Errata

Corrections and clarifications to the text of the printed version of the book appear here.

p. 10 (Example E2.1) The second note ① is a bit careless: int truncates a floating point number towards zero rather than "rounding down" in casting it to an integer. For example, int(-1.4) is -1, not -2.

p. 17 (Table 2.4) The list of Python 3 keywords is incomplete: in addition to those given, False, True, None, as and with are reserved keywords. The identifier print is no longer a keyword in Python 3 but it does refer to the print function and so should be avoided as a variable name.

p. 34 (E2.13) There is no space after Fortran in the string b, so this word will not get an exclamation mark after it as a result of c = b.replace(' ', '!\n'). This is correctly shown when the string literal c is echoed back at the command prompt, but the print(c) call following that incorrectly shows Fortran! as the fourth line of output.

p. 41 (P2.3.4) The NASA page of planet symbols has moved to https://solarsystem.nasa.gov/resources/680/solar-system-symbols/.

p. 56 (P2.4.7) The file defining the list of protein lengths to use in the second part of this exercise on Benford's Law is called protein_lengths.py, not ex2-4_e_ii_protein_lengths.py. It can be downloaded from the online version of the exercise..

p. 76 (§2.7.4) "the it points to" $\rightarrow$ "the object it points to". This whole sentence should then read:

When a name is passed to a function, the "value" that is passed is, in fact, the object it points to.

p. 89 (P3.1.3) There is a missing minus sign in the exponential defining the Gaussian function, which should read $$g(x) = \frac{1}{\sigma\sqrt{2\pi}}\exp\left( -\frac{x^2}{2\sigma^2} \right).$$ [Thanks to Ivan Yeung for spotting this typo].

p. 91 The URL in footnote 2 should be https://matplotlib.org/api/markers_api.html.

p. 151 The last format specifier in the print statement is incorrect. This line should read

print('The balance of account number {:d} is {:s}{:.2f}'
.format(self.account_number, self.currency, self.balance))

p. 216 (P6.1.3) There is a missing minus sign in the exponential defining the Gaussian function, which should read $$g(x) = \frac{1}{\sigma\sqrt{2\pi}}\exp\left( -\frac{(x-\mu)^2}{2\sigma^2} \right)$$ [Thanks to Ivan Yeung for spotting this typo].

p. 218 (E6.6) The "missing data" entries in the blood pressure column should be -/- instead of - for Listing 6.4 on the following page to work properly. [Thanks to Stafford Baines for spotting this].

p. 232 (P6.3.2) np.hist should be np.histogram

p. 245 (P6.4.1) The exponent of time in the equation for $R(t)$ should be $+\frac{2}{5}$: $R(t) = CE^{\frac{1}{5}}\rho_\mathrm{air}^{-\frac{1}{5}}t^{\frac{2}{5}}$

p. 247 (P.6.4.4) The constant, $R = 8.314\;\mathrm{J\,K^{-1}\,mol^{-1}}$, should have been defined for this problem.

p. 262 (P6.6.3) The classification of conic sections in terms of its matrix representation should read as follows:

• If $\mathrm{det} \mathbf{Q} = 0$, the conic is degenerate in one of the following forms:

• if $\mathrm{det} \mathbf{Q}_{33} < 0$, the equation represents two intersecting lines,

• if $\mathrm{det} \mathbf{Q}_{33} = 0$, the equation represents two parallel lines,

• if $\mathrm{det} \mathbf{Q}_{33} > 0$, the equation represents a single point.

• If $\mathrm{det} \mathbf{Q} \ne 0$:

• if $\mathrm{det} \mathbf{Q_{33}} < 0$ the conic is a hyperbola,

• if $\mathrm{det} \mathbf{Q_{33}} = 0$ the conic is a parabola,

• if $\mathrm{det} \mathbf{Q_{33}} > 0$, the conic is an ellipse:

• if $A=C$ and $B=0$, the ellipse is a circle.

