Physical Mathematics: Errata | Physical Mathematics

Cahill, K., 2013, 2014

Physical Mathematics

Cambridge University Press

Copyrighted material. All rights reserved by the author and Cambridge University Press.

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Errata for Physical Mathematics

2014
2013

Errata in and enhancements of the 2014 printing

Chapter 1, section 1.13, added explanation after equation 1.148
Chapter 1, section 1.20, added explanation after equation 1.179
Chapter 1, section 1.20, extended equations 1.195--196
Chapter 1, section 1.20, added an example
Chapter 1, section 1.25, added explanation after equation 1.251 and dropped the last term in equation 1.254
Chapter 1, section 1.28, simplified equation 1.299
Chapter 1, section 1.28, example 1.39, paragraphs 2 and 3 (Thanks to Tsukasa Tada of the Nishina Center!)
Chapter 1, section 1.29, equation 1.318 (Thanks to Stephen Pietromonaco of UNM!)
Chapter 1, section 1.31, before equation 1.346
Chapter 1, section 1.31, example 1.47
Chapter 1, section 1.35, equation 1.418 (Thanks to Stephen Pietromonaco of UNM!)
Chapter 1, section 1.37, Schwarz not Schwartz (twice) (Thanks to Professor Robert Burckel of Kansas State University!)
Chapter 1, exercise 1.37
Chapter 2, section 2.3, caption to figure 2.2 and text after equation 2.17
Chapter 2, section 2.4, removed extra factor of 2 from equation 2.21
Chapter 2, section 2.4, text after equation 2.26, extra step included in equation 2.28, and minor corrections to example 2.5; section 2.5, before equation 2.33 (Thanks to Stephen Pietromonaco!)
Chapter 2, section 2.8, example 2.10, before equation 2.86 (Thanks to Stephen Pietromonaco!)
Chapter 2, section 2.10, equation 2.114 (Thanks to Alireza Seif!)
Chapter 3, section 3.1, clarified text between equations (3.1) and (3.2)
Chapter 3, section 3.1, clarified equation (3.14)
Section 3.9, example 3.12, page 126: In equations 3.132--3.135, the prefactor \(\tau\) should be \(\tau^{-1}\). The last line of equation 3.135 is then \begin{equation*} L(t) ={} \frac{\sin(\omega t) - \omega \tau \cos(\omega t)} {1 + (\omega\tau)^2}. \end{equation*}
Chapter 3, section 3.10, clarified equation (3.143)
Chapter 4, section 4.11, example 4.15: The condition Re \( \alpha > 0 \) is unnecessary. (Thanks to Changhao Yi of UNM.)
Chapter 4, section 4.13, before equation 4.127
Chapter 4, exercise 4.22
Chapter 5, section 5.2, equations 5.26-27
Chapter 5, section 5.11, clarification of equation 5.98
Chapter 5, section 5.14, example 5.19 , last paragraph
Chapter 5, section 5.14, example 5.23, line before equation (5.151)
Chapter 5, section 5.16, clarification of example 5.30
Chapter 5, section 5.18, example 5.36, figure 5.9 and equation 5.249
Chapter 5, exercise 5.10
Chapter 6, section 6.2, line before equation 6.17
Chapter 6, section 6.4, before and after equation 6.36
Chapter 6, section 6.5, example 6.6, after equation 6.54
Chapter 6, section 6.40, before equation 6.417 (Thanks to Paul Greninger of UNM!) and between equations 6.417 and 6.418 (Thanks to Bobby Middleton of UNM!)
Chapter 6, exercises 6.21 and 6.22.
Chapter 8, clarification of section 8.12 and typo fix just before equation (8.109).
Chapter 9, section 9.1, after equation 9.12
Chapter 9, section 9.1, after equation 9.35
Chapter 9, section 9.1, example 9.3 simplified
Chapter 9, section 9.2, after equation 9.71
Chapter 10, section 10.7, part 2 of Schur's lemma and equations 10.25-26, and section 10.9, after equation 10.31.
Chapter 10, section 10.10, example 10.13 (Thanks to David Amdahl!)
Chapter 10, section 10.21, equations 10.152-155, and section 10.23, example 10.23
Chapter 10, section 10.25
