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MATHEMATICAL METHODS
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CONTENTS, Interpolation and Curve Fitting, Algebraic equations transcendental equations numerical. differentiation integration, Numerical differentiation of O D E. Fourier series and Fourier transforms, Partial differential equation. Vector Calculus, TEXT BOOKS, Advanced Engineering Mathematics by Kreyszig . John Wiley Sons , Higher Engineering Mathematics by Dr B S .
Grewal Khanna Publishers, REFERENCES, Mathematical Methods by T K V Iyengar . B Krishna Gandhi Others S Chand , Introductory Methods by Numerical Analysis by. S S Sastry PHI Learning Pvt Ltd , Mathematical Methods by G ShankarRao I K . International Publications N Delhi, Mathematical Methods by V Ravindranath Etl . Himalaya Publications , REFERENCES, Advanced Engineering Mathematics with.
MATLAB Dean G Duffy 3rd Edi 2013 CRC Press, Taylor Francis Group . 6 Mathematics for Engineers and Scientists Alan, Jeffrey 6ht Edi 2013 Chapman Hall CRC. 7 Advanced Engineering Mathematics Michael, Greenberg Second Edition Pearson Education. Interpolation and Curve Fitting, Finite difference methods. Let xi yi i 0 1 2 n be the equally spaced data of the. unknown function y f x then much of the f x can be extracted. by analyzing, the differences of f x , Let x1 x0 h.
x2 x0 2h, , , , xn x0 nh be equally spaced points where the function. value of f x , be y0 y1 y2 yn, Symbolic operators. Forward shift operator E , It is defined as Ef x f x h or Eyx yx h. The second and higher order forward shift operators are. defined, in similar manner as follows, E2f x E Ef x E f x h f x 2h yx 2h. E3f x f x 3h , , , Ekf x f x kh , Backward shift operator E 1 .
It is defined as E 1f x f x h or Eyx yx h, The second and higher order backward shift operators are. defined in similar manner as follows, E 2f x E 1 E 1f x E 1 f x h f x 2h yx 2h. E 3f x f x 3h , , , E kf x f x kh , Forward difference operator . The first order forward difference operator of a function f x . with increment h in x is given by, f x f x h f x or f k f k 1 f k . k 0 1 2 , 2f x f x f x h f x f k 1 f k , k 0 1 2 .
, , Relation between E and , f x f x h f x , Ef x f x Ef x f x h . E 1 f x , E 1 E 1 , Backward difference operator nabla . The first order backward difference operator of a function f x . with increment h in x is given by, f x f x f x h or f k f k 1 f k k 0 1 2 . f x , f x f x h f x , , f k 1 f k k 0 1 2 , , . Relation between E and nabla , nabla f x f x h f x .
Ef x f x Ef x f x h , E 1 f x , nabla E 1 E 1 nabla. Central difference operator , The central difference operator is defined as. f x f x h 2 f x h 2 , f x E1 2f x E 1 2f x , E1 2 E 1 2 f x . E1 2 E 1 2, INTERPOLATION The process of finding a missed value in. the given table values of X Y , FINITE DIFFERENCES We have three finite differences.
1 Forward Difference, 2 Backward Difference, 3 Central Difference. RELATIONS BETWEEN THE OPERATORS, IDENTITIES , 1 E 1 or E 1 . 2 1 E 1, 3 E 1 2 E 1 2, 4 E1 2 E 1 2 , 5 E E E1 2. 1, 6 1 1 , , Newtons Forward interpolation formula . REFERENCES Mathematical Methods by T K V Iyengar B Krishna Gandhi amp Others S Chand Introductory Methods by Numerical Analysis by S S Sastry PHI Learning Pvt

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