Tribhuvan University
Faculty of Management
Office of the Dean
Bachelor of Business Management (BBM)
Course Description
:This course deals on linear inequalities and linear programming, integration and applications in production, first-order differential equations and applications, dynamics of market price, linear algebra and applications, numerical methods for solving systems of linear equations, input/output analysis, functions of sev eral variables and their applications in business and economics, difference equations and dynamic economic analysis. Course Details
Course Objective
:The course introduces mathematical techniques through examples of their application to economic and business concepts. It also tries to get students tackling problems in economics and business using these techniques as soon as possible so that they can see how useful they are. The purpose of the course, then, is to present mathematical skills and concepts, and to apply them to ideas that are important to the management students. In addition, the course includes the basics of spreadsheet operations relating to applications of integration in business and economics, linear programming, Solving linear equations by matrix and determinant methods, application of differential equation, applications of difference equations and some numerical methods as well.
Course Contents:
Lecture hours show the approximate classroom time allocated to each unit.
Unit 1. Linear inequalities and linear programming
Linear Inequalities in two variables, Introduction to linear programming problem, Formulation of linear programming problem, Methods of solving linear programing problems: Graphical method, Simplex method (two variables), Duality and standard minimization linear programing problems. Online: Simplex method
Unit 2. Linear algebra and applications
Introduction to matrice s and types of matrices, Operation on matrices: Addition and subtraction of matrices, Scalar multiplication of a matrix, Multiplication of matrices, Transpose of matrix, Determinant of a sq uare matrix, Minors and cofactors of matrix, Singular and non -singular of matrix, Adjoint and inverse matrices, Elementary row operations, Methods of solving linear equations: Cramer’s rule, Inverse matrix method (Application of linear equation for solvi ng business and economics related problems), Gauss elimination method and Gauss - Jordan method, Input/output analysis, Technology coefficient matrix, Hawkins-Simon conditions for the viability of the system. Lab. Work: Excel for linear algebra Online: Ga uss elimination method for solving system of linear equations, Gauss -Jordan method for solving system of linear equations and finding inverse matrices
Unit 3. Integration and applications
Concept of integration, Techniques of integration (Standard form, substitution method and integration by parts), Integration of algebraic, logarithmic and exponent ial functions, Methods of evaluating definite integrals, Application of integration in business and economics ( including consumers’ surplus and producers’ surplus), Area under a curve.
Unit 4. Functions of several variables
Functions of several variables, Applications of functions of two variables in business and economics, Partial differentiation, Applications of partial differentiation, Elasticity of demand, Utility, Production, Graphical Representations, Unconstrained optimization, constrained optimization and Lagrange multipliers.
Unit 5. First-order differential equations and applications
Introduction to differential equation, Order and degree of differential equation, Solution of differential equations, First -order linea r differential equations with constant coefficient and constant term, Differential equation for limited and unlimited growth, Dynamics of market price, First order differential equation with variable - coefficient and variable term, Exact differential equat ions, Nonlinear differential equations of the first order and first degree.
Unit 6. Dynamic economic analysis and Difference equations
Introduction to difference equations, Solution of first order difference equations (homogeneous and non -homogeneous), Economic applications of first order difference equation: Cobweb model, Lagged Keynesian macroeconomic model, Duopoly price adjustment.
References:
Alpha C. Chiang, Fundamental Methods of Mathematical Economics, McGraw-Hill, Inc. Frank S. Budnick , Applied Mathematics for Business, Economics, and the Social Sciences , McGraw-Hill Ryerson Limited. G. S. Monga, Mathematics for Management and Economics , Vikas Publishing House Pvt. Ltd., New Delhi. Mike Rosser, Basic Mathematics for Economists, Routledge Taylor & Francis Group. Ronald J. Harshbarger, James J. Reynolds, Mathematical Applications for the Management , Life, and Social Sciences, Houghton Mifflin Company. Srinath Baruah, Basic Mathematics and its Application in Economics, Macmillan India Ltd. Teresa Bradley, Essential Mathematics for Economics and Business, John Wiley & Sons Ltd. Vassilis C. Mavron, Timothy N. Phillips, Mathematics for Economics and Finance , Springer- Verlag.