
Trigonometry Trigonometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
June 10th, 2014, 06:10 AM  #11 
Newbie Joined: Apr 2014 From: Singapore Posts: 7 Thanks: 0 
Btw, I realised that while the values are close, the gradients are rather different. Is there any way to make the gradients similar too? Thanks 
June 10th, 2014, 07:45 AM  #12 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,398 Thanks: 2477 Math Focus: Mainly analysis and algebra 
The limit as $n \to \infty$ of the Fourier Series is the original function $sin{x}$. So at the limit the gradients and the values are the same. In other words, you should take more terms. Of course, the closer you get to $x = n\pi$ the greater the dfference in the gradient, because $sin{x}$ is not smooth at $x = n\pi$ while the Fourier Series is smooth everywhere. 
June 11th, 2014, 04:43 AM  #13 
Newbie Joined: Apr 2014 From: Singapore Posts: 7 Thanks: 0 
Btw, I realised that while the values are close, the gradients are rather different. Is there any way to make the gradients similar too? Thanks 
June 11th, 2014, 04:59 AM  #14 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,127 Thanks: 716 Math Focus: Physics, mathematical modelling, numerical and computational solutions  

Tags 
function, positive, sine, smooth, strictly 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
nonpiecewise smooth function  mariam  Applied Math  1  December 27th, 2013 05:56 AM 
Smooth function on a smooth manifold  martexel  Real Analysis  1  November 26th, 2010 11:49 AM 
Prove an odd function is strictly increasing  xsw001  Real Analysis  3  October 24th, 2010 11:01 AM 
smooth function and its derivatives  regfor3  Real Analysis  3  November 10th, 2008 06:53 AM 
yet another smooth function problem  NoSoup4u  Real Analysis  2  November 6th, 2008 06:11 PM 