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.
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.
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