[Thanks to Stuart Anderson for spotting this.]

p. 275 The first two lines of code at the bottom of this page:

In [x]: spec = 2/n * np.abs(F[:n/2])
In [x]: pylab.plot(freq[:n/2], spec, 'k')

should use integer division in the array slice:

In [x]: spec = 2/n * np.abs(F[:n//2])
In [x]: pylab.plot(freq[:n//2], spec, 'k')

p. 279 (P6.8.3) The line of code:

sample_rate, wav = wavfile.read(\emph{<filename>})

sample_rate, wav = wavfile.read(<filename>)

where <filename> is the name of the .wav file to read in.

p. 281 (§7.1.1) The code line:

line_quad, = ax.plot(x, x**2 / 2)

line_quad, = ax.plot(x, 1 + x**2 / 2)

p. 293 (Paragraph under "Error bars" subheading): The pyplot function referred to is called errorbar, not errorbars.

p. 293 The three NumPy arrays, x, y and yerr should be created by calling np.array rather than simply array if NumPy has been imported as np, as recommended.

p. 297 (E7.8) The data should be loaded into an array with dtype='f8' (ie double precision floating point) to avoid a deprecation warning (earlier NumPy versions) or error (later NumPy versions) upon division by 1000 in the conversion from GWh to TWh. That is,

data = np.loadtxt('germany-energy-sources.txt', skiprows=2, dtype='i4')

should be

data = np.loadtxt('germany-energy-sources.txt', skiprows=2, dtype='f8')

[Thanks to Joseph Karpinski for pointing this out].

Some other recent changes to Matplotlib mean that the hatching looks better if the specifiers

hatch = ['o', '', 'xxxx', '/']

are replaced by

hatch = ['oo', '', 'xxxx', '//']

and the bar edgecolor is set explicitly in the following line:

bars[i] = ax.bar(years, bottom=bottom, height=data[:,i+1], color='w',
hatch=hatch[i], align='center', edgecolor='k')

p. 302 (Listing 7.10) The diffusion equation is not implemented exactly as given in Example E7.10 (the factor of $1/4\pi$ should be $1/\sqrt{4\pi}$). That is, the code line

theta = theta0 + H/cp/A/np.sqrt(D*t) / 4/np.pi * np.exp(-x**2/4/D/t)

should be

theta = theta0 + H/cp/A/np.sqrt(D*t * 4*np.pi) * np.exp(-x**2/4/D/t)

This does not alter the output qualitatively, but has been corrected in the online example. [Thanks to Naresh Gurbuxani for spotting this error].

p. 305 The URL in footnote 9 should be https://matplotlib.org/api/text_api.html.

p. 310 (Listing 7.15) The axisbg argument to Figure.add_subplot was deprecated in Matplotlib version 2.0 and replaced with facecolor. The line

ax = fig.add_subplot(111, axisbg='k')

should therefore be replaced with

ax = fig.add_subplot(111, facecolor='k')

if using more recent versions of the Matplotlib library.

p. 312 (E7.16) The URL for the journal article by Heinz et al. no longer works, but it can be found at https://doi.org/10.1080/10691898.2003.11910711. The necessary data file has also disappeared from the publisher's website, but can be downloaded here as body.dat.txt.

[Thanks to Joseph Karpinski for noticing this].

p. 314 (Listing 7.17) The axisbg argument to Figure.add_subplot was deprecated in Matplotlib version 2.0 and replaced with facecolor. The line

ax = fig.add_subplot(111, axisbg='k', aspect='equal')

should therefore be replaced with

ax = fig.add_subplot(111, facecolor='k', aspect='equal')

if using more recent versions of the Matplotlib library.

p. 316 (P7.1.5) Some readers may find it helpful to have the values of the following physical constants provided in this question:

# Physical constants in SI units: Planck's constant (J.s),
# the speed of light (m.s-1), Boltzmann's constant (J.K-1)
h, c, kB = 6.62606957e-34, 299792458, 1.3806488e-23

p. 317 The URL in footnote 14 no longer works. A suitable alternative is https://matplotlib.org/tutorials/colors/colormaps.html.

p. 318 (Listing 7.18) Following a change to the Matplotlib API in v1.5.1, the levels provided to Axes.contour must be in increasing order. To make the code in Example E7.18 work under versions v1.5.1+, the following line:

levels = list(-levels) + list(levels)

should be changed to:

levels = sorted(list(-levels) + list(levels))

p. 320 (and Listing 7.20) In recent versions of Matplotlib, interpolation='nearest' is the default and interpolation='bilinear' now has to be explicitly set in the call to plt.imshow if required. The online example has been updated to accommodate this change.

p. 322 (Listing 7.21) In recent versions of NumPy, indexing with non-integers is now an error. Replace the line:

ix, iy = width / 2 + x * width / 10, y * height / 12

with:

ix, iy = int(width / 2 + x * width / 10), int(y * height / 12)

p. 325 (Listing 7.23) The code line:

dt = dx2 * dx2 / (2 * D * (dx2 + dy2))

should be

dt = dx2 * dy2 / (2 * D * (dx2 + dy2))

