Advanced Numerical Analysis Prof Pp Gupta Gs Malik Jp Chauhan by Prof. P.p. Gupta, G.s. Malik, J.p. Chauhan B0967WNH5M instant download after payment.

<span>YLLABUS- ADVANCED NUMERICAL ANALYSIS,</span><br><span>Unit I</span><br><span>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.</span><br><span>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.</span><br><span>Unit II</span><br><span>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.</span><br><span>Unit III</span><br><span>Numerical differentiation- Differentiation methods based on Newton’s forward and backward formulae, Differentiation by central difference formula.</span><br><span>Numerical integration: Methodology of numerical integration, Rectangular rule, Trapezoidal rule, Simpson’s 1/3rd and 3/8th rules, Romberg Integration, Gauss-Legendre quadrature formula.</span><br><span>Unit IV</span><br><span>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.</span><br><span>Unit V</span><br><span>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.</span></br></br></br></br></br></br></br></br></br></br></br></br>