A very applied first course in Partial Differential Equations,
Prentice Hall, New Jersey, 2002.
1) p 29: Laplacian in spherical coordinates, second term must be:
1/(r^2 sin(theta)) d/(d theta) ( sin(theta) (d u)/(d theta)).
2) p 48: Ex 3.2.4. An "=0" has to be added to the end of the Korteweg de Vries equation.
3) p 54: section 3.4 first paragraph. The energy argument is not correct. 1/2 k x^2 is not the potential energy
of a moving body, but the potential energy of a sping with extension x.
4) p 56: last formula, the nominator "2" below c^2 has to be erased.
(thanks to David)
5) p 65: line 10 from below: the factor -c in front of (\partial F(x-ct))/\partial t), and the factor $c$ for the
corresponding expression with $G$, are misleading and confusing. The author means the partial derivative
of the function v(x,t)=F(x-ct), but in the form as it is written there one has to apply the chain-rule, then one
would get c^2 (from the inner derivative), which is the wrong choice.
6) p 91: Def 19: One has to include that discontinuities are jump-discontinuities. Otherwise the tan-example would be included.
7) p 99: lines 7-10: these
formulas are a total disaster. The "x" and "L" belong into the
corresponding brackets .. anyway, it is easier just to do it on
8) p101: equations (4.21) and (4.22) are identical.
9) p183: line 7, "The only solution technique ... " is missleading, because we also have learned the Matheod of Characteristics and D'Almbert's solution.
10) p188: Exercise 5.6.1: It must be x^2 - y^2, and not x^2+y^2. (thanks to David, Yu-Li, ...).
11) p287: Textline after formula (8.29): It must be phi(x) and not sigma(x).
12) p289: Conclusion of the proof after formula (8.40) is wrong. A counterexample is \phi_1(x) = (L/2 x^2 - x^3/3) \phi_2(x). This satisfies the relation after formula (8.40). The correct proof can be found in the book of Haberman. (This is the most severe mistake so far. All other misprints can be found and corrected by the students, but it is much more involved to cure this one).
13) p290: Exercise 8.2.2. needs a condition that beta(x)>0
14) p290 Exercise 8.2.3. This exercise caused much confusion. These equations can not properly been written in Sturm Liouville form, because the Sturm Liouville problem is a problem to find pairs of (lambda, phi) simultaneously (by definition of a SL problem). Here lambda is kind of given, but not really, since no boundary data are given. If one considers "n" as a free parameter than it is not clear why it can't be a real number. Anyway. Some more careful formulation would help.
15) p293: In the formula for \lambda_n it must be \phi_n all the time.
16) p299: In the formula for \lambda_n it must be + \alpha...
17) p361: Exercises 10.2.4, 10.2.5: This can only be done on this level if we assume the Omega is a disk, or a sphere, or a cylinder?
18) p408: Example 11.1, definition of f(x), It must be 0<x<=1, not 0<c<=1
19) p413 line before formula (11.25), it must be d\xi, not du
20) p414 formula (11.32), the author should think if it is better to write d\theta at the end of the integral. I know that the author uses a notation which is standard in physical text's, but it is confusing
21) p242: the error-function has an error. The second integral must be from x to \infty, NOT from 0 to \infty.
22) p242: same for the definition of erfc
23) p453: formula after (11.134): This formula is simply WRONG!!! It costed me a whole sunday night to cure this error. ALso wrong is the corresponding formula in the table F.1 in the appendix. I come to that later. To arrive at the correct solution the author uses the principle of even numbers of mistakes. The one mistake makes up for an earlier one. The second mistake here is:
24) p253: the first line of equation (11.135) should not have the factor 1/(2 Pi) !
25) p494: Appendix F, Tabl F.1: The table is wrong !!! What is the point of a table if it contains wrong information ? I checked item 1. and 5. which are not correct and I suspect that the others are also wrong. It appars that the formula is based on the definition of FT with 1/sqrt(2 Pi), whereas the author uses the factor 1 to define FT.
26) p471: line 5 from below: it must be - \epsilon ; two times.