| 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) | ||