Quantitative Methods

Contents . . .

Mathematical Techniques [40 Marks]

Algebra of vectors and matrices and determinants: Addition, subtraction, multiplication and inversion of vectors and matrices, solution of systems of linear equations with the help of matrix algebra.

Calculus: Variables, constants and functions – graphs of functions – limits of algebraic functions, simple differentiation of algebraic function – meaning of derivatives – evaluation of first and second order derivatives, partial differentiation; solution of problems involving maxima and minima of algebraic functions.

Integration (by substitution and by parts ) : Determining indefinite and definite integrals for simple functions – application of integration to evaluate areas and volume of solids and revolution.

Optimisation of functions under constraints , Linear programming and simplex method of solution ; other operations research methods Eg: Game theory, simulation, transportation, queuing etc.

Statistical Techniques [30 Marks]

Probabilities — meaning and definition of probability, mutually exclusive and collectively exhausting events, repeated trials, combinatorial analysis. Addition and multiplication rules. Bayes theorem and its application.

Population and samples — sampling methods, uses of random numbers, simulated sampling, concept of sampling distribution and standard errors, confidence intervals for means and percentages, testing hypothesis and sues of z, t, chi-square tests.

Decision making under risks and uncertainty ; decision tree analysis.

Simple regression and correlation.

Economic Techniques [30 Marks]

Demand Analysis — the basis of demand, market demand function, industry demand versus firm’s demand ; the demand curve ; relation between demand function and demand curve ; change and shift in demand ; demand relation and managerial decisions ; theory of consumer behaviour ; substitution and income effects ; price, income and cross elasticities of demand, other demand elasticities; time impact on elasticity ; price elasticity for derived products ; revenue concepts ; demand estimation.

Forecasting — forecasting methodologies. Time series analysis, trend protection, barometric or leading indicator method; index number analysis – composite and diffusion indices. Econometric models, curve fitting and least square methods ; correlation and regression analysis, multiple and partial correlation – input – output analysis ; fore-casting with input – output tables, criteria for forecasting demand for existing and new products.

Empirical production function analysis, empirical cost analysis, short and long run cost estimation, factor demand, joint product and multi – product firm, uncertainty in production function, profit planning under risk & uncertainty.

Recommended Books

• Kalyani Publishers
  1. Quantitative Methods
     • N. K. Nag
• Heineman
  1. Mathematics for Accountants Managers
     • R. D. Whurst
• Prentice Hall of India
  1. Applied General Statistics
     • Croxton, Cowden & Klein
• Kitab Mahal
  1. Fundamentals of Statistics
     • D. N. Elhans
• Tata Mc Graw Hill
  1. Quantitative Techniques in Management
     • N. D. Vohra
• Sultan Chand
  1. Operation Research
     • V. K. Kapoor

Other Relevant Books