Undergrad Rewriting a piecewise function using step functions

Click For Summary
The discussion centers on rewriting a piecewise function using the Heaviside step function. The original function is defined as f(t) = exp(c*t) for 0 <= t < 2 and f(t) = 0 for t >= 2. Participants explore the formulation f(t) = exp(at)*[H(t-0) - H(t-2)] and seek to determine the value of a. There is also a note that the function is not defined for t < 0, which raises questions about its behavior in that interval. The conversation emphasizes the importance of clearly defining the function across all intervals.
selig5560
Messages
38
Reaction score
0
TL;DR
Function properties
Suppose we have a piecewise function

f(t) = exp(c*t) when 0 <= t < 2 and f(t) = 0 when t >= 2.

Can the above be rewritten as

f(t)= exp(at)*[H(t-0) - H(t-2)],

H is a heaviside function.
 
Mathematics news on Phys.org
What is ##a##?
 
You didn't specify f(t) for t < 0.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

Undergrad Best way to fit three functions
  • · Replies 2 ·
Replies
2
Views
1K
High School Finite linear combination of continuous functions is continuous?
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Calculating the inverse of a function involving the error function
  • · Replies 3 ·
Replies
3
Views
2K
High School Sine Multiplication
  • · Replies 5 ·
Replies
5
Views
2K
MHB Piecewise-defined Function....1
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad Relevant Literature for Noisy Linear Dynamical Systems
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Alternating Harmonic Numbers are cool, spread the word!
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad My attempt to understand horizontal transformations of functions
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Looking for S-shaped function with range 0 to 1 (but not asymptotic)
  • · Replies 3 ·
Replies
3
Views
1K
MHB Evaluate Piecewise-Defined Function....1
  • · Replies 2 ·
Replies
2
Views
1K