Introduction to Mathematical Physics -- errata

• "Riccati" is consistently misspelled as "Ricatti" in many places, starting in the table of contents (p. vii, section 5.2.2). There are several other occurrences in chapter 5, the first of which is on the second line of p. 212.
• p. 7, Def. 1.8 should read "... at least one point of S other than x itself."
• p.2 4, eq. (1.102) - the prefactor e^{-z} on the right-hand side should be deleted. Thanks to Joel Eidsath for this one.
• p. 181, Theorem 4.1 should specify that the points z_k of the sequence must be distinct from z₀ itself.
• p. 181, eq. (4.66) -- the inequality should be <= rather than >.
• p. 204, last book noted -- the third author is C. E. Pearson (not Pierson).
• p. 214, line -5 (5th from end) needs a ? after "explicitly".
• p. 218, the section heading should be "Riccati equation".
• p. 234, eq. (5.142). the argument of the hypergeoemtric function is missing a "|1", so that the equation should read
  
  P_{\lambda}(z) = F(-\lambda, \lambda + 1|1|\half(1 - z))
  
  
• p. 236, the left-hand side of eq. (5.156) should be "q_n-1(z)", and the sentence following should read
  
  [Show that q_n-1(z) is actually a polynomial ...].
  
  
• p. 250, the right-hand side of eq. (5.C60) should read
  
  - (1 + k²)u + 2k² u³
  
  The stated conclusion is correct.
• p. 247, line 4, remove unwanted "." before "(see Section 6.5)".
• p. 254, The book by Chandrasekharan is published by Springer (not "Springe").
• p. 257, problem 9 should read "Find the coefficients $c_n(t)$ in the expansion ..." (not $c_n(z)$).
• p. 257, problem 11, the equation for W'/W should read
  
  {1\over W}{dW\over dz} = -{2z\over z² - 1}
  
  (as a consequence of this, we then have $\ln W = -\ln(z² -1)$).
• p. 258, problem 14 -- the argument of the Bessel function on the RHS of the first equation should be z (not s). In the second equation, the first factor should be $\sqrt{\pi\over 2z}$ (not simply $\sqrt{\pi}$), and the constant C should have subscript $\lambda+\frac{1}{2}$ (not simply $\lambda$) in terms of the constant defined in the preceding problem.
• p. 291. The discussion of the associated Legendre functions is unclear, and not quite correct. The argument for the orthogonality of the functions is clarified by the modification given on the short pdf page provided. Thanks to Mark Ashbaugh for a correspondence on this discussion.
• p. 354, at the end of line 10, "singe" should be "single" (spell-checkers don't catch everything).
• p. 354, line 12, "... that arises" should read "... that arise".
• p. 375, first line after eq. (8.128) should read "$n = \ell+1,\ell+2,\ldots$."
• p. 375, second line after eq. (8.128) should read "... Appendix A of Chapter 6."
• p. 376. line after eq. (8.134) should read "This is an equation of continuity similar to ..."
• p. 377, last line of paragraph after eq. (8.142) should read "lie in the past, i.e. for t < 0."
• p. 392, line 5 should read
  
  if g = g₁g₂ then D(g) = D(g₁)D(g₂)
  
  
• p. 394, the equation in Def. 9.3 should read
  
  a'b' = (ab)'
  
  
• p. 396, Def. 9.9 should read "...semisimple if it contains no proper Abelian invariant subgroups.
• p. 412, line -7 should read "... characters of g in the inequivalent irreducible finite-dimensional ..."
  [the Kronecker delta in eq. (9.75) is equal to one if the irreps a and b are equivalent and zero if they are not].
• p. 412, the sentences beginning on line -4,
  
  "If K₁ = ... and that ... is the character ... in the irreducible representation $\Gamma^a$. Then Eq. (9.75) is equivalent to ..."
  
  should be joined together to read
  
  "If K₁ = ... and that ... is the character ... in the irreducible representation $\Gamma^a$, then Eq. (9.75) is equivalent to ..."
• p. 414, the left-hand side of eq. (9.87) should read
  
  D_j D_k = ... [instead of D_k D_k = ...]
  
  
• p. 416, line 2. The cycle structures for the even permutations are (1⁴), (22) and (31) [not (4)].
• p. 438, line -6. "It is a homogeneous polynomial of degree " - insert "N(N+1)/2".
• p. 461, start of subsection 10.2.1. It must be understood that the finite-dimensional vector space Vⁿ is complex, as there are real matrices that cannot be expressed as an exponential of a real matrix.
• p. 462, second line after eq. (10.11) - "... generators form a Lie algebra, as defined in Section 9.1.3."
  Here "defined" should be replaced by "introduced", as only examples are given in Sec. 9.1.3.
• p. 463, in Def. 10.1, "one-to-one mapping" should be "linear mapping", and in the third line,
  "can be expressed a direct sum" should be "can be expressed as a direct sum".
• p. 465, line -9. "The Lie algebra of SO(n) is also simple, except ...", should read "... simple for n >= 3, except ...".
• p. 466, in the paragraph after Exercise 10.6, "a constant C₂ then defines the surface ..." is more accurately stated as "the surface defined by a constant value of the quadratic form C₂ is ...".