Chapter 10, section 10.31, equation 10.241, after equation 10.244, equation 10.245, and after equation 10.248, and section 10.32, equation 10.250
Chapter 10, section 10.32, after equation 10.253, before equation 10.258, equation 10.267, before equation 10.274, and equation 10.280, and section 10.33, around equations 10.288 and 10.294, and equations 10.296-7.
Chapter 10, section 10.36, in and just before equation 10.311, \( \sigma_2 \zeta^* \) should be \( {} - \sigma_2 \zeta^* \).
Chapter 11, section 11.7, equation 11.37
Chapter 11, section 11.10, after equation 11.71
Chapter 11, section 11.12, the last \(\partial x^j\) in equation 11.102 should be \(\partial x'^j\).
Chapter 11, section 11.13, on the right-hand side of equation 11.113, the first \(\wedge\) should be omitted.
Chapter 11, section 11.13, after equation 11.114. Thanks to Stephen Pietromonaco of UNM!
Chapter 11, section 11.14, equations 11.121-124
Chapter 11, section 11.20, equation 11.162 (Thanks David Amdahl of UNM and AFRL!)
Chapter 11, section 11.25, equations 11.184 and 187
Chapter 11, section 11.26, equation 11.206
Chapter 11, section 11.27, equation 11.215
Chapter 11, section 11.32, equation 11.247: Technically, the first term should be multiplied by one-half.
Chapter 11, section 11.37, equation 11.309
Chapter 11, section 11.38, new equations 11.328-330
Chapter 11, section 11.43: in equations 11.377 & 378, c⁴ should be c³; and in equation 11.380, - 1/2 should be - 1/2c.
Chapter 11, section 11.44, equations 11.380-383
Chapter 11, section 11.48, paragraphs 1-3
Chapter 11, section 11.48, equation 11.397: In the third equation, \( \Gamma^0_{22} \) should be \( \Gamma^0_{33} \); in equation 11.410, \(3p\) should be \( 3p/c^2 \); in equation 11.411, \( p \) should be \( p/c^2 \); in equations 11.411, 412, 414, 417, 419, & 422, \( k \) should be \( c^2 k \);
Chapter 11, section 11.49, each \( p \) should be \( p/c^2 \), and each \( k \) should be \( c^2 k \)
Chapter 11, section 11.49, example 11.28
Chapter 13, section 13.1, text before equation 13.6
Chapter 13, section 13.3, equation 13.46
Chapter 13, section 13.5, equation 13.67 needs more parentheses.
Chapter 13, section 13.5, example 13.7, equation 13.78 (Thanks to Chulho Choi of KIAS!)
Chapter 13, section 13.11, equation 13.150 and before equation 13.161 (Thanks to Chulho Choi!)
Chapter 13, section 13.12, equation 13.177
Chapter 13, section 13.13, equations 13.200 and 13.201 (Thanks to Chulho Choi!)
Chapter 13, section 13.14, equation 13.213 (Thanks to Chulho Choi!)
Chapter 13, section 13.16, near equation 13.239
Chapter 13, section 13.20, example 13.17, line 2, and example 13.18, lines 2 and 3, last paragraph, and figure 13.6
Chapter 14, section 14.3, page 570, "AN =1" should be "AN = 0.1." (Thanks to Zhou Yang of UNM.)
Chapter 15, section 15.2, after equation 15.13 and example 15.1, equations 15.18-19
Chapter 15, section 15.4, equations 15.28 (Thanks to Ian Barker!)
Chapter 15, section 15.5, equation 15.53 and example 15.3
Chapter 16, section 16.3, equations 16.25-16
Chapter 16, section 16.11, after equation 16.120
Chapter 16, section 16.13, equation 16.171 (Thanks to David Amdahl of UNM!)
Chapter 16, section 16.14: Equations 16.218-219 have extra integral signs.
Chapter 18, in equation 18.10, \(x_n - 1\) should be \( 1 - x_n \). (Thanks to Alexandre F. Mills!)
Chapter 19, section 19.2, equation 19.6 (Thanks to Stephen Pietromonaco of the University of British Columbia!)
Chapter 19, section 19.3: In the caption to Fig.19.1, \( T_0 E^2 \) should be \( E^2/(2 \pi \hbar c \, T_0) \).
Chapter 19, section 19.7, first paragraph (Thanks to Stephen Pietromonaco of UBC!)

