Computer Oriented Numerical Methods Syllabus

Course Code: BCA311

Course Title: Computer Oriented Numerical Methods (4 Credits)




Course Contents


 Unit 1: Errors and Computations Mathematical Preliminaries -Significant digits or Significant figures-Numbers rounded-off to n significant digits-Errors and their computations-Absolute, Relative and Percentage errors. (BC0043 – Old Unit)


Unit 2: Approximations and Round-off Errors: The Taylor Series, Error propagation, Total Numerical Error, Blunders, Formulation Errors, and data Uncertainty. (Newly Added)


Unit-3: Finite differences: E operators and relation between them, Differences of a polynomial, Factorial polynomials, differences of zero, summation series (Newly Added)


Unit 4:  Algebraic and Transcendental Equations covers Graphical and Analytical methods- Interval Halving Method - Regula-Falsi Method - Successive Approximation Method -Newton–Raphson Method, Ramanujan’s Methood. (BC0043 – Old Unit)


Unit 5:  Matrices and Solutions of Systems of Linear Equations - Direct Methods Existence of Solution of systems of linear equations-Direct Methods: Matrix Inversion method, Gauss- Jordan Method, Cramer’s rule, Gauss Elimination method, LU decomposition.  (BC0043 – Old Unit with new additions)


Unit 6: Solution System of Linear Equations – Iterative Methods deals with Gauss Jacobi Method - Gauss Seidal Method-Eigen Values and Eigen Vectors- Power Method. (BC0043 – Old Unit)


Unit 7: Curve Fitting covers method of Curve fitting - Graphical Method (Linear Law)- Method of group averages-Method of moments-Method of least squares. (BC0043 – Old Unit)


Unit-8: Interpolation with equal intervals: Newton's forward and backward interpolation formulae. Central differences formulae- Gauss forward and backward formulae, Sterling's formula and Bessel's formula. (Newly Added)


Unit-9: Interpolation with unequal intervals: Divided differences and Newton's divided differences formula for interpolation and Lagrange's formula for interpolation, Inverse Interpolation - Lagrange's method. (Newly Added)


Unit 10: Numerical Differentiation - deals with Maximum and Minimum value of a tabulated function, differentiation using Newton’s Formulae-Derivatives Using General Interpolation Formula-Difference Equations. (BC0043 – Old Unit with new additions)


Unit 11: Numerical Integration - covers Trapezoidal rule-Simpson’s one third rule-Simpson’s three eight rule, Gaussian quardrature formula. (BC0043 – Old Unit with new additions)


Unit 12: Numerical Solution of Ordinary Differential Equations – I -  Initial Value Problems-Taylor’s series method-Eulers method-Modified Euler’s (BC0043 – Old Unit with new additions)


Unit-13: Numerical Solution of Ordinary Differential Equations –II: Runge-Kutta method -Runge-Kutta second order method-Runge-Kutta fourth order method, Predictor Corrector Method: Miline's method and Adams-Moulton's method. (BC0043 – Old Unit with new additions)


Unit-14: Boundary Value Problem: Method of finite difference- Solution of BVP in PDE. (BC0043 – Old Unit)