NUMERICAL METHOD NOTES FOR ENGINEERING

SYLLABUS

1. Introduction 2

1.1 Introduction to Numerical Method

1.2 Needs of Numerical Methods

1.3 Number and their accuracy

1.4 Errors (Absolute, Relative, rounding off error, truncation error, general error formula)

1.5 Convergence

2. System of non-linear equations 8

2.1 Introduction

2.2 Graphical Method

2.3 The interaction Method

2.4 The bisection Method

2.5 Newton Raphson Method

2.6 Secand Method

2.7 Fixed point interaction

2.8 Zeros of polynomials by horner's method

3. Interpolation 10

3.1 Introduction

3.2 Polynomial forms

3.3 Linear interpolation

3.4 Language interpolation polynomial

3.5 Spline interpolation

3.6 Chebyshev interpolation polynomial

3.7 Least square method of fitting continuous and discrete data or function

4. Numerical differentiation and integration 5

4.1 Introduction

4.2 Numerical differentiation

4.3 Numerical integration

4.4 Numerical double integration

5. Matrices and linear systems of equations 10

5.1 Introduction

5.2 Review of the properties of matrices

5.3 Solution of linear system-direct methods

5.4 Solution of linear system- iterative methods

5.5 The eigenvalue Problem

5.6 Singular value decomposition

6. Numerical solution of ordinary differential equations 7

6.1 Introduction

6.2 Euler's method for solving ordinary differential equation of first order

6.3 Runga-Kutta methods

6.4 Predictor- Corrector methods

6.5 Simultaneous and higher order equations

6.6 Initial value problems

6.7 Boundary value problems

7. Numerical Solution of partial differential equations 3

7.1 Introduction

7.2 Finite-difference approximations to derivates

7.3 Laplace's Equation

7.4 Parabolic Equations

7.5 Iterative methods for the solution of equations

7.6 Hyperbolic equation

Laboratory:

There shall be 12 laboratory exercises using high level programming language

References:

1. Computer Oriented Numerical Methods, V. rajaraman
2. Introductory methods of Numerical analysis, S.S. Sastry
3. An Introduction to numerical computations, S. Yakowitz and F. Szidarovszky.

THE NOTES FOR ABOVE SYALLABUS  IS GIVEN IN LINK BELOW :

CLICK HERE : NEMERICAL METHOD NOTES

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