List of Figures

1. Recommended Text Books.
2. Running a Computer Program.
3. NumPy Module Organization.
4. SciPy Modules.
5. Level of precision.
6. Computer numbers with six bit representation.
7. Upper: number line in the hypothetical system, Lower: IEEE standard.
8. Output of sinser.py
9. Output and Plot of trunroun.py
10. Output of newtsqrt.py
11. Variation of energy density with wavelength/frequency in blackbody radiation.
12. Testing for a change in sign of f(x) will bracket either a root or singularity.
13. Code and plot of the function: $f(x)=3x + sin(x) - e^x$
14. The stopping criterion for a root-finding procedure should involve a tolerance on $x$, as well as a tolerance on $f(x)$.
15. Graphical illustration of the Secant Method.
16. Graphical illustration of the Newton's Method.
17. Forward-difference approximation for $f(x)=e^x sin(x)$.
18. Backward-difference approximation for $f(x)=e^x sin(x)$.
19. Central-difference approximation for $f(x)=e^x sin(x)$.
20. Time change of position and velocity in motion under the force F=-kx.
21. Simple pendulum.
22. The trapezoidal rule.
23. Integration for $f(x)=e^x$ by the trapezoidal rule.
24. Solution of the differential equation $dy/dx=x+y$ in the interval [0, 1] by Euler method.
25. Solution of the differential equation $dy/dx=x+y$ in the interval [0, 1] by Euler method.
26. Numerical solution of projectile motion with and without air friction. (Example py-file: airfriction.py)
27. Numerical solution of planetary motion. There can be closed orbits (ellipse), or solutions going to infinity (unbounded, hyperbola) for different velocities. (Example py-file: planetarymotion.py)
28. First guess.
29. Second guess.
30. Expected result.
31. Solution for the Boundary Value Problem for the ODE: $y''(x)-(4x^2-2)y=0$.
32. Solution for the Boundary Value Problem for the ODE: $y''(x)-(4x^2-2)y=0$.
33. The region between two spherical shells of different potential.
34. Solution for the Boundary Value Problem for the ODE: $V''=-\frac {2}{r}V'$.
35. Solution for the Boundary Value Problem for the ODE: $V''=-\frac {2}{r}V'$.
36. Solution for the Eigenvalue Problem for the ODE: $\frac {dy_2}{dx}=-k^2y_1$.
37. Solution for the Eigenvalue Problem for the ODE: $\frac {dy_2}{d\rho }=\left [ \frac {l(l+1)}{\rho ^2} -\left ( \frac {\lambda }{\rho }-\frac {1} {4}\right ) \right ] y_1$.
38. Solution for the Eigenvalue Problem for the ODE: $\frac {dy_2}{d\rho }=\left [ \frac {l(l+1)}{\rho ^2} -\left ( \frac {\lambda }{\rho }-\frac {1} {4}\right ) \right ] y_1$.
39. First 6 Legendre Polynomials $P_{\ell }(x)$ with Recursion Relation: $P_{\ell }(x)=\frac {1}{\ell }[(2\ell -1)xP_{\ell -1}(x)-(\ell -1)P_{\ell -2}(x)]$.
40. Plot of first 6 $P_{\ell }(x)$.
41. First 6 Hermite Polynomials $H_{k}(x)$ with Recursion Relation: $H_{k+1}(x)=2xH_k(x)-2k H_{k-1}(x)$.
42. Plot of first 6 $H_{k}(x)$.
43. Wavefunction representations for the first 5 bound eigenstates, $\nu = 0 - 4$.
44. Corresponding probability densities.
45. Steps in Gaussian elimination and back substitution without pivoting.
46. Kirchhoff's Rules in Gaussian elimination & back substitution. No pivoting.
47. Steps in Gaussian elimination and back substitution with pivoting.
48. (a) Without Pivoting (b) With Pivoting.
49. Mass-Spring system.
50. Polynomial Interpolation.
51. Polynomial Interpolation - Gasoline Case.
52. Lagrange Polynomial Interpolation - Gasoline Case.
53. Fitting with different degrees of the polynomial.
54. Fitting with quadratic in subinterval.
55. Linear spline.
56. Cubic spline.
57. Resistance vs Temperature graph for the Least-Squares Approximation.
58. Minimizing the deviations by making the sum a minimum.
59. Polynomial Least-Square Approximation.
60. Millikan oil-drop experiment.