These are errata which appear in Powers & Sen, “Mathematical Methods in Engineering,” Cambridge University Press, 2015.

In many places "non-linear" appears that should be "nonlinear".  This is found on pages 248, 559, 559, 566, 566, 566. 
p. 98:   Sec. 2.6.3:  In the analysis of Eqs. (2.346-2.348), several factors of 1/2 are missing; e.g. dx_1 should be replaced by (dx_1)/2 in Eq. (2.346).
p. 89, 91, 112, 113: We would be better to employ an opposite sign convention for torsion $\tau$.
p. 98:   Note: some sources define $\div \bf T  = \nabla {\bf T}^T = \partial T_{ji} \over \partial x_i.$  As long as the analysis is internally consistent, as it is here, it is correct.
p. 111:  Problem 4g is a repeat of Problem 1.
p. 113:  Problem 22--The first equation in the problem may need to be t . d^2t/ds^2 x dt/ds = kappa^2 tau [check this]
p. 113:  Problem 30 should have corners at (0,0,0), (0,1,0), (1,1,0), and (1,0,0).
p. 113:  Problem 30 should have "f(x,y,z) =...."
p. 114:  Problem 38 should read "...one finds that the three principal..."
p. 114:  Problem 38 should have $q_i = -k_{ij}\partial T/\partial x_j$....
p. 144:  Problem 22:  not clear a unique real solution exists for any a.
p. 145:  Problem 29:  There are many more solutions than b = 2.2617.
p. 214:  Problem 29:  There may be an error in the equation for P.  Needs checked.  Buche's solutions indicate an error.
p. 216:  Problem 4.52, should read “…of the two masses and the potential energy of the three springs.”
p. 217:  Problem 4.53 needs an additional factor of "2" in the error function, so as to be consistent with the correct Eq. (A.103) on p. 594.
p. 219:  "..is not is..." should be "...is not..."
p. 230:  Fig. 5.5’s caption should be dy/dx = -\sqrt{x} y 
p. 236:  The second term in Eq. (5.146) be 2k(1 + x + (1/4)x^2 + ...) instead of 2k(1 + x + (1/2)x^2 + ...)
p. 239:  Eq. (5.179) should be y = x + x^2/2 + x^4/12+ ....
p. 257:  Eq. (5.319) should have y(x) = y_0(x) + ....
p. 269:  Just before Eq. (5.429) should be \xi^2 + \eta^2 = r^2
p. 272:  Problem 15 is identical to Example 5.11.
p. 276:  Problem 55 repeats Problem 50.
p. 277:  Problem 57 repeats Problem 18.
p. 296:  The equation appearing just before Eq. (6.92) should receive a number.
p. 302:  In Example 6.19, ||x||_2 = 3.873 not 3.870.
p. 311:  In Fig. 6.9, need more space in needed in the term “-.23 sin 4t.”
p. 316:  Eq. (6.239) needs an approximate equals sign rather than an equals sign.
p. 327:  Eq. (6.335) has a \cdot between the matrix and the vector and should not.
p. 363:  Eq. (6.693)  should have \alpha \phi(t) instead of c \phi(t).
pp. 364-5:  In Eqs. (6.702), (6.703), one could replace (t^5/4)^{2/5} by t^{1/2}.  Additional simplification is possible that is easily achieved with computer algebra.
p. 371:  Eq. (6.754) should have ...\lambda t^3.... instead of \lambda t^2.
p. 378:  The y-axis of the rightmost graph of Fig. 6.28 is mis-labeled.  It should be y(t=1).
p. 379:  Problem 10 is too similar to Example 6.39.
p. 381:  Problem 27: the inner product should be enclosed by angle brackets instead of parentheses.
p. 381:  Problem 30 is a repeat of Problem 18.
p. 381:  Problem 31 is a repeat of Problem 8.
p. 381:  Problem 33 is a repeat of Problem 4.
p. 382:  Problem 37 is a repeat of Problem 11.
p. 384:  Problem 57 is a repeat of Problem 14.
p. 385:  Problem 61 is a repeat of Problem 56.
p. 385:  Problem 66 is a repeat of Problem 64.
p. 386:  Problem 72 may benefit from changing the lower limit to -infinity.
p. 423:  One additional equation after (7.218) would clarify:
                = I.I - 4 uu^T + 4uu^T.uu^T.
         Because u^T.u=1, this reduces to
		= I.
p. 424:  Eq. (7.229) should actually employ uu^T; it presently incorrectly uses u^T.u, though Eq. (7.230) is correct.
p. 426:  Eq. (7.240) should read I - 2 uu^T.  The actual numerical values are correct.
p. 440:  Eq. (7.337) has an unneeded dot in the matrix product.
p. 450:  Columns of Q's should be the NORMALIZED eigenvectors, not just the eigenvectors.
p. 457:  More nuance is needed for the projection matrix P. P as defined by (7.477) is guarnateed symmetric with spectral norm of 1.  And it guarantees P.x = P.P.x, as required.  However if P = {{1,0},{1,0}}, we find a) P.x = P.P.x, b) eigenvalues of P are 1 and 0; c) P is asymmetric, d) the spectral norm of P is sqrt(2), thus P can stretch vectors of certain orientatiion, e.g. if x = (1,0)^T, P.x = (1,1)^T.  So, in constast to statements on p. 458, some authors might not require ||P||=1.
p. 460:  Eq. (7.497) needs another "dot" within its matrix multiplication.
p. 469:  In Eq. (7.593), we should have q_11 = 1/sqrt(10).
p. 475:  Problem 32 has no Cholesky decomposition as the matrix is not positive definite.
p. 486:  Figure 8.2 needs negative signs on some numbers on the y axis.
p. 491:  Some confusion exists here.  The phi_i of Eq. (8.72) is orthonormal.  The phi_i of Eq. (8.73) is not.  It's written carefully, but it is confusing. It could and should be reformulated for more clarity.
p. 518:  Just after Eq. (9.159), should read “eigenvectors ${\bf e}_k, k=1,2,...,K$, as possible.”
p. 553:  In the caption of Fig. 9.13, one should replace dx/dx by dx/dt.
p. 562:  Eq. (9.494) should have an 8 in the numerator of both terms, not 4\sqrt{2}.
p. 562:  Eq. (9.495) should have additional sqrt{2} on both terms because this is part of the basis function.