Crash Course in Scientific Computing

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

1. Computers
2. Operating Systems
3. Software
4. $\TeX$ and $\LaTeX$
5. Computation
6. Computer Programming
7. Julia
8. Plotting
9. Numbers
10. Random numbers
11. Algorithms–the idea
12. Algorithms–applications
13. Root finding
14. Linear Equations
15. Interpolation and Extrapolation
16. Fitting
17. Integrals
18. Derivatives
19. Ordinary Differential Equations
20. Differential calculus of vector fields
21. Partial Differential Equations
22. Finite elements and finite volumes
23. Fourier and DFT
24. Chaos and fractals
25. Fun problems

or do you mean

1. Operating Systems
2. $\TeX$ and $\LaTeX$
3. Computer Programming
4. Julia
5. Plotting
6. Numbers
7. Random numbers
8. Algorithms–the idea
9. Algorithms–applications
10. Complexity
11. Integrals
12. Derivatives
13. Root finding
14. ODE: Euler
15. ODE: Heun & Runge-Kutta
16. Higher Dimensions
17. Linear algebra
18. Fourier and DFT
19. Interpolation
20. Extrapolation
21. Stability and Convergence
22. Chaos and fractals
23. Objects
24. Librairies
25. 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:

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.