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\begin{document}
\begin{center}

{\LARGE \bf ERRATA AND ADDITIONS: \\ \em{SECOND EDITION}} \\
{\large \bf \VERSIONDATE}

{\bf COMPLEX VARIABLES, \\ INTRODUCTION AND APPLICATIONS}

M. Ablowitz and A. Fokas \\
Cambridge University Press, 2003

Corrections and small additions;
asterisks ({\bf *}) indicate more important corrections

\end{center}

\hrule{}

{\bf p.8}  Problem 4. Spelling: change: ``Estabilish'' to
	``Establish''
	
{\bf p. 34} An Alternative form to Theorem 2.1.1:

{\bf Theorem 2.1.1}  If the function $f(z)=u(x,y)+iv(x,y)$ is differentiable at a point $z=x+iy$ of a region in the complex plane, then $u,v$ satisfy the Cauchy-Riemann conditions (Eq. (2.1.4)) at $z=x+iy$. If $u_x,u_y,v_x,v_y$ are continuous and satisfy the Cauchy-Riemann conditions at $z=x+iy$ then $f'(z)$ exists.

{\bf p.48} 4 lines  from top, replace "On the other hand, if we took.." by 
"On the other hand we reiterate, if we took.."
	

{\bf p.99} 3 lines from top. Replace: "If $f$ is a differentiable function..." by "If $f$ is a continuously differentiable function..."

\onsamepage
In Theorem 2.6.7: change: ``\ldots bounded by a simple
	closed contour $C$, then at any interior point $z$''
	to  ``\ldots bounded by a simple closed contour $C$,
	and if $f$ is continuous on $C$, then at any interior point $z$''

{\bf p.113} Line 3 change: ``Theboundedness\ldots''
	to ``The boundedness\ldots''

\onsamepage   In the two equations following line 3, change:
	``$ |b_1(z)|<B$ hence $ |b_n(z)|<BM^{n-1}$'' to
	``$ |b_1(z)| \le B$ hence $ |b_n(z)| \le BM^{n-1}$''
	
{\bf p.114} Problem 5b replace $R<|Re z| \leq 1$ by $R<Re z \leq 1$ 


{\bf p.145} In Example 3.5.2 replace "Describe the singularities of the function" by "Describe the singularity of the function at $z=0$"


{\bf p.148} 3 lines above Eq. (3.5.5) after ``\ldots{}
	$\ldots{} f(z) \rightarrow 0$ as $r \rightarrow 0.$''
	add: ``Also for $\theta= \pm \pi/2, |f(z)|=1$.''

\onsamepage   2 lines above Eq. (3.5.5)
	change ``\ldots{} namely, $r=(1/R)\cos \theta$
	(i.e the points\ldots{}'' to ``\ldots{}namely,
	$r=(1/R)\cos \theta, R \neq 0$, (i.e., the points\ldots{}''

\onsamepage   last two lines, change:
	``Thus $|f(z)|$ may take on any positive value other than
	zero by the appropriate choice of $R$'' to
	``Thus $|f(z)|$ may take on any positive value in
	the neighborhood of $z=0$''.

{\bf p.181} In Theorem 3.7.3: change:
	``\ldots{} simply connected domain $D$, then the linear\ldots{}''
	to  ``\ldots{} simply connected domain $D$ containing $z_0$,
	then the linear\ldots{}''

{\bf p.185} line after Eq. (3.7.41), before:
	``($z=0$ can be translated to $z=z_0$ if we wish)''
	insert: ``$z \neq 0,\omega_{m,n}$''

\onsamepage   line after Eq. (3.7.43), before
	``The function \ldots{}'' insert:
	``Alternatively, by taking the derivative of
	Eq.(3.7.42) $w$ satisfies
	``$w'' = 6w^2-\frac{g_2}2$''.

{\bf p.186} line immediately after Eq. (3.7.45) insert
	(no new paragraph):
	``Also note that $w_1$ satisfies the second order ODE 
	$w_1''=2k^2w_1^3-(1+k^2)w_1$.''

{\bf p.198}  2nd line above Example 3.8.2 change
	``\ldots{} time T with \ldots{}'' to
	``\ldots{} distance with \ldots{}''
	
{\bf  Section 4.1} Take care to note that the contours $C_j$ are to be distinguished from the Laurent coefficients $C_j$. In most places it is clear. One can replace the contours $C_j$ by $\cal{C}_j$ esp. on p. 207,208 to be clear.
	
{\bf p.206} 3 lines from bottom replace "...contour lying in $D$." by "...contour lying in $D$ enclosing $z_0$."


{\bf p.212}  One can eliminate the equation number (4.1.14) (but do not eliminate the equation).


{\bf p.257} Problem 14, 3rd line, change:
	``\ldots{}where $C_R$ is the \ldots{}'' to
	``\ldots{}where $C_R$ is the outside part of the \ldots{}''

{\bf p.258} Problem 14, part (c) change the sign of the right
	hand side:  from
	``$= \pi b_{n+2}$''
	to ``$= -\pi b_{n+2}$''

{\bf p.266} problem 6. Change the last two lines from:
	``Consider the two functions $-f_0$ and $ f(z)-f_0$,
	and use \ldots{} to deduce that $f(z)=f_0$'' to:
	``Consider the two functions $-f_0$ and $ f(z)$.
	Then Rouch\'e's Theorem implies that the functions
	$-f_0$, $f(z)-f_0$ have the same number of zeroes.''

{\bf p.268}  line 10-11-12 from top, omit:
	``(sometimes referred to as bounded mean oscillations (BMO))''; also omit "(i.e. in BMO)" in the following line.
	
{\bf p.270} In Eq. (4.5.10) the term $\delta (x-x_0)$ in the second integral (which has a $lim_{\epsilon \rightarrow 0}$) should be replaced by $\Delta (x-x_0;\epsilon)$

{\bf p.272} In Eq. (4.5.17) middle line replace $e^{ikx'} g(x')$ by $e^{-ikx'} g(x')$

\onsamepage 2 lines after Eq. (4.5.18) replace $f(x)=\delta(x-x')$ by  $f(x)=\delta(x)$; then in the 3rd line of the following paragraph replace "... evaluating Eq. (4.5.17) at $x=0$: " by  "..evaluating Eq. (4.5.18) at $x=0$: " 



	
{\bf p.563} First equation in 2nd paragraph for $\Phi(k)$. Inside integral (add a left parens.): change
$\frac{f(l)}{X^+(l)l-k)}$ to $\frac{f(l)}{X^+(l)(l-k)}$
	
	

\end{document}