The book entitled Advanced Numerical Analysis book by Krishna Series has been written with a prime object to take care of fast development in the knowledge of the subject and to meet the requirements of the students of M.A./M.Sc. IIIrd Sem. of C.C.S. University, Meerut. The topics covered in this book are strictly according to the Syllabus of C.C.S. University, Meerut and which is common in most Indian Universities.
This book is important for UPSC Optional, IIT JEE Mains, Graduation College Students (For IIIrd Sem. M.A./M.Sc. Students of all Colleges affiliated to C.C.S. University, Meerut) Banking And Other Competitive Examination.
|Name of Book||Advanced Numerical Analysis|
|Author||Prof. P.P. Gupta, G.S. Malik, J.P. Chauhan|
This book is prepared as an outline series containing brief text and solved problems. Covers the complete syllabus and requirements of M.A./M.Sc. IIIrd Sem. Students.
Errors in Computation– Floating Point Representation of Numbers, Significant Digits, Rounding and Chopping a Number and Error due to these, Absolute and Relative Errors, Computation of Errors using Differentials, Errors in Evaluation of Some Standard Functions, Truncation Error. Linear Equations-Gauss Elimination Method, LU Decomposition Method, Gauss-Jordan Method, Tridiagonal System, Inversion of Matrix, Gauss-Jacobi Method, Gauss-Seidal iterative methods and their convergence Method.
Non-linear Equations-Iterative method, Secant method, Rate of convergence of Regula- Falsi method, Newton-Raphson method, Convergence of Newton-Raphson method for simple and multiple roots, Birge-Vieta method, Bairstow’s method and Graffe’s root squaring method for polynomial equations.
Numerical differentiation– Differentiation methods based on Newton’s forward and backward formulae, Differentiation by central difference formula.
Numerical integration: Methodology of numerical integration, Rectangular rule, Trapezoidal rule, Simpson’s 1/3rd and 3/8th rules, Romberg Integration, Gauss-Legendre quadrature formula.
Algebraic Eigen Values and Eigen Vectors: Power method, jacobi’s method, Given’s method, Householder’s method Approximation: Least square polynomial approximation, polynomial approximation using orthogonal polynomials, Approximation with algebraic and trigonometric functions.
Ordinary Differential Equations– Initial and boundary value problems, Solutions of Initial Value Problems, Single and multistep methods, Picard’s method, Taylor series method, Euler’s and Modified Euler’s methods, Runge-Kutta second order and fourth.