Errata
Partial Differential Equations: Analytical and Numerical Methods
Mark S. Gockenbach
(SIAM 2002)

Note: Positive line numbers start at the top of the page, negative line numbers start at the bottom.

1. Page 21, Exercise 14: The units for $u_0$ and $u_{\ell}$ should be $\mbox{g}/\mbox{cm}^3$.
2. Page 28, Figure 2.5: The illustration is supposed to be a curve with arrowheads at the two ends.
3. Page 31, line -1: ${\cal R}({\bf A})$ should be ${\cal R}({\bf f})$.
4. Page 36, Exercise 2: $f:\rm {\bf R}\rightarrow\rm {\bf R}$ should be $f:[0,\infty)\rightarrow\rm {\bf R}$.
5. Page 39, line -9: ${\cal R}(A)$ should be ${\cal R}({\bf A})$ (that is, $A$ should be boldface).
6. Page 47, line -8: ${\cal R}(A)$ should be ${\cal R}({\bf A})$ (that is, $A$ should be boldface).
7. Page 49, Exercise 12: $f\in{\cal R}(L_n)$ should be $f\in{\cal R}(L_N)$.
8. Page 50, line 6: $x_1{\bf v}_1+x_2{\bf v}_2+cldots+x_n{\bf v}_n$ should be
   $x_1{\bf v}_1+x_2{\bf v}_2+\cdots+x_n{\bf v}_n$.
9. Page 133, Figure 5.1: Graph on bottom right is incorrect. The incorrect graph is of
   
   $$\frac{d^3u}{dx^3}(x)=\left\{\begin{array}{ll} 1,&0<x<\frac{1}{2},\\ [4pt] -1,&\frac{1}{2}<x<1.\end{array}\right.$$
   
   
   It is supposed to show
   
   $$\frac{d^3u}{dx^3}(x)=\left\{\begin{array}{ll} -1,&0<x<\frac{1}{2},\\ [4pt] 1,&\frac{1}{2}<x<1.\end{array}\right.$$
   
   

10. Page 188, equation (5.49) should read
    $$\begin{eqnarray*} -\frac{d}{d x} \left(k(x)\frac{d u}{d x}\right)&=&f(x),\ 0<x<\ell,\\ u(0)&=&0,\hspace{150pt}(5.49)\\ u(\ell)&=&0 \end{eqnarray*}$$
    
    

11. Page 198, Equation (5.59), third line: $(f,\phi_n)$ should be $(f,\phi_{n-1})$.
12. Page 216, line 14: ``...decay rapidly with $x$.'' should be ``...decay rapidly with $n$.''
13. Page 221, line 7:
    
    $$\frac{\partial u}{\partial t}(x,t)-D\frac{\partial^2u}{\part... ...n^2\pi^2}{100^2}\right) \sin{\left(\frac{n\pi x}{100}\right)}.$$
    
    
    should be
    
    $$\frac{\partial u}{\partial t}(x,t)-D\frac{\partial^2u}{\part... ...2}{100^2} a_n(t)\right) \sin{\left(\frac{n\pi x}{100}\right)}.$$
    
    

14. Page 262, Figure 6.12: There is a slight error in the graph, barely discernible on this scale (you might notice if you try to reproduce the graph and compare your results carefully with Figure 6.12).
15. Page 272, line -5:
    
    $$=ih^2-\frac{h}{4},$$
    
    
    should be
    
    $$=ih^2-\frac{h}{2},$$
    
    

16. Page 293, line 10:
    
    $$a_n(t)=b_n\cos{\left(\frac{cn\pi}{\ell}(t-t_0)\right)}+\frac{d_n\ell}{cn\pi} \sin{\left(\frac{cn\pi t}{\ell}(t-t_0)\right)}.$$
    
    
    should be
    
    $$a_n(t)=b_n\cos{\left(\frac{cn\pi}{\ell}(t-t_0)\right)}+\frac{d_n\ell}{cn\pi} \sin{\left(\frac{cn\pi}{\ell}(t-t_0)\right)}.$$
    
    

17. Page 310, footnote 48: ``...the use of the finite element obscures...'' should be ``...the use of the finite element method obscures....''
18. Page 375, line 12: ``smallest period'' should be ``longest period''.
19. Page 384, line 17: Missing new line after $K_{69}$. The list should be
    
    $$\begin{array}{l} K_{11},K_{12},K_{14},K_{15}\\ K_{21},K_{22... ...K_{87},K_{88},K_{89}\\ K_{95},K_{96},K_{98},K_{99} \end{array}$$
    
    

20. Page 392, line -2: ``...Bessel function...'' should be ``...Bessel functions...''.
21. Page 446, lines -1 and -8: ``neglible'' should be ``negligible''.
22. Page 466, lines 17, 18: $T_{12}$ and $T_{13}$ should be $T_{11}$ and $T_{12}$, respectively.
23. Page 488, line -3: $x$ should be boldface in $k(x)$.
24. Page 490, line 17: `` $\ldots\nabla g$ is a good approximation to $\nabla g$.'' should be `` $\ldots\nabla g$ is a good approximation to $\nabla f$.''
25. Page 549, solution to Exercise 6.1.11: According to the description of the problem, the boundary conditions should be $u(0,t)=5$, $u(100,t)=0$. The solution mistakenly assumes $u(0,t)=0$, $u(100,t)=5$. (So pages 549-550 give the correct solution to the wrong problem.)