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Crash course in Scientific Computing

Latest revision as of 16:24, 8 March 2021

Crash Course in Scientific Computing

or, as officially known, The Wolverhampton Lectures on Physics: VI — Scientific Computing.

or do you mean

Crash course in Julia (programming)

When plotting pure functions, you might find that the density of points (PlotPoints in Mathematica) is not enough. This can be increased by specifying the step in the range, but in this case beware not to query your functions outside of its validity range, which would work otherwise. Compare:

plot(x->sqrt((15/x^2)-1),0,4,linewidth=5,linealpha=.5,linecolor=:red,ylims=(0,3))
plot!(x->sqrt((15/x^2)-1),0:.0001:3.8729,linewidth=2,linecolor=:blue,ylims=(0,3))

The first version can plot over the range 0–4 but does so by not plotting the full function, while the second (with x-steps of 0.0001 allowing for the nice curvature) shows everything but would return an error if going over the limit where the argument gets negative.

— • 16:24, 8 March 2021

@@ Line 3: / Line 3: @@
 or, as officially known, [[The Wolverhampton Lectures on Physics]]: [[Wolverhampton Scientific Computing|VI — Scientific Computing]].
-# [[WLP VI/I|Operating Systems]]
+{{WLPVI-content}}
-# [[WLP VI/II|$\TeX$ and $\LaTeX$]]
-# [[WLP VI/III|Computer programming]]
+or do you mean
-# [[WLV VI/IV|Julia]]
-# [[WLV VI/V|Numbers]]
+# [[WLV VI/OS|Operating Systems]]
-# [[WLV VI/VI|Random numbers]]
+# [[WLV VI/TeX|$\TeX$ and $\LaTeX$]]
-# [[WLV VI/VII|Algorithms - the idea]]
+# [[WLV VI/CP|Computer Programming]]
-# [[WLV VI/VIII|Algorithms - applications]]
+# [[WLV VI/Julia|Julia]]
-# [[WLV VI/IX|Integrals]]
+# [[WLV VI/Plotting|Plotting]]
-# [[WLV VI/X|Derivatives]]
+# [[WLV VI/Numbers|Numbers]]
-# [[WLV VI/XI|Root finding]]
+# [[WLV VI/RandomNumbers|Random numbers]]
-# [[WLV VI/XII|Better root finding]]
+# [[WLV VI/Algo1|Algorithms–the idea]]
-# [[WLV VI/XIII|Differential equations: Euler]]
+# [[WLV VI/Algo2|Algorithms–applications]]
-# [[WLV VI/XIV|Differential equations: Heun and Runge-Kutta]]
+# [[WLV VI/Complexity|Complexity]]
-# [[WLV VI/XV|Oscillators]]
+# [[WLV VI/Integrals|Integrals]]
-# [[WLV VI/XVI|Stability]]
+# [[WLV VI/Derivatives|Derivatives]]
-# [[WLV VI/XVII|Functions]]
+# [[WLV VI/Roots|Root finding]]
-# [[WLV VI/XVIII|Objects]]
+# [[WLV VI/ODE1|ODE: Euler]]
-# [[WLV VI/XIX|Librairies: the world]]
+# [[WLV VI/ODE2|ODE: Heun & Runge-Kutta]]
-# [[WLV VI/XX|Librairies: private bits]]
+# [[WLV VI/ND|Higher Dimensions]]
-# [[WLV VI/XXI|Linear algebra]]
+# [[WLV VI/LinearAlgebra|Linear algebra]]
-# [[WLV VI/XXII|DFT]]
+# [[WLV VI/DFT|Fourier and DFT]]
-# [[WLV VI/XXIII|Hyperspace]]
+# [[WLV VI/Interpolation|Interpolation]]
-# [[WLV VI/XXIV|Advanced topics]]
+# [[WLV VI/Extrapolation|Extrapolation]]
-# [[WLV VI/XXV|Fun problems]]
+# [[WLV VI/Stability|Stability and Convergence]]
+# [[WLV VI/Chaos|Chaos and fractals]]
+# [[WLV VI/OOP|Objects]]
+# [[WLV VI/Lib|Librairies]]
+# [[WLV VI/Fun|Fun problems]]
+----
+= Crash course in Julia (programming) =
+When plotting pure functions, you might find that the density of points (PlotPoints in [[Mathematica]]) is not enough. This can be increased by specifying the step in the range, but in this case beware not to query your functions outside of its validity range, which would work otherwise. Compare:
+<syntaxhighlight lang="python">
+plot(x->sqrt((15/x^2)-1),0,4,linewidth=5,linealpha=.5,linecolor=:red,ylims=(0,3))
+plot!(x->sqrt((15/x^2)-1),0:.0001:3.8729,linewidth=2,linecolor=:blue,ylims=(0,3))
+</syntaxhighlight>
+<center><wz tip="High sampling-density (blue) vs automatic (red) but less trouble-making plot of a function that becomes ill-defined outside of its domain.">[[File:Screenshot_12-03-2020_184242.jpg|400px]]</wz></center>
+The first version can plot over the range 0–4 but does so by not plotting the full function, while the second (with x-steps of 0.0001 allowing for the nice curvature) shows everything but would return an error if going over the limit where the argument gets negative.