101: Business Mathematics
Objective: The objective of this paper is to enable the students to have such minimum knowledge of Mathematics as is applicable to business and economic situations.
UNIT-I (20 Marks)
Theory of Sets: Definitions, types of sets, operations on sets, verification of the laws of algebra of sets, order of a set, application of sets. Arithmetic Progression (A.P.) and Geometric Progression (G.P.): Definition, sum of A.P. and G.P. series, arithmetic and geometric means, application of A.P. and G.P. in solving business problems.
Logarithm: Introduction, laws of logarithm, logarithmic tables.
Compound Interest and Annuities: Compound amount at changing rates, normal and effective rates of interest, present value, equation of value, discount, depreciation, methods of computing annual depreciation, types of annuities, present value and amount of an annuity, amortization of loans, sinking funds.
UNIT-II (20 Marks)
Determinants and Matrices: Determinants of second and third order, properties of determinant, simple problems, solutions of simultaneous equations and solutions of business problems involving simultaneous equations by Cramer’s rule, definition of matrices over real numbers, types of matrices, matrix operations, transpose of a square matrix, inverse of a matrix through adjoint, application of matrices in solving business problems.
Permutation and Combination: Permutation: fundamental principle, factorial notation, permutation of things all different, permutation in which things may be repeated, simple problems; Combination: Combination of things all different, simple problems Statement of binomial theorem for positive integral index.
UNIT-III (10 Marks)
Co-ordinate Geometry of Two Dimensions: Idea of cartesian co-ordinates; slope or gradient of a line; equation of a line passing through (i) one given point, (ii) two given points; equation of a line in slope-intercept from (y = mx+c) and intercepts from (x/a+ y/b= 1); application of equations of straight lines in solving business problems, point of intersection of two lines.
UNIT-IV (20 Marks)
Calculus (Theorems and problems involving trigonometric functions are excluded)
Differential Calculus: Concepts of function, limit and continuity, graphs of functions, definition of derivative, rules for differentiation, geometrical interpretation of derivative, derivative of a function of a function, derivative as a rate measurer, second order derivative, maximum and minimum of functions involving one variable only, concept of partial derivative.
Integral Calculus: Integration as anti-derivative; integration of xn, logx, ex; rules for integration, integration by substitution and by parts, concept of definite integral and simple problems.
Application of calculus: Emphasis must be given on the application of calculus in solving economic and business problems. Problems relating to production, cost, revenue, profits, producer’s surplus, consumer’s surplus, evaluation of marginal products in case of two factor inputs are to be treated.
UNIT-V (10 Marks)
Linear Programming (L.P.): Meaning, assumption, formulation, uses, limitation, solutions of LPP involving two variables by graphical method.
1. Business Mathematics, D.R. Agarwal, Vrinda Publications (P) Ltd.
2. A. Textbook of Business Mathematics, Padmalochan Hazarika, S. Chand.
3. Business Mathematics and Statistics –A.p. Verma, Asian BooksPvt. Ltd.
4. Business Mathematics, J.K. Singh, Himalaya Publishing House.
5. Business Mathematics, and Statistics, R.K. Ghosh, S. Saha, New Central Book Agency (Pvt.) Ltd.
6. Basic Mathematics- RGD Allen- Macmillan, New Delhi.
7. Mathematics for Economics –Dowling E.T. –Schawn Series, McGraw Hill, London.
8. Mathematics for Business studies –J.K. Thukural –Mayoor Paperbacks.
9. Mathematics and Statistics –Goel, Ajoy and Aloka, Taxman Allied Servies (P) Ltd.