**DESCRIPTION OF COURSES**

**AS 550 MATHEMATICAL METHODS (4L+0P) I**

**Objective**

This course lays the foundation of all other courses of Statistics / Agricultural Statistics discipline by preparing them to understand the importance of mathematical methods in research. The students would be exposed to the basic mathematical tools of matrix algebra, real analysis, calculus, differential equations and numerical analysis. This would prepare them to study their main courses that involve knowledge of Mathematics.

**Theory**

UNIT I

Calculus: Variables and functions, Limit and continuity, differentiation of functions, successive differentiation, partial differentiation, mean value theorems. Taylor and Maclaurin’s series. Application of derivatives, L’hospital’s rule.

UNIT II

Integration of rational, irrational and trigonometric functions. Differential equation: Differential equations of first order, linear differential equations of higher order with constant coefficient. Applications of integration in agricultural research with special reference to economics, genetics, engineering etc.

UNIT III

Matrix Algebra: Basic terminology, linear independence and dependence of vectors. Row and column spaces, Echelon form. Determinants, rank and inverse of matrices. System of linear equations. Special matrices – idempotent, symmetric, orthogonal. Eigen values and eigen vectors. Vectors and vector spaces, Matrices, notations and operations, laws of matrix algebra; transpose and inverse of matrix; Eigen values and eigen vectors. Determinants - evaluation and properties of determinants, application of determinants and matrices in solution of equations.

UNIT IV

Set theory-set operations, finite and infinite sets, operations of set, function defined in terms of sets. Numerical Analysis: Simple interpolation, Divided differences, Numerical differentiation and integration. Linear Programming: Formulation and graphical solution, simplex method, duality, transportation and assignment problem.

**Suggested Readings**

- Ahsan, Z. 2004.
*Differential Equations and Their Applications.*Prentice-hall of India Pvt. Ltd. - Bartle, R.G. 1976.
*Elements of Real Analysis.*John Wiley. - Chatterjee, S.K. 1970.
*Mathematical Analysis.*Oxford and IBH Publishing Co. - Coddington, E.A. 1989.
*An Introduction to Ordinary Differential Equations.*Dover Publications. - Frank, A. 1962. Schaum’s
*Outline of Theory and Problems of Matrices.*McGraw-Hill. - Frank, A. 1967.
*Theory and Problems of Differential Equations.*McGraw-Hill. - Gibson, G.A. 1954.
*Advanced Calculus.*Macmillan. - Hadley, G. 2002.
*Linear Programming.*Narosa Book Distributors Private Ltd. - Henrice, P. 1964.
*Elements of Numerical Analysis.*John Wiley. - Hildebrand, F.B. 1956.
*Introduction to Numerical Analysis.*Tata McGraw Hill,. - Mital, K.V. 1976.
*Optimisation Methods in Operations Research and Systems Analysis.*New Age International. - Narayan, S. 1953.
*A Text Book of Matrices.*S. Chand and Company. - Narayan, S. 1962.
*A Course of Mathematical Analysis.*S.Chand and Company, Narayan, S. 1962.*Calculus.*S. Chand and Company, - Priestley, H.A. 1985.
*Introduction to Complex Analysis.*Clarenton Press. - Rai, B., Choudhury, D.P. and Freedman, H.I. 2002.
*A Course in Ordinary Differential Equations.*Narosa - Rudin, W. 1985.
*Principles of Mathematical Analysis.*McGraw Hill. - Sauer, T. 2006.
*Numerical Analysis with CD-Rom.*Addison Wesley. - Saxena, H.C. 2007.
*Finite Differences and Numerical Analysis.*S. Chand and Company. - Scarborough, J.B. 1976.
*Numerical Mathematical Analysis.*Oxford and IBH Publishing Co. - Searle, S.R. 1982.
*Matrix Algebra Useful for Statistics.*John Wiley. - Stewart, J. 2007.
*Calculus.*Thompson. - Taha, H.A. 1996.
*Operations Research – An Introduction.*Prentice Hall. - Thomas, G.B. Jr. and Finney, R.L. 1996.
*Calculus.*Pearson Education, Inc. - Walsh, G.R. 1985.
*An Introduction to Linear Programming*. John Wiley. - Walter R. 1976.
*Principles of Mathematical Analysis.*McGraw-Hill.