Errata/improvements to  "A Guided Tour of Mathematical Methods for the Physical Sciences"
(Second Edition)
• p. 12, in equation (2.30), "=" should be "~"
• p. 13, in equation (2.31), "=" should be "~"
• p. 52, equations (5.13) and (5.14), delete "x hat"
• p. 66, 5th line of section 6.2, add after "off the surface ." the following text "We have ignored the variation of v_x over the surfaces. This variation gives a correction proportional to dy or dz, which vanishes when dx, dy, and dz go to zero."
• p. 80, problem b, "axisymmetric" should be "cylindrically symmetric"
• p. 81, in equation (6.22), "3r^3" should be "3r^2"
• p. 96, problem f, replace "result of problem e" by "result of problem d"
• p. 145, line 7 of section 11.5, replace "For simplicity ......... given by (11.29)" by "By analogy of expression (11.29), we assume that  ....... given by"
• p. 151, equation (11.61) should be: sum_j half d_i ( v_j v_j ) = sum_j (v_j v_i) - sum_j (d_j v_j) v_i
• p. 192, line 2, replace "in time as e^(-i omega t)" by "in time as e^(-i omega t), and we consider the motion with the same time dependence."
• p. 206,  2nd line from bottom, "zero" should be "one"
• p. 214, problem e, (8.7) should be (8.6)
• p. 241, equation (15.76) should have a factor "2pi" in the right hand side
• p. 248, line, replace "properties of harmonic functions" by "properties of analytic functions"
• p. 265, first line below problem g, replace "from (17.33)" by "from (17.34"
• p. 279, eq. (18.32), u_B (r_B ) should be u_B
• p. 328, four lines below eq. (20.52), insert after ".... in this section." the sentence "The constant A is determined by the employed normalization of Bessel functions."
• p. 342, the right hand side of expression (20.82) should be "( k_1 / ik_0 )( k_0 - ik_1 )/(k_0+ik_1 )"
• p. 343, replace the text from the top of the page through " ...... of the guided waves." (1 line below problem j) by "Using expressions (20.79) and (20.83), one can write equation (20.82) as a relation between omega and k. This is an complicated equation that has no knowns solutions in closed form. Such an equation is called a transcendental equation. Through numerical methods one can solve for k as a function of omega."
• p. 351, problem g: "the mass is equal to: should be "the mass is proportional to"
• p. 365, "problem i" should be "problem k"
• p. 369, "problem g" should be "problem f"
• p 400-40, labels of problens of section 21.9 are not correct
• p 414, in the second line of eq. (23.7), "2 epsilon x_0 x_2" should be "2 epsilon x_0 x_1"
• p. 419-420,  problems of section 23.2 are not correctly labelled
• p. 426, two lines below eq. (23.54), "xdot(0)=0" should be "xdot_1(0)=0"
• p. 428, line above eq. (23.62), "2 pi omega / c" should be "2 pi c /  omega"
• p. 430, 1st line of problem e, "F_1 (x')" should be "F_1 (xi)"
• p 436, problem e: "z_1 = -1/2" should be "z_1 = -1/8", in equation (23.90) " -1/2" should be "-1/8", and equation (23.91) should be: "x=1.982    and     x=2.069"
• p. 436, equation (23.92) should be
• "x=1.928:    x^3 - 4x^2 + 4x = 0.009994 = 0.01 - 5 times 10_6"
• "x=2.069:    x^3 - 4x^2 + 4x = 0.00985 = 0.01 - 0.00015"
• p. 439, eq. (24.10), coeffcient of last term (-1/12) should be +3/4
• p. 442, eq. (24.23), delete "(n-1)" from the last term
• p. 449, problem e, "b=-ia" should be "b=+ia"
• p. 459, second "Problem g" should be "Problem i"
• p. 463, equation (25.10), the second component of the vector should be "r(phi) sin(phi)"
• p. 485, line 1: "expression (25.87)" should be "expression (25.88)"
• p. 488, eq. (25.116), in the last term  "sqrt(  1 +  ydot^2  )" should  be "(  1 +  ydot^2  )"
• p. 489, problem f,  "lambda = B^-1 cosh(  X/2  )" should be "lambda = B^-1 cosh(  BX/2  )"
Thanks to Aaron Girard, Nathan Hancock, Ted Jacobson, Wouter Kimman, Sum Mak, Alex Sumner for helping to making me aware of these mistakes/improvements.