Contents

1. Errors

1.1 Introduction

1.2 Rounding off numbers to n-significant digits and to …

1.3 Absolute, relative and percentage errors

2. Solution of Equations

2.1 Introduction

2.2 Location of roots

2.3 Descartes rules

2.4 Sturm’s theorem

2.5 Methods to find the roots

2.6 Bisection method (Half-interval Method)

2.7 Regula falsi method (The Method of False Positions)

2.8 Newton raphson method

2.9 Gauss-seidel method

3. Interpolation

3.1 Introduction

3.2 The operators ?, ? and E and their relations

3.3 Fundamental theorem of difference calculus

3.4 Newton–gregory (Forward) interpolation formula for…

3.5 Lagrange’s interpolation formula

4. Numerical Differentiation

4.1 Introduction

4.2 Derivative from newton’s forward difference formula

5. Numerical Integration

5.1 Introduction

5.2 General quadrature formula (For Equidistant Arguments)

5.3 Trapezoidal rule

5.4 Simpson’s rule: (Simpson’s One-third Rule)

5.5 Simpson’s the rule

6. Numerical Solutions of Differential Equations

6.1 Introduction

6.2 Euler’s method

6.3 Modified euler’s method

6.4 Runge–kutta methods