If we consider fourier f1 be Fourier cosine series and f2 be sin series after half range expansion then can we say that f1+f2 will converge at Fourier series of function f before half range expansion?
At 9:34 if you see this example, then even extension, call the function h, will have Fourier cosine series and odd extension, call the function g, will have Fourier sine series..when we add these series we will get the Fourier coefficients of the function h+g.. note that h+g is 0 on interval-4 to 0 and it will be 2 on the interval 0 to 4 which is not our initial function.
In that scenario, we take that interval itself as a full range and find it Fourier series. When we need cosine/ sine series then only we treat given range as half range. If we dont need sine / cosine then we treat given range as the whole range.
If we r asked to find Fourier cosine extension of function f(x) ,x€ [0,L] then how to express final series ,either in summation (An.cos(2nπx/L)) or in summation (An.cos(nπx/L) )
Depends on the question..if they say find sine series then we extend it in such that a say the function becomes odd and when we find its FS we only get series involving sine terms
It's neither even nor odd over real numbers. The question is to find cosine series expansion for the given function. When we want to find cosine series, we extend the function in such a way that it becomes an even function.
You have given us a wonderful concept. Thank you.
Thank you 😊
Thank u....it was really helpful....
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1000 time better than my college lectures😂❤
@@zunairashahzad3863 😀😀🙏
@@DrMathaholic sachii
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If we consider fourier f1 be Fourier cosine series and f2 be sin series after half range expansion then can we say that f1+f2 will converge at Fourier series of function f before half range expansion?
At 9:34 if you see this example, then even extension, call the function h, will have Fourier cosine series and odd extension, call the function g, will have Fourier sine series..when we add these series we will get the Fourier coefficients of the function h+g.. note that h+g is 0 on interval-4 to 0 and it will be 2 on the interval 0 to 4 which is not our initial function.
SIR BUT IF WE HAVE TO FIND FOURIER EXPANSION IN TERMS OF BOTH SINE AND COSINE TERMS OF A FUNCTION WHICH IS DEFINED ONLY ON HALF OF ITS PERIOD.
In that scenario, we take that interval itself as a full range and find it Fourier series. When we need cosine/ sine series then only we treat given range as half range. If we dont need sine / cosine then we treat given range as the whole range.
OK SIR,THANKU
If function is defined from (0, L)... Then what should be limits 0 to L or 0 to 2L
0 to L will be the limit.
If we r asked to find Fourier cosine extension of function f(x) ,x€ [0,L] then how to express final series ,either in summation (An.cos(2nπx/L)) or in summation (An.cos(nπx/L) )
A_0+ sum a_n con(n π x/L)
Why don't we can expand f(x) in full range series??
Is half range only for convenience??
Depends on the question..if they say find sine series then we extend it in such that a say the function becomes odd and when we find its FS we only get series involving sine terms
@@DrMathaholic okay then it is depend on the question.
If there is nothing say in question, I can expand f(x) in full range expansion.
Am i right??
@@sutopamodak6247 Yes , if in the question they don't say that find sine/ cosine series then you find the FS of given function over the given interval
@@DrMathaholic thank you for quick response
@@sutopamodak6247 welcome 😊
why did you consider f(x)=2-x as even function? it is supposed to be odd. very bad video.
It's neither even nor odd over real numbers.
The question is to find cosine series expansion for the given function. When we want to find cosine series, we extend the function in such a way that it becomes an even function.