BCA-301 COMPUTER ORIENTED NUMERICAL ANALYSIS(MJPRU) Unit-I Introduction: Numbers and their accuracy, Computer Arithmetic, Mathematical preliminaries, Errors and their Computation, General error formula, Err or in a series approximation Solution of Algebraic and Transcendental Equation: Bisection Method, Iteration method, Method of false position, Newton-
Raphson method, Methods of finding complex roots, Muller’s method, Rate of convergence of Iterative methods, Polynomial equations. Unit-II Interpolation: Finite Differences, Difference tables, Polynomial Interpolation: Newton’s forward and
backward formula, Central Difference Formulae: Gauss forward and backward formula, Stirling’s, Bessel’s, Everett’s formula. Interpolation with unequal intervals: Langrange’s Interpolation, Newton Divided difference formula, Hermite’s Interpolation, Unit-III Numerical Integration and Differentiation: Introduction, Numerical differentiation Numerical
integration: Trapezoidal rule, Simpson’s 1/3 and 3/8 rule, B oole’s rule, Waddle’s rule. Unit-IV
Solution of differential Equations: Picard’s Method, Euler’s Method, Taylor’s Method, Runge -Kutta Methods, Predictor Corrector Methods, Automatic Error Mo nitoring and Stability of solution Unit-V Statistical Computation: Frequency chart, Curve fitting by method of least squares, fitting of straight lines, polynomials, exponential curves etc, Data fitting with Cubic splines, Regression Analysis, Linear and Non linear Regression, Multiple regression, Statistical Quality Control methods.
MC A106 Computer Oriented Numerical Methods (MJPRU) 1. Numerical Solution of Algebraic & Transidental Equation: Bisection method, iteration method , Newton Raphson method, Regula Falsi Method., 2. Numerical Solution of System of Equations:LINEAR EQUATIONS: Direct method Matrix inversion, Gauss Elemination, Gauss Jordon, In- teractive method-Jacobi, Gauss scidel, and their error analysis. NON-LINEAR EQUATIONS: Method of iteration, Newton Raphson Method, Eigen values & Eigen vectors, and their error analysis. Programming assignment based on above methods. 3. Interpolation & Extrapolation: Finite differences, above Methods Newton interpolation formula, Languages, Hermite interpolation and their error analysis. 4.Numerical Differentiation & Integration: Trapezoidal, Simpson’s 1/ 3 & 3/8 rule, Gauss quadridature, Conte formula. 5.Numerical Solution to Ordinary Differential Equations: Taylor series Method , Picond Method, Euler Method, Runge Kutta methods & their er ror analysis.
MCA-212: COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES (UPTU) Unit-I Floating point Arithmetic: Represe ntation of floating point numbers, Operations, Normalization, Pitfalls of floating point representation, Errors in numerical computation Iterative Methods: Zeros of a single t ranscendental equation and zeros of polynomial using Bisection Method, Iteration Method, Regula-Falsi method, Newton Raphson method, Secant method, Rate of convergence of iterative methods. Unit-II Simultaneous Linear Equations: Solutions of system of Linear equations, Gauss Elimination direct method and pivoting, Ill Conditioned system of equations, Refinement of solution. Gauss Seidal iterative method, Rate of Convergence Interpolation and approximation: Finite Differences, Difference tables Polynomial Interpolation: Newton’s forward and backward formula
Central Difference Formulae: Gauss forward and backward formula, Stirling’s, Bessel’s, Everett’s formula.
Interpolation with unequal intervals: Langrange’s Interpolation, Newton Divided difference formula, Hermite’s Interpolation Approximation of function by Taylor’s se ries and Chebyshev polynomial Unit-III Numerical Differentiation and Integration: Introduction, Numerical Differentiation, Numerical
Integration, Trapezoidal rule, Simpson’s rules, Boole’s Rule, Weddle’s Rule Euler- Maclaurin Formula Solution of differential equations: Picard’s Method, Euler’s Method, Taylor’s Method, Runge-Kutta methods, Predictor-corrector method, Automatic er ror monitoring, stability of solution. Unit-IV Curve fitting, Cubic Spline and Approximation: Method of least squares, fitting of straight lines, polynomials, exponential curves etc Frequency Chart: Different frequency chart like Histogram, Frequency curve, Pi-chart. Regression analysis: Linear and Non-linear regression, Multiple regression Unit-V Time series and forcasting: Moving averages, smoothening of curves, forecasting models and methods. Statistical Quality Controls methods Testing of Hypothesis: Test of significance, Chi-square test, t-test, ANOVA, F-Test Application to medicine, agriculture etc.
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES (UPTU) Unit-I Introduction: Numbers and their accuracy, Computer Arithmetic, Mathematical preliminaries, Errors and their Computation, General error f ormula, Error in a series approximation Solution of Algebraic and Transcendental Equation: Bisection Method, Iteration method, Method of false position, Newton-Raphson method, Methods of finding complex roots, Muller’s method, Rate of convergence of Ite rative methods, Polynomial Equations. Unit-II
Interpolation:Finite Differences, Difference tables Polynomial Interpolation: Newton’s forward and backward formula Central Difference Formulae: Gauss forward and backward formula, Stirling’s, Bessel’s, Everett’s formula. Interpolation with unequal intervals: Langrange’s Interpolation, Newton Divided difference formula, Hermite’s Interpolation, Unit-III Numerical Integration and Differentiation: Introduction, Numerical differentiation Numerical Integration: Trapezoidal rule, Simpson’s 1/3 and 3/8 rule, Boole’s rule, Waddle’s rule. Unit-IV
Solution of differential Equations: Picard’s Method, Euler’s Method, Taylor’s Method, Runge -Kutta Methods, Predictor Corrector Methods, Automatic Error Mo nitoring and Stability of solution Unit-V Statistical Computation: Frequency chart, Curve fitting by met hod of least squares, fitting of straight lines, polynomials, exponential curves etc, Data fitting with Cubic splines, Regression Analysis, Linear and Non linear Regression, Multiple regression, Statistical Quality Control methods