Errata in and enhancements of the 2013 printings

Chapter 1, after end of example 1.16
Chapter 1, section 1.12, after equation 1.141 (Thanks to Mark Ruiz of the Central University of Venezuela!)
Chapter 1, section 1.13, added explanation after equation 1.148
Chapter 1, section 1.19, above equation 1.174
Chapter 1, section 1.20, added explanation after equation 1.179
Chapter 1, section 1.20, extended equations 1.195--196
Chapter 1, section 1.20, added an example
Chapter 1, section 1.25, added explanation after equation 1.251 and dropped the last term in equation 1.254
Chapter 1, section 1.26, example 1.35, equations 1.267-268 (Thanks to Nick Haynes of Duke University!)
Chapter 1, section 1.28, simplified equation 1.299
Chapter 1, section 1.28, example 1.39, paragraphs 2 and 3 (Thanks to Tsukasa Tada of the Nishina Center!)
Chapter 1, section 1.29, equation 1.318 (Thanks to Stephen Pietromonaco!)
Chapter 1, section 1.31, before equation 1.346
Chapter 1, section 1.31, after equation 1.364
Chapter 1, section 1.31, example 1.47
Chapter 1, section 1.35, equation 1.418 (Thanks to Stephen Pietromonaco!)
Chapter 1, section 1.37, Schwarz not Schwartz (twice) (Thanks to Professor Robert Burckel!)
Chapter 1, exercise 1.37
Chapter 2, section 2.3, caption to figure 2.2 and text after equation 2.17
Chapter 2, section 2.4, removed extra factor of 2 from equation 2.21
Chapter 2, section 2.4, text after equation 2.26, extra step included in equation 2.28, and minor corrections to example 2.5; section 2.5, before equation 2.33 (Thanks to Stephen Pietromonaco!)
Chapter 2, section 2.7, equation 2.57
Chapter 2, section 2.8, example 2.10, before equation 2.86 (Thanks to Stephen Pietromonaco!)
Chapter 2, section 2.10, equation 2.114 (Thanks to Alireza Seif!)
Chapter 2, section 2.13, equation 148
Chapter 3, section 3.1, clarified text between equations (3.1) and (3.2)
Chapter 3, section 3.1, equations 3.12-3.14
Chapter 3, section 3.5, before equation 3.95, and section 3.6, after equation 3.104 and primes in equations 3.105-111 and after equation 3.113, and section 3.8, equation 3.123
Section 3.9, example 3.12, page 126: In equations 3.132--3.135, the prefactor \(\tau\) should be \(\tau^{-1}\). The last line of equation 3.135 is then \begin{equation*} L(t) ={} \frac{\sin(\omega t) - \omega \tau \cos(\omega t)} {1 + (\omega\tau)^2}. \end{equation*}
Chapter 3, section 3.10, clarified equation (3.143)
Chapter 4, section 4.5, after equation 4.56 and equations 4.61-62 and 4.65-66 (Thanks to Ming-Tso Wei of Duke University!)
Chapter 4, section 4.10, example 4.12, equations 4.99 and 4.101
Chapter 4, section 4.11, example 4.15: The condition Re \( \alpha > 0 \) is unnecessary. (Thanks to Changhao Yi of UNM.)
Chapter 4, section 4.12, equation 4.113 and deletion after equation 4.114
Chapter 4, section 4.13, before and after equation 4.127
Chapter 4, exercise 4.22
Chapter 5, section 5.2, equations 5.26-27
Chapter 5, section 5.11, clarification of equation 5.98
Chapter 5, section 5.14, example 5.19, last paragraph
Chapter 5, section 5.14, example 5.23, line before equation (5.151)
Chapter 5, section 5.16, equation 5.184 (Thanks to Nick Haynes of Duke University!)
Chapter 5, section 5.16, clarification of example 5.30 (Thanks to Ming-Tso Wei of Duke University!)
Chapter 5, section 5.18, example 5.36, after equation 5.233
Chapter 5, section 5.18, example 5.36, figure 5.9 and equation 5.249
Chapter 5, section 5.20, line 1
Chapter 5, section 5.21, equation 5.292
Chapter 5, exercise 5.2
Chapter 5, exercises 5.12 and 5.13
