# Errata for J. David Logan, Applied Mathematics, 3rd Ed.

• p.8, #4: energy yield e should be E
• p.38, 3rd eqn: u(x) should read u(t)
• p.40, 3rd bullet: t^\alpha \sin(\beta \ln t) rather than t^\alpha \sin \ln(\beta t). Similarly for cos type.
• p.40, #1c: y should be u
• p.64-65: -' symbols are for a bullet list, not minus signs (misleading).
• p.65 line 3: \lambda>0 rather than \lambda<0 with a dot
• p.68, #6: double-dot should be on x not on m
• p.79, end 1st para: See Fig. 1.23' is not relevant.
• p.79, #1a: doesn't work out that 2nd critical point involves integers so is a mess
• p.79, last line: x' should read y'
• p.96, end 1st para: f(eps)<< g(eps) rather than f(eps)
• p.98, line 4,8: E(t,eps) = O(eps^3) not O(eps^2)
• p.100, #1: answer (ybar')^2 should be ybar'|ybar'| for resistive sign
• p.103, #14: there's no exact solution (...is there?)
• p.109, last line: t's should be x's
• p.123, #10: u(b) should be u(1); f(t) should be f(x)
• p.128, last 2 eqns: missing factors, should read \dot{a} = -2ka^3b, and \dot{a}=k_1 a b + k_2 c
• p.137, 3rd from bottom line of equations: no plus-or-minus symbol needed
• p.138, Ex 2.13: y(0)=1 (rather than 0) should be the first BC
• p.139, middle of page: Schrodinger is one word
• p.143, 3rd eqn from bottom: I(lambda) =<' shouldn't be there
• p.143, Eq (2.102): e^{lambda t} should be e^{-lambda t}.
• p.143, after (2.102): reference to Figure 2.8 but there is no such figure.
• p.215, #7c: Eqn (3.16) should be (4.5).
• p.227, 6 lines above (4.16): missing left bracket in (K-lambda.I)
• p.227, 5th line: \lambda=0 not \lambda\equiv 0
• p.243, #2: cases are not very interesting since never hit an eigenvalue. I suggest c) $A\mbf{x}-5\mbf{x} = (1, -1/2, 0)^\tbox{T}$ and d) $A\mbf{x}-5\mbf{x} = (1, 4, 0)^\tbox{T}$.
• p.244, #7d: Currently is same situation as a. I suggest cos(3x) for the RHS instead, which makes it soluble.
• p.244, #4a: u(y) not u(u)
• p.245, #12: cos n\pi x not cos nx, surely?
• p.245, #14: Operator has zero eigenvalue (infinite multiplicity) so question should read, determine if it has nonzero eigenvalues, maybe?
• p.245, #15: should have k(x,y) rather than k(x,u) under the integral.
• p.246, #22: remove "y(x)="
• p.249, #9: lower limit is -\infty? Otherwise solution is u = ce^{2t} with c=0.
• p.343 Eqn (6.3): c is missing, and should be for (x,t) in D not (x,y) in D.
• p.363 Thm 6.15: Missing initial "If ..." (unless a claim on existence is to be made).
• p.365 #1: transformation should be w = e^{u/k} instead.
• p.373 #11: this problem is duplicate of #13 p.367.
• p.382 #3: Need also q(x)>0 in order to get positivity in part b. (Only p(x)>0 is given, which is needed). Also, Lu = - div(p grad u) + qu, has + sign on q.
• p.390, middle of 2nd block of eqns: missing factor of i\xi once integration by parts been done.
• p.393, text below 3rd eqn down: a(\xi) should be c(\xi)
• p.394, Table 6.2: Delta distribution appears three times, sinc function missing a bracket, \delta(t-a) should read \delta(x-a), and F(\xi)G(\xi) should read \hat{u}(\xi)\hat{v}(\xi).
• p.398 #15: an arbitrary constant can be added to the solution.
• p.423, above Ex 7.1: definitions of dispersive' and `hyperbolic' should be swapped.

Please contact me, Alex Barnett, with additions or corrections. Thanks to Shiao-Ke Chin-Lee, Matthew Miller, Chetan Mehta, Patrick Karas, Emily Marshall, Rob Taintor, Jun Li, Lisa Davis, Kyle Konrad, Aryeh Drager, and Brad Nelson for helping find these.