Contents

1. Errors

1. Introduction

2. Accuracy of Numbers

3. Errors

4. A General Formula for Error

2. Algebraic and Transcendental Equations

1. Introduction

2. Location of Roots

3. Methods to Find the Roots

4. Newton Raphson Method

3. Calculus of Finite Differences

1. Introduction  

2. Forward Difference, Backward Difference and Shift Operators   

3. Fundamental Theorem on Differences of Polynomial  

4. Estimation of Error by Difference Table     

5. Technique to Determine the Missing Term     

4. Interpolation with Equal Interval

1. Introduction

2. Newton-Gregory Formula for Forward Interpolation (Equal Intervals)

3. Newton’s –Gregory formula for Backward Interpolation (For Equal Intervals)

3. Central Difference Formulae

4. Bessel’s Interpolation Formula

5. Interpolation with Unequal Interval

1. Introduction

2. Lagrange’s Interpolation Formula

3. Divided Differences

4. Newton’s Divided Difference Formula (Interpolation with Unequal Intervals)

5. Hermite’s Interpolation Formula

6. Numerical Integration     

1. Introduction  

2. General Quadrature Formula(For Equidistant Arguments)   

3. Trapezoidal Rule    

4. Simpson’s rd Rule   

5. Simpson’s thRule    

6. Euler-Maclaurin’s Formula  3

7. Numerical Solution of Ordinary Differential Equation

1. Introduction  

2. Euler’s Method

3. Euler’s Modified Method 

4. Runge – Kutta Methods