Chapter 5, exercises 5.10, 5.12, and 5.13
Chapter 5, exercise 5.31, equation 5.352 (Thanks to Nick Haynes of Duke University!)
Chapter 6, section 6.2, line before equation 6.17
Chapter 6, section 6.4, before and after equation 6.36
Chapter 6, section 6.5, example 6.6, before and in equation 6.55, and after equation 6.56, and section 6.6, example 6.7, equation 6.62
Chapter 6, section 6.16, before example 6.23
Chapter 6, section 6.19, equation 6.185 (Thanks to Ming-Tso Wei of Duke University!) and example 6.29, line3
Chapter 6, section 6.27, equation 6.235
Chapter 6, section 6.33, equation 6.329 (Thanks to James Hendrie of UNM!)
Chapter 6, section 6.39, equations 6.413-6.416, and section 6.40, before equation 6.417 (Thanks to Paul Greninger of UNM!) and between equations 6.417 and 6.418 (Thanks to Bobby Middleton of UNM!)
Chapter 6, section 6.40, equations 6.428-6.433
Chapter 6, exercises 6.5, 6.16, 6.17, 6.18 (Thanks to Ming-Tso Wei of Duke University!), 6.20 (Thanks to Stephen Pietromonaco of UNM!), 6.21, 6.22, and example 6.29, first paragraph
Chapter 8, section 8.7, equation 8.55, and section 8.8, equations 8.56 and 8.58
Chapter 8, section 8.12, equation 8.97
Chapter 8, clarification of section 8.12 and typo fix just before equation (8.109).
Chapter 8, example 8.8, Planck satellite data
Chapter 9, section 9.1, after equation 9.12
Chapter 9, section 9.1, after equation 9.35
Chapter 9, section 9.1, example 9.3 simplified
Chapter 9, section 9.1, equation 9.62
Chapter 9, section 9.2, after equation 9.71
Chapter 9, section 9.4 and exercises 9.4, 9.6, 9.11, 9.18, and 9.23
Chapter 10, section 10.3, equation 10.13, and section 10.4, example 10.8, and section 10.5, fourth paragraph
Chapter 10, section 10.7, part 2 of Schur's lemma and equations 10.25-26, and section 10.9, after equation 10.31.
Chapter 10, section 10.10, example 10.13 (Thanks to David Amdahl!)
Chapter 10, section 10.18, equations 10.121-122
Chapter 10, section 10.21, equations 10.152-155, and section 10.23, example 10.23
Chapter 10, section 10.25
Chapter 10, section 10.27, equation 10.184
Chapter 10, section 10.31, equation 10.241, after equation 10.244, equation 10.245, and after equation 10.248, and section 10.32, equation 10.250
Chapter 10, section 10.32, after equation 10.253, before equation 10.258, equation 10.267, before equation 10.274, and equation 10.280, and section 10.33, around equations 10.288 and 10.294, and equations 10.296-7.
Chapter 10, section 10.34, equation 10.305, and exercises 10.9, 10.22-25, 10.28, 10.32, 10.37-44
Chapter 10, section 10.36, in and just before equation 10.311, \( \sigma_2 \zeta^* \) should be \( {} - \sigma_2 \zeta^* \).
Chapter 11, section 11.5, equation 11.23
Chapter 11, section 11.7, equation 11.37
Chapter 11, section 11.10, after equation 11.71
Chapter 11, section 11.12, the last \(\partial x^j\) in equation 11.102 should be \(\partial x'^j\).
Chapter 11, section 11.13, after equation 11.114
Chapter 11, section 11.14, equations 11.121-124
Chapter 11, section 11.20, equation 11.162 (Thanks to David Amdahl!)
Chapter 11, section 11.25, equations 11.184 and 187
Chapter 11, section 11.26, equation 11.206
Chapter 11, section 11.27, equation 11.215
Chapter 11, section 11.32, equation 11.247: Technically, the first term should be multiplied by one-half.
Chapter 11, section 11.37, equation 11.309
Chapter 11, section 11.38, new equations 11.328-330
Chapter 11, section 11.41, equation 11.343
Chapter 11, section 11.43: in equations 11.377 & 378, c⁴ should be c³; and in equation 11.380, - 1/2 should be - 1/2c.
