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We feel happy and honoured while presenting this book Advanced Mathematics for engineering students studying in B. Tech. IV Semester (EE and EC Branch) of Rajasthan Technical University and all Indian Universities. In this book we have presented the subject matter in very simple and precise manner. The treatment of the subject is systematic and the exposition easily understandable. All standard examples have been included and their model solutions have also been given. This book falls into five units In first and second unit we have discussed the Numerical Analysis. The unit I deals with Finite Difference—Forward, Backward and Central difference, Newton’s formula for Forward and Backward differences, Interpolation, Stirling’s formula and Lagrange’s interpolation formula. Solution of nonlinear equations in one variable by Newton-Raphson method, Simultaneous algebraic equation by Gauss and Regula-Falsi method, Solution of simultaneous equations by Gauss elimination and Gauss Seidel methods, Fitting of curves (straight line and parabola of second degree) by method of least squares are also discussed. In unit II, we have discussed Numerical differentiation, Numerical Integration, Trapezoidal rule, Simpson’s one-third and three-eighth rules. Numerical solution of ordinary differential equations of first order, Picard’s method, Euler’s and modified Euler’s methods. Miline’s method and Runga-Kutta fourth order method, Simple linear difference equations with constant coefficients are also discussed in the unit. Unit III deals with the special functions, Bessel’s functions of first and second kind, Simple recurrence relations, Orthogonal property of Bessel’s transformation and generating functions. Legendre’s function of first kind, Simple recurrence relations, Orthogonal property and generating function are also discussed. In unit IV, the basic principles of probability theory is given in order to prepare the background for its application to various fields. Baye’s theorem with simple applications, Expected value, Theoretical probability distributions—Binomial, Poisson and Normal distributions are discussed. Unit V deals with Lines of regression, concept of simple Co-relation and Rank correlation. Ztransforms, its inverse, simple properties and application to difference equations are also discussed. We are grateful to New Age International (P) Limited, Publishers and the editorial department for their commitment and encouragement in bringing out this book within a short span of period