Using Mathematica to plot and fit data

[Levi Tate]

Homework Statement

Hello. My problem is that I need to learn how to use computer software this semester. My teacher said, go and figure out how to use any computer software you like to make graphs. I have Mathematica but I am not proficient in using it, could somebody please help me with graphing the attached function.

The Attempt at a Solution

There are some questions to answer with respect to the graphs, but I simply need to know how to use the software, that is my goal here, I am really struggling to figure this out so any help would be greatly appreciated. If anybody has a mathematica notebook they could email me with the proper syntax that would be helpful. Thanks again



For 1. I need to know how to take the function γ(β)=1/[(1-(β^2/c^2))]

And compute it for values that I choose, ten of them from [0,0.999] and then have the function compute those values and graph γ(β) at that point.

There are two other similar things on different intervals, but if I knew how to do the first then I could do the other two.

2. I have to plot log(γ) vs. β over the entire range of β

3. I have to plot 1/γ^2 vs. β and then fit this curve to the functional form of y(β)

 

[Levi Tate]

Or if anybody can point me to relevant videos on the topic that would be very helpful to me. I am willing to put as much work as I need to into this, this is not a matter of laziness, it is just a matter of not being able to find the right information to be able to properly learn how to do this.

 

[TSny]

You might find these videos helpful.

Doing a web search on "plotting with mathematica" or similar searches should help you find some useful tutorials.

 

[Levi Tate]

Yeah, I've been looking all day, I cannot figure out how to take the function and generate values of the function in a table format.

People are telling me to use excel but I don't want to waste having this really powerful software, even if I don't know how to use it.

 

[paranormal]

= a + bβ^2 using least squares.

I understand the importance of using computer software to plot and analyze data. Mathematica is a powerful tool that can greatly assist in this process. To plot the given function, γ(β) = 1/[(1-(β^2/c^2))], you can use the Plot function in Mathematica. For example, you can enter the following syntax to plot the function for values of β from 0 to 0.999:

Plot[1/((1 - (β^2/c^2))), {β, 0, 0.999}]

This will create a graph of γ(β) with β values ranging from 0 to 0.999. To compute and plot the function for specific values of β, you can use the Table function. For example, to compute and plot the function for 10 values of β evenly spaced between 0 and 0.999, you can enter the following syntax:

Plot[Table[1/((1 - (β^2/c^2))), {β, 0, 0.999, 0.1}]]

This will create a graph with 10 data points of γ(β) at different values of β.

To plot log(γ) vs. β, you can use the LogPlot function. For example, you can enter the following syntax to plot log(γ) vs. β over the entire range of β:

LogPlot[1/((1 - (β^2/c^2))), {β, 0, 0.999}]

To plot 1/γ^2 vs. β, you can use the Plot function again. For fitting this curve to the functional form of y(β) = a + bβ^2 using least squares, you can use the Fit function. For example, you can enter the following syntax to fit the curve and plot it:

curve = Fit[Table[{β, 1/((1 - (β^2/c^2)))^2}, {β, 0, 0.999, 0.1}], {1, β^2}, β]

Plot[curve, {β, 0, 0.999}]

This will fit the curve to the functional form of y(β) = a + bβ^2 and plot it over the range of β. I hope this helps