Chapter 11, section 11.44, equations 11.380-383
Chapter 11, section 11.48 (Planck data)
Chapter 11, section 11.48: in equation 11.397 (third subequation) \( \Gamma^0_{22} \) should be \( \Gamma^0_{33} \); in equation 11.401, \( \Gamma^3_{23} = \cot \theta = \Gamma^3_{32} \); in equation 11.403, \( \dot a/a \) should be \( \dot a/ca \) ; in equations 11.404 and 11.405, \( \dot a/a \) should be \( \dot a/ca \) and \(\ddot a/a \) should be \(\ddot a/c^2 a \); in equation 11.407, \( \ddot a \) should be \( \ddot a/c^2 \) and \( \dot a^2 \) should be \( \dot a^2 / c^2 \); in equation 11.408, \( \rho \) should be \( c^2 \rho \); in equation 11.410, \(3p\) should be \( 3p/c^2 \); in equation 11.411, \( p \) should be \( p/c^2 \); in equations 11.411, 412, 414, 417, 419, & 422, \( k \) should be \( c^2 k \);
Chapter 11, section 11.48, equation 11.418 and between equations 11.421 and 11.423; section 11.49, equations 11.430-431, examples 11.25 and 11.27-29
Chapter 11, section 11.49, each \( p \) should be \( p/c^2 \), and each \( k \) should be \( c^2 k \)
Chapter 11, sections 11.50 and 11.51, equation 11.480
Chapter 11, exercises 11.20, 11.25, 11.30, and 11.37-40
Chapter 12, section 12.2, equation 12.21
Chapter 12, section 12.2, equation 12.37
Chapter 12, section 12.3, equation 12.78
Chapter 13, section 13.1, text before equation 13.6
Chapter 13, section 13.3, equation 13.46 and 13.53
Chapter 13, section 13.5, equation 13.67 needs more parentheses.
Chapter 13, section 13.5, example 13.7, equation 13.78 (Thanks to Chulho Choi of KIAS!)
Chapter 13, section 13.10, equations 13.142-144
Chapter 13, section 13.11, equation 13.150 and before equation 13.161 (Thanks to Chulho Choi!)
Chapter 13, sections 13.12, equations 13.177 and 13.189, and section 13.13, equations 13.194 and 13.205
Chapter 13, section 13.14, equation 13.213 (Thanks to Chulho Choi!)
Chapter 13, section 13.16, near equation 13.239
Chapter 13, section 13.20, example 13.17, line 2, and example 13.18, lines 2 and 3, last paragraph, and figure 13.6
Chapter 13, section 13.21, equation 13.324
Chapter 13, exercises, 13.14, 13.20, and 13.36-38
Chapter 14, section 14.2, equation 14.3
Chapter 14, section 14.4, primes needed before equation 14.8, equation 14.13, and a less-than sign before equation 14.15
Chapter 14, exercise 14.3
Chapter 14, section 14.3, page 570, "AN =1" should be "AN = 0.1." (Thanks to Zhou Yang of UNM.)
Chapter 15, section 15.2, after equation 15.13 and example 15.1, equations 15.18-19
Chapter 15, section 15.4, equations 15.28 (Thanks to Ian Barker!)
Chapter 15, section 15.5, equation 15.53 and example 15.3
Chapter 16, section 16.3, equations 16.25-26
Chapter 16, section 16.5, equation 16.55
Chapter 16, section 16.11, after equation 16.120
Chapter 16, section 16.13, after equation 16.164
Chapter 16, section 16.13, equation 16.171 (Thanks to David Amdahl of UNM!)
Chapter 16, section 16.14: Equations 16.218-219 have extra integral signs.
Chapter 16, exercises 16.6, 16.11, and 16.21
Chapter 17, section 17.1, equations 17.2, 17.4, and 17.16
Chapter 17, section 17.2, equations 17.35-37
Chapter 17, section 17.3, equations 17.35-36 and 17.49-53
Chapter 18, in equation 18.10, \( x_n - 1 \) should be \( 1 - x_n \). (Thanks to Alexandre F. Mills!)
Chapter 19, section 19.2, equation 19.6 (Thanks to Stephen Pietromonaco of UBC!)
Chapter 19, section 19.2, clarification of equation 19.15
Chapter 19, section 19.3: In the caption to Fig.19.1, \( T_0 E^2 \) should be \( E^2/(2 \pi \hbar c \, T_0) \).
Chapter 19, section 19.7, first paragraph (Thanks to Stephen Pietromonaco!)