Can you please differentiate the both using some practical or numerical examples?
Assumptions can be any thing, right or wrong!
Approximations starts from some 'exact' form and then the process of simplification begins.
However, some assumptions can also be similarly non-sensical. For example, you cannot consider a cube as a sphere, both from the point of view of assumptions and approximations!
In very simple divination, it can described as follows:
Assumption means value that you can assume, while approximation means the range.
Dear esteemed colleagues,
Yes there is difference between assumption and approximation. Assumption value may not be true value but approximation value is within the exact value. We assume to prevail upon a problem in order to arrive at a solution. For example, we which to calculate the period of oscillation of a simple pendulum and we do not know the exact acceleration due to gravity of that location. In order to solve the existing problem we have to assume a value for the acceleration due to gravity which may not be the exact value of the acceleration of that location when experimented. Then in assuming, we use the word taking the acceleration due to gravity to be 9.8 mls2 which we know may not be 100 % correct but we have to use the value to solve the problem in order to move on. The knowledge of value to be used for assumption are some things obtained from literature (that is value of that physical quantity obtained in another location).
For approximation, value are approximated when figures of the value obtained are complex or look ambiguous.
Example let say the value obtained from the calculation of the period of oscillation of the simple pendulum is
T = 2.35485939549384938484873948734899587939494 seconds
then we may decide to approximate to 2 d.p in order for the value obtained to be more clearer. it is just that the more you approximate the figures the less accurate the value obtain is.
Best regards.
Assumptions can be any thing, right or wrong!
Approximations starts from some 'exact' form and then the process of simplification begins.
However, some assumptions can also be similarly non-sensical. For example, you cannot consider a cube as a sphere, both from the point of view of assumptions and approximations!
I also agree with Prof Sengupta. Thank you very much for the simple but lucid explanation.
Cheers & Regards,
Sivakumar Subramanian
Dear colleague,
Assumptions could either be numerical or mathematical. In other words, we use assumptions to ease engineering problems by means of computational or experimental aspects. Some mathematical terms can be assumed or ignored as well as some specific numbers when such assumption have a little influences or ignored ones or when they are subjected to engineering experience. Usually, some assumptions can be taken after sensitivity analysis is conducted on some parameters.
On the other hand, approximations can be taken into account when some range of error is accepted especially when the studied problem suffers from high uncertainty.
With best regards
Nizar
For ideal condition, we start with assumption to obtain some relevant answers. However, the approximation means near known value and comparing the results with the predetermined solution or value.
layman idea: assumption- its better to have something rather nothing.
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