Graphing with Mathematica and Parameters

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SUMMARY

This discussion focuses on graphing with Mathematica, specifically for varying parameters in functions. Users are encouraged to utilize the Plot function with parameter assignments, demonstrating methods such as direct assignment, Block structures, and replacement rules. The suggested approach for plotting multiple parameter values involves using the Evaluate function to streamline the process. The conversation emphasizes practical techniques for visualizing mathematical functions based on parameter variations.

PREREQUISITES
  • Familiarity with Mathematica syntax and functions
  • Understanding of mathematical functions and parameters
  • Knowledge of the Plot function in Mathematica
  • Basic programming concepts such as variable assignment and scope
NEXT STEPS
  • Explore advanced plotting techniques in Mathematica
  • Learn about the Block function for variable scoping in Mathematica
  • Investigate the use of replacement rules in Mathematica for parameter substitution
  • Study the Evaluate function in Mathematica to optimize plotting
USEFUL FOR

Students, educators, and researchers in mathematics or engineering who need to visualize functions with varying parameters using Mathematica.

Automaton2000
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Homework Statement



Problem.jpg


Second part of Part C is: Use mathematica to draw graphs for a few values of the parameters. [ Consider the cases b > 0 and b< 0]

Homework Equations


I think you use the answer to Part A
PartA.jpg




The Attempt at a Solution


Not sure how to graph with mathematica with parameters
 
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You don't, that's why it says "for a few values of the parameters."

So you can use your favorite method to assign the parameters,
varying from the ugly
Code:
a = 1;
b = -1;
A = 6;
Plot[P[t], {t, .., ...}]
or the better
Code:
Block[
 {a = 1, b = -1, A = 6},
 Plot[P[t], {t, .., ...}]
]
to my preferred
Code:
Plot[P[t] /. {a -> 1, b -> -1, A -> 6}, {t, .., ...}]

Using something like
Code:
Plot[P[t] /. {a -> {1, 2, 3, 4}, b -> 1, A -> -2} // Evaluate, {t, 1, 
  6}]
you can even plot multiple ones in the same plot.
 

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