Introduction and Objectives: In today’s world the practical problems are quite complex and it may not be possible to find their analytical solutions. Hence we have to resort to oriented numerical methods for solving them. Numerical analysis provides knowledge of various techniques to get mathematical entities involved in solving the problems.
Floating–Point Arithmetic and Errors, Rounding and Chopping of a Number and Associated Errors, Floating Point Representation of Numbers, Truncation errors and Taylor’s Series
Unit 2 : Solution of Linear Algebraic EquationsPreliminaries, Direct Methods, Gauss Elimination Method (Basic), Gauss Elimination Method (Row Interchanges: Pivotal condensation),Iterative Methods, Gauss Jacobi Iterative Method, The Gauss-Seidel Iteration Method, Comparison of Direct and Iterative Methods
Unit 3 : Solution of Non-linear EquationsNon Linear Equations, Solution of Non Linear Equations, Successive Substitution Method(Fixed point method), Bisection Method ,Newton-Raphson Method, Regula-falsi Method, Secant Method
What is Interpolation, Some Operators and their Properties, Interrelation between operators, Applications of operators on some functions
Unit 2 : Interpolation with Equal IntervalsDifference Table, Interpolation Methods, Newton Forward Difference Formula, Newton Backward Difference Formula, Central Difference Formula, Stirling’s Formula, Bessle’s Formula
Unit 3 : Interpolation with Unequal IntervalsLagrange’s Method, Divided Difference Method, Divided Difference Table, Newton’s Divided Difference Method
Differentiation by Forward/Backward Difference Formula, Differentiation by Central Difference Formula
Unit 2 : Numerical IntegrationMethodology’s of Numerical Integration, Rectangular Rule, Trapezoidal Rule, Simpsons (1/3) Rule
Unit 3 : Ordinary Differential EquationInitial Value and Boundary Value Problem, Euler’s Method, Improved Euler’s Method, Runge Kutta (R-K) Methods (of Order 2 and 4)
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