Is exp(-ax) a Piecewise Smooth Function?

  • Thread starter Thread starter jaejoon89
  • Start date Start date
  • Tags Tags
    Functions Smooth
jaejoon89
Messages
187
Reaction score
0
I'm trying to find a Fourier series for exp(-ax) where a is a positive constant. How is exp(-ax) piecewise smooth?
 
Physics news on Phys.org
It is piecewise smooth in one big piece :smile:

If you take piecewise smooth to mean: smooth in all but finitely many points, it satisfies the definition because the number of points in which it is not smooth is zero (< \infty).
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

Fourier Transform - Solutions Error?
Replies
5
Views
1K
Finding a Piecewise Smooth Parametric Curve for the Astroid
Replies
2
Views
2K
I have troubles finding the limit of this piecewise function
Replies
9
Views
2K
Liapunov’s Second Method proof
Replies
6
Views
1K
What is the Exponential Fourier Transform of an Even Function?
Replies
8
Views
2K
Show uniqueness in Dirichlet problem in unit disk
Replies
6
Views
1K
Write |exp(2z+i)| in terms of x and y
Replies
6
Views
2K
What Does exp Mean in Mathematical Expressions?
Replies
5
Views
1K
Fourier Series Help: Piecewise Smooth | x=-1 to 1
Replies
3
Views
2K
Proving piecewise function is k-differentiable
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top