Skip to main content

Numerical Analysis lec-1 Introduction

Hi, Numerical analysis is all about mathematics, don't worry its easy subject easy to learn and to teach, So what Actually Numerical analysis is,

Simple Definition: 
When a mathematical problem can be solved analytically, its solution may be exact, but more frequently there may not be a known method of obtaining its solution.

Definition of an Errors: 
The knowledge we have of the physical world is obtained by doing experiments and making measurements. it is important to understand how to express such data and how to analyze and draw meaningful conclusion from it. in doing this it is crucial to understand that all measurements of physical quantities are subject to uncertainties. it is never possible to measure anything exactly. it is good, of course to make the error as small as possible but it is always there. and in order to draw valid conclusion the error must be indicated and dealt with properly. take the measurement of a person's height as an example:

assuming that his height has been determined to be 5' 8", how accurate is out result?
Well the height of a person depends on how straight he stands whether he just got up.

Source of Errors:
A numerical method for solving a given problem will in general, involve an error of one or several types. Although different sources initiate the error, they all cause the same effect: diversion from the Exact Answer. some errors are small and may be neglected while others may be devastating if overlooked. in all cases error analysis must accompany the computational scheme, whenever possible.

The main sources of Error are:
- Gross Errors
- Round Errors
- Truncation Errors

we will discus about types of errors in next lec.   
  
Note : read more about numerical analysis. 

Comments

Popular posts from this blog

Numerical Analysis lec-3 False Position Method

Hi, today we'll going to learn the second method of numerical analysis the False Position Method out of 40 methods FALSE POSITION METHOD False Position Method is an alternative method and is more efficient then bisection method, it is the oldest method for finding the real root of an equation F( X ) = 0 and is similar to the bisection method. Consider the equation F( X ) = 0 let [ X0 , X1 ] be two different values of X such that  F( X0 ) - F( X1 ) < 0. OR A simple modification of a secant method produces a method which is usually converges. the new method is called regula falsi (False Position) and also Linear interpolation . it needs two initial approximations X0 and X1 so that F( X0 ) F( X1 ) < 0 i.e the two functions must have the opposite signs. The Modified False Position Method In this method the F( X ) value of a stagnant end point is halved if that point has repeated twice or more. the end point that repeats its called a stagnant point, the excepti...

Software Engineering lec-2 About Software Engineering!

Hi, today we'll going to learn about Software requirements, specifications, applications and lots of more let's start with software engineering definition. Software Engineering -Software engineering is an engineering discipline that is concerned with all aspects of   software production form the early stages of system specification through to maintaining   the system after it has gone into use. -The economies of all developed nations are dependent on software. -More and more systems are software controlled software engineering is concerned with   theories, methods and tools for professional software development. -Expenditure on software represents a significant fraction of GNP in all developed countries. - Engineering discipline:  Using appropriate theories and methods to solve problems bearing in mind organizational   and financial constraints. - All aspects of software productions:  Not just technical process of developmen...

Computer Architecture lec-3 Computer System Organization

Hi, today we'll going to learn about  computer system organization & Processors so, are you ready for it.....................you will be. Computer System Organization A digital computer consists of an interconnected system of processors,  memories, and (I/O) input/output devices, This lecture is an introduction to these three  components and to their interconnection, as background for the detailed examination  of specific levels in the five succeeding lectures. Processors, memories, and (I/O)  input/output are key concepts and will be present at every level, so we'll start  our study of computer architecture by looking at all three in turn. Processors The organization of a simple bus-oriented computer is shown in Picture below. The  CPU (Central Processing Unit) is the ‘‘brain’’ of the computer. Its function is to  execute programs stored in the main memory by fetching their instructions, examining  them, and then executing them on...