Understanding the Heaviside Function: Solving the Equation for a Graph

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SUMMARY

The discussion focuses on the Heaviside function and its application in defining piecewise functions. The equation discussed is u(t) - 2u(t-2), which represents a function that is 0 for t < 0, 1 for 0 ≤ t < 2, and -1 for t ≥ 2. Participants confirm the understanding of the function's behavior, clarifying that g(t) equals 1 for 0 < t < 2, -1 for t > 2, and 0 for t < 0. The conversation highlights the importance of correctly interpreting the Heaviside function in mathematical modeling.

PREREQUISITES
  • Understanding of the Heaviside step function (u(t))
  • Familiarity with piecewise functions
  • Basic knowledge of mathematical modeling
  • Ability to interpret function graphs
NEXT STEPS
  • Study the properties of the Heaviside function in detail
  • Learn about piecewise function definitions and applications
  • Explore mathematical modeling techniques using step functions
  • Investigate the use of the Heaviside function in differential equations
USEFUL FOR

Students, mathematicians, and engineers who are working with piecewise functions and mathematical modeling, particularly those interested in the applications of the Heaviside function in various fields.

morry
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hey guys, I am having a bit of trouble finding the equation for the following graph.

I know it should look something like: u(t)-2u(t-2), but I don't really understand it.

Can someone point me in the right direction?
 

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We can't view the graph yet as it is listed as an "Attachment Pending Approval". Describe it, e.g.

u(t)-2u(t-2), is 0 for t<0, 1 for 0<=t<2, and -1 for t>=2.

Note that I have assumed that u(t) is 0 for t<0 and 1 for t>=0.
 
Oh ok. Sorry about that.

Well: g(t)= 1 for 0<t<2
and g(t)= -1 for t>2

And g(t)=0 for t<0

edit: I just read what you wrote. It sounds like what I've got. Looks like I did kinda understand what I was doing afterall. Cheers.
 
Last edited:

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