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Contents
Front Matter
1.
Introduction to Numerical Methods and Errors
2.
Root Finding Problem: (Bisection Method)
3.
Sources and Types of Errors
4.
Iterative Methods to solve equation f (x) = 0: Method of False Position
5.
Iterative Methods to solve equation f (x) = 0: Secant Method
6.
Successive approximation method for finding roots of an equation f(x) = 0
7.
Newton Raphson method for finding roots of an equation f(x) = 0
8.
Roots of polynomial equations - I
9.
Roots of polynomial equations-II
10.
Introduction and Lagrange Interpolation
11.
Lagrange Interpolation
12.
Newtons Divided Difference Interpolation-1
13.
Newton’s Divided Difference Interpolation-2
14.
Interpolation with equally spaced nodes-1
15.
Interpolation with equally spaced nodes - 2
16.
Piecewise Polynomial Interpolation
17.
Inverse Interpolation
18.
Polynomial Curve Fitting
19.
Non-Linear Curve Fitting
20.
Function Approximation
21.
Numerical Differentiation-I
22.
Numerical Differentiation-II
23.
Introduction to Numerical Integration
24.
Trapezoidal Rule and its Error Term
25.
General Newton Cotes Integration Formulas: (Particular cases: Simpsons 1/3 rule and Simpsons 3/8 rule)
26.
Error Analysis in Composite Simpsons 1/3 and 3/8 rule
27.
Open Integration formulas: Gauss Quadrature
28.
Systems of Linear equations: Motivation and Introduction
29.
Systems of Linear equations: Motivation and Introduction II
30.
Systems of Linear equations: Direct Methods-2
31.
Iterative methods for solving Systems of Linear equations
32.
Eigenvalues and Eigenvectors of real matrices-1
33.
Eigenvalues and Eigenvectors of real matrices-2
34.
Ordinary Differential Equations-I
35.
Ordinary Differential Equations-II
36.
Ordinary Differential Equations-III
37.
Numerical Analysis – Case studies
Back Matter
Numerical Methods
28
Systems of Linear equations: Motivation and Introduction
V.D. Pathak
Systems of Linear equations: Motivation and Introduction
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