## Certificate course

**CERTIFICATE COURSE**;

**1 2018-2019 Vedic Mathematics**

30hours/3 Months.Text Book :Jagadguru Swami Sri Bharti Krishna Tirithaji Maharaja (1884-1960) Chapter 1 Introduction to Vedas

Definitions,Vedas,Upa Vedas.Sutras.The Work of Ancient Gurus (5hours)

Chapter 2 Applications of Vedic Sutras

Arthemetical Computations, Multiplications etc.Nikhilam Method,

Parsvartha Method ( 15 Hours)

Chapter 3 Factorisations Techniques,Qudratics And Cubics.

Partial Fractions.Pithagorozes Theoem (10 Hours)

Examination; Durations 2 Hours. External 40 Marks .Internal. 10 Marks

**2 2019-2020**** ****Mathematics for the competitive examinations**

** Syllabus** .Mathematics for the competitive examinations:

__Sequence of real numbers__, convergence of sequences, bounded and monotone sequences, convergence criteria for sequences of real numbers, Cauchy sequences, subsequences, Bolzano-Weierstrass theorem. Series of real numbers, absolute convergence, tests of convergence for series of positive terms – comparison test, ratio test, root test;Leibniz test for convergence of alternating series.__Functions of One Real Variable__: Limit, continuity, intermediate value property, differentiation, Rolle’s Theorem, mean value theorem, L’Hospital rule, Taylor’s theorem, maxima and minima.Functions of Two or Three Real Variables: Limit, continuity, partial derivatives, differentiability,maxima and minima.

__Integral Calculus__: Integration as the inverse process of differentiation, definite integrals and their properties, fundamental theorem of calculus. Double and triple integrals, change of order of integration,calculating surface areas and volumes using double integrals, calculating volumes using triple integrals.

__Differential Equations__: Ordinary differential equations of the first order of the form y’=f(x,y), Bernoulli’s equation, exact differential equations, integrating factor, orthogonal trajectories, homogeneous differential equations, variable separable equations, linear differential equations of second order with constant coefficients, method of variation of parameters, Cauchy-Euler equation. __Vector Calculus__: Scalar and vector fields, gradient, divergence, curl, line integrals, surface integrals,Green, Stokes and Gauss theorems.