Plotting Time Step Range for Temperature Profiles in Matlab/Mathematica

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Discussion Overview

The discussion focuses on plotting temperature profiles using a series approximation in Matlab or Mathematica, specifically for a range of time steps within the dimensionless time interval $t\in [0,4]$. Participants explore methods for visualizing these profiles on the same set of axes.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant presents a series approximation for temperature profiles and seeks guidance on plotting these in Matlab or Mathematica.
  • Another participant suggests a method in Mathematica involving multiple plots for different time steps and combining them using the Show function.
  • A further reply confirms the approach and emphasizes the importance of ensuring the $x$ range is appropriate for the problem context.

Areas of Agreement / Disagreement

Participants appear to agree on the general approach to plotting in Mathematica, but there is no explicit consensus on the implementation details or any potential issues that may arise.

Contextual Notes

Details regarding the specific implementation in Matlab remain unspecified, and there may be assumptions about the function definition and the range of $x$ that are not fully articulated.

Dustinsfl
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Using this series approximation, plot the temperature profiles on the same set of axes for a range of time steps in the dimensionless time interval $t\in [0,4]$ in order to visualize the process.
$$
\begin{alignat*}{3}
T(x,t) & = & 1.7624\cos(0.86x)e^{-0.86^2t} - 0.1638\cos(3.426x)e^{-3.426^2t} + 0.476\cos(6.437x)e^{6.437^2t}\\
& - & 0.0218\cos(9.529x)e^{-9.529^2t} + 0.0124\cos(12.645x)e^{-12.645^2t} - 0.0080\cos(15.771x)e^{-15.771^2t}\\
& + & 0.0055\cos(18.902x)e^{-18.902^2t} - 0.0041\cos(22.036x)e^{-22.036^2t} + 0.0031\cos(25.172x)e^{-25.172^2t}\\
& - & 0.0025\cos(38.31x)e^{-28.31^2t}
\end{alignat*}
$$
How can I do this in Matlab or Mathematica?
 
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In Mathematica, you could do something like this:

f[x_,t_]=your_function
PlotOne=Plot[... at t=0]
PlotTwo=Plot[... at t=0.5]
PlotThree=Plot[... at t=1]
.
.
.
Show[PlotOne,PlotTwo,PlotThree].
 
PlotOne = Plot[f[x,0],{x,-10,10}]

Like this?
 
Exactly. Just make sure your $x$ range corresponds to the region of interest for the problem.