TCS-302 Computer Based Numerical & Statistical Techniques
Unit-I
Introduction: Numbers and their accuracy, Computer Arithmetic, Mathematical preliminaries,
Errors and their Computation, General error formula, 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 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, Boole’s rule, Waddle’s rule.
Introduction: Numbers and their accuracy, Computer Arithmetic, Mathematical preliminaries,
Errors and their Computation, General error formula, 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 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, Boole’s rule, Waddle’s rule.
Solution of differential Equations: Picard’s Method, Euler’s Method, Taylor’s Method, Runge-Kutta Methods, Predictor Corrector Methods, Automatic Error Monitoring and Stability of solution.
Unit-IV
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.
Text Books:
1. Rajaraman V, “Computer Oriented Numerical Methods”, PHI, 3rd edition.
2. Pradip Niyogi, “Numerical Analysis and Algorithms”, TMH, 1st Edition.
3. Jain, Iyengar and Jain, “Numerical Methods for Scientific and Engineering.Computations”, New Age Int
http://findpdf.net/ebooks/books-about-numerical-methods-for-scientific-and-engineering-computation-jain-free-download.html
read online herehttp://www.math.upenn.edu/~wilf/DeturckWilf.pdf
http://www.math.upenn.edu/~wilf/website/CombinatorialAlgorithms.pdf
References:
1. Gerald & Whealey, “Applied Numerical Analyses”, AW
2. Grewal B S, “Numerical methods in Engineering and Science”, Khanna Publishers, Delhi.
3. Numerical Method Principles, analysis and algorithms ,Srimamta Pal (Oxford Highered)
4. Sastry S. S, “Introductory Methods of Numerical Analysis”, Pearson Education.
Unit-IV
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.
Text Books:
1. Rajaraman V, “Computer Oriented Numerical Methods”, PHI, 3rd edition.
2. Pradip Niyogi, “Numerical Analysis and Algorithms”, TMH, 1st Edition.
3. Jain, Iyengar and Jain, “Numerical Methods for Scientific and Engineering.Computations”, New Age Int
http://findpdf.net/ebooks/books-about-numerical-methods-for-scientific-and-engineering-computation-jain-free-download.html
read online herehttp://www.math.upenn.edu/~wilf/DeturckWilf.pdf
http://www.math.upenn.edu/~wilf/website/CombinatorialAlgorithms.pdf
References:
1. Gerald & Whealey, “Applied Numerical Analyses”, AW
2. Grewal B S, “Numerical methods in Engineering and Science”, Khanna Publishers, Delhi.
3. Numerical Method Principles, analysis and algorithms ,Srimamta Pal (Oxford Highered)
4. Sastry S. S, “Introductory Methods of Numerical Analysis”, Pearson Education.