(though it doesn't make any difference for the identical values of dx and dy chosen in this example).

p.346 (Example E8.7) scipy.special.ellipe actually evaluates $$E(m) = \int_0^{\pi/2} \sqrt{1-m\sin^2\theta}\,\mathrm{d}\theta,$$ as given correctly on the previous page. Therefore, for the orbital perimeter we need

In [x]: pe = 4 * a * ellipe(e*e)
In [x]: print(pe)
939887967.974

and the difference from the circular orbit,

(pc - pe) / pe * 100
0.0067215663638305143

Is only 0.0067% instead of 0.42%.

p.347 (Example E8.9) The expression for the normalized Gaussian profile is missing a square in the exponent. It should be:

$$G(x;\sigma) = \frac{1}{\sigma\sqrt{2\pi}}\exp\left(-\frac{x^2}{2\sigma^2}\right)$$

The accompanying code is correct. [Thanks to Chen Ying for spotting this].

p. 359 The URL in footnote 7 should be https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.quad.html.

p. 370 (Q8.2.2.e.) Compare this integral with the value of $2\pi I_0(z)$, not $I_0(z)/2\pi$.

p.371 (P8.2.4: The Brusselator) The second of the scaled differential equations should read $$\frac{\mathrm{d}y}{\mathrm{d}t} = bx - x^2y$$ (note the minus sign).

p. 384 (Definitions of the Jacobian and Hessian functions) The definitions for functions dx and ddx do not have the correct syntax; they should be

def df(X):

and

def ddf(X):

respectively. [Thanks to Alex Hogg for spotting this].

p. 391 (Demonstration of the leastsq function in Section 8.4.2) The variable pfit is never assigned. It should hold the list of best-fit parameters, returned as plsq and output earlier on the page. Use:

pfit = plsq
pylab.plot(t, f(t, *pfit), c=’k’, label=’Fit’)

[Thanks to Javier Elexpuru for spotting this].

p. 394 (Example E8.22) The function jac should simply return the derivatives,

return -da, -de

(i.e. remove the following line, which is never executed, return np.array((-da, -de)).T.)

p. 396 (§8.4.3) The bracketing interval $[a,b]$ should be such that $\mathrm{sgn}[f(a)] = -\mathrm{sgn}[f(b)]$. That is, $f(a)$ and $f(b)$ should bracket the root and have opposite signs. It is not necessary, of course, that $f(a) = -f(b)$.

p. 397 (Caption to Figure 8.23): The function plotted is $f(x) = \frac{1}{5} + x\cos(3/x)$ (NB not $\sin$). [Thanks to Alex Hogg for pointing this out].

p. 400 (Q8.4.3): The cosine in the formula for $z$ in this question should be squared:

$$z = x\tan\theta_0 - \frac{g}{2v_0^2\cos^2\theta_0}x^2.$$

Minor typos

p. 66 (§2.6): to acheive $\rightarrow$ to achieve

p. 112 (§4.2.2) keys to to be copied $\rightarrow$ keys to be copied

p. 122 (§4.3.1) L9: acheived $\rightarrow$ achieved

p. 136 (P4.4.2) The lower case $r$ in the haversine formula should be $R$.

p. 189 (Table 6.2) "floatng" $\rightarrow$ "floating"

p. 212 "respecively" $\rightarrow$ "respectively"

p. 217 "picked off an assigned" $\rightarrow$ "picked off and assigned"

p. 233: "define a the object" $\rightarrow$ "define the object"

p. 239: in Figure 6.7 the caption should read $n = 0,1,2,3,4$ instead of $x = 0,1,2,3,4$

p. 272 (P6.7.3) L5: "process known as chemotaxis" $\rightarrow$ "a process known as chemotaxis"

p. 296 (Table 7.9): The explanation of the argument height appears twice in this table.

p. 339 (Last bullet point): jn_zeros(n, nt) appears twice.

p. 341 (Example E8.4) There should be no period after "1953".

p. 345 (Footnote) "instead $m$" $\rightarrow$ "instead of $m$"

p. 366 (top of the page): $\frac{\mathrm{d}x_2}{\mathrm{d}t_2}$ should be $\frac{\mathrm{d}x_2}{\mathrm{d}t}$

p. 368 "Drag consant" $\rightarrow$ "Drag constant"

p. 390 (§8.4.2) The function to be fit is $f(t) = Ae^{-t/\tau}\cos 2\pi\nu t$, so $\tau$ is positive.

p. 447 (Index): plt.errorbars $\rightarrow$ plt.errorbar