DESCRIPTION OF COURSES

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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