Home › Third Year Semester II

Computing Algorithms and Applications

IE 313  Computing Algorithms and Applications

 

Teaching Scheme

    Examination Scheme
Lectures : 3 hrs/week   Mid-Sem – 30, Assignments, Quiz -20
    End-Sem Exam- 50.

 

Unit 1

  [ 07 hrs]
Errors in Numerical Calculations: Numbers and their Accuracy, Mathematical Preliminaries, Errors and their Computation, A General Error Formula, Error in a Series Approximation Solution of Algebraic and Transcendental Equations: The Bisection Method, The Iteration Method, Acceleration of Convergence: Aitken's  -process, The Method of False Position, Newton-Raphson Method Generalized Newton's Method 2.6 Ramanujan's Method, Muller's Method, Graeffe's Root-Squaring Method, Lin-Bairstow's Method, The Quotient-Difference Method, Solution of Systems of Nonlinear Equations  
Unit 2   [ 07 hrs]
Interpolation: Errors in Polynomial Interpolation, Finite Differences, Detection of Errors by Use of Difference Tables, Differences of a Polynomial, Newton's Formulae for Interpolation, Central Difference Interpolation Formulae, Practical Interpolation, Interpolation with Unevenly Spaced Points, Interpolation with Cubic Splines, Divided Differences and their Properties, Inverse Interpolation, Double Interpolation  
Unit 3   [ 07 hrs]
Curve Fitting, B-Splines and Approximation Least-Squares Curve Fitting Procedures, Weighted Least Squares Approximation, Method of Least Squares for Continuous Functions, B-splines, Approximation of Functions 
Unit 4   [ 07 hrs]
Numerical Differentiation and Integration Numerical Differentiation, Maximum and Minimum Values of a Tabulated Function Numerical Integration, Euler-Maclaurin Formula, Adaptive Quadrature Methods Gaussian Integration, Numerical Evaluation of Singular Integrals, Numerical Calculation of Fourier Integrals, Numerical Double Integration 
Unit 5   [ 08 hrs]
Numerical Solution of Ordinary Differential Equations Solution by Taylor's Series, Picard's Method of Successive Approximations, Euler's Method, Runge-Kutta Methods, Predictor-Corrector Methods, The Cubic Spline Method, Simultaneous and Higher Order Equations, Boundary Value Problems Numerical Solution of Partial Differential Equations: Finite-Difference Approximations to Derivatives, Laplace's Equation, Parabolic Equations, Iterative Methods for the Solution of Equations, Hyperbolic Equations  
Unit 6   [ 07 hrs]
Numerical Solution of Integral EquationsFinite-Difference Methods, Chebyshev Series Method, The Cubic Spline Method, Method of Invariant Imbedding, Method Using Generalized Quadrature, A Method for Degenerate Kernels The Finite Element Method Boundary and Initial-boundary Value, Functionals, ase Functions, Methods of Approximation, The Rayleigh-Ritz Method, The Galerkin Method, Application to Two-dimensional Problems, Finite Element Method for One-dimensional Problems
Text Books    
*Introductory Methods Of Numerical Analysis by S.S. Sastry, PHI  
Reference Books    
*Numerical Analysis by Francis Scheid, TMH (Schaum’s Outlines)