectors, Matrices and Linear Systems, Dimension, Rank and Linear Transformations, The Vector Space Rn, Determinants, Eigenvalues and Eigenvectors, Orthogonality, Change Basis, Solving Large Linear Systems, Implicit Functions, the Implicit Function Theorem, Introduction to Differential Equations, Modeling with Differential Equations, First Order Differential Equations, Higher Order Differential Equations, Solutions of Second Order Linear Homogeneous Differential Equations with Constant Coefficients, Solutions of Second Order Linear Nonhomogeneous Differential Equations with Constant Coefficients, Applications of Higher Order Differential Equations. Difference Equations, Calculus of Functions with Multiple Variables, Partial Derivatives, Differentiability, Extreme Values of Functions, Optimization Functions Constrained Optimization, the Method of Lagrange Multipliers