 ## Typos and Errata for First Edition

(Go back to Second Edition)

For typos from the First Edition of the book, you will need to locate the Printing of your book. To do so, turn to the page in the front with the copyright (immediately preceding the dedication page). In the middle of this page, you will see a decreasing sequence of numbers, e.g.,

10 9 8 7 6 5 4 3 2
The last number that you see is the Printing of the book. In the above example, this is the Second Printing of the book. Scroll to the appropriate place below or click on the link to take you there.

Typos from First Printing

Typos from Second and Third Printing

## Typos from First Printing

Last updated Jan. 26, 2009

p. 6, Computer Code 1.1 for Matlab: A ' is missing before the c--' in the 8th line. The line should read
plot(x,y3,'c--')

p. 13, Computer Code 1.2 for Matlab: The y in the 2nd line should be an x.

p. 16, Computer Code 1.3 for Matlab: (2 errors) There is no '.' needed before the ^ in the fourth line. The line should read int('exp(t^2)',t,2,3)
The line
syms t
also needs to be inserted between the 4th and 5th lines.

p. 19. use "[ ]" instead of "{ }" in the implicitplot line in Maple code:
implicitplot([eq2,eq3,eq4,eq5,eq6,eq7,eq8,eq9], x=...rest is okay);

The code will run fine with "{ }" but you cannot use the "color" option with it.
p. 26, problem #39: First x is missing power of 5; Equation should read
2x^5dy+(x^2y^4+1)ydx=0

p. 62, Computer Code 1.9 for Matlab: M-file is called Example5.m. Thus we need to change the call to it (first line on p. 63) to 'Example5.m'.

p. 63, Computer Code 1.9 for Maple: The third line should not have "." before the "^". It should be
eq1:=(x^2+1)*diff....(the rest is fine)

p. 90, Computer Code 2.2 for Matlab: The correct final x-value in the first line should be 'xf=-1.2'

p. 101, problem #8: Change the IC in the last line to y(1)=0, to be consistent with stated problem.

p. 126, explicit solution on #8: The last term is negative:
y=(-1/2)(cos(x)+sin(x)-5exp(x))

p. 139, explicit solution on #8: The last term is negative:
y=(-1/2)(cos(x)+sin(x)-5exp(x))

p. 157, Problems 2, 3, 4: The middle term on the left side should have y', not y.

p. 161, Computer Code 3.1 for Maple: Remove "diff" from 3rd line, 4th line, and 5th line in order to have example match up with that of Matlab and Mathematica.

p. 204, Computer Code 4.1 for Maple: A ";" is missing at the end of the first line.

p. 211, 5th line: The general solution is from "Example 7 above"

p. 232, 3rd line (1st equation): The second term on the rhs is missing a "c2"

p. 250, 2nd eqn above (4.45): The 'D x sin x' should be 'E x sin x'

p. 231. The appropriate change of variables is "x=e^t".

p. 240. Right-hand-side of problem #3 should be cos(3x) for the first ODE and 12 cos(3x) for the second ODE.

p. 252, Computer Code 4.4 for Maple: Need "eval" around rhs of 3rd line. Code should read
eq1:=eval(simplify(subs(eqyp, eqODE)));

p. 315. Formula (3.15) is wrong and should be corrected in ALL corresponding places (for example, both equations before it, the one after it, etc.) as:
int((1/f^2)*exp(int(-a1/a0)dx)dx)
That is, the f^2 in the denominator needs to be outside of the exponential. The c does not need to be there.

p. 321, Computer Code 5.3 for Mathematica: On the third line, MatrixForm is spelled incorrectly The line should be
MatrixForm[RowReduce[Transpose[A]]]

p. 330. Delete "and eigenvalues" from the third sentence. It should read
However, students often prefer to have "nicer looking" eigenvectors.
p. 336, 2nd line after equation (5.55): The second row is just the first row multiplied by i (not -i as stated).

p. 337, Problem 4c: The matrix should be -3, 6 in the first row and 2, 1 in the second row.

p. 340, last eqn in corollary 5.5.1: The factor on the right should be exp(at), i.e., the t should be in the exponent, not multiplied times the exp(a).

p. 367. Insert the following sentences immediately preceding Remark 1:
"Important note: we point out that the above method won't work for any arbitrary basis of eigenvectors but will always work for some basis of eigenvectors. That is, in certain situations we may not be able to get past step (a) and the problem is that we need to choose a different basis from which to start. Starting from a "good" basis allows the above algorithm to work and we mention the following: Remark 1 ..."

p. 418, Problem 3: The first part of the assumption should be ".95x.9 were initially susceptible".

p. 419, Problem 8c: The rhs of the s' equation of (6.59) should additionally have "+alpha*i*s" and the rhs of the i' equation of (6.59) should additionally have "+alpha*i^2"

p. 421, Problem 7b: The equations should be x' = x+3y, y' = -3x+y.

p. 430. Second equation (integral of exp(-st)*sin(bt)dt...). Insert a minue sign between the two fractions on the rhs.

p. 444. In Theorem 7.3.1, remove from the 2nd part of piecewise definition the ">". That part should read:
f(t-a), t "greater than or equal to" a.
p. 451. In Problem #5, last inequality should read:
0, t>5.
p. 466, Problem 14: The coefficient of dy/dx should be 7 (not 'y').

p. 478, Computer Code 7.4 for Maple: A ";" is missing at the end of the last three lines.

p. 483, Problem 39: The 't' on the right hand side of first equation should be in the exponent: '-e^(2t)'.

p. 483, Problem 40: The 't' on the right hand side of first equation should be in the exponent: '-5e^(3t)'.

p. 531, Computer Code 8.3 for Matlab (multiple errors): The 4th line should reference "eqODE" so that it is
eq1=collect(eqODE)
The lines that calculate the c-values should all reference eq4 (not eq3). Thus the two sets of lines should be
c1=subs(eq4.c1)
c2=subs(eq4.c2)
c3=subs(eq4.c3)

p. 532, Computer Code 8.3 for Maple: The 6th line should be commented out with a "#" for Maple; thus, # goes at the beginning of the line

p. 559, Problems 6: The 'p' should be a 'p^2' in the ODE.

p. 559, Problems 7 (2 typos): The 2nd power series to multiply by is e^{-x/(2t)}. The left hand side of the equation has base 'e' (the exponential).

p. 559, Problems 8: The coefficient of y in the ODE should be 'e^(-2t)'.

p. 577, Computer Code Example 4 for Maple: The 3rd line should be commented out with a "#" for Maple, instead of the "%" as written

p. 572. Rewrite the function on the rhs of ans1:
ans1=nthroot(x^2+y^2,4);

p. 603, Computer Code C.1 for Maple: A ";" is missing at the end of the line that uses the linsolve command (9th command line from the bottom).

p. 610, equation (C.27): The "-2R_1" should be "-4R_1"

p. 610, Figure C.1: The second equation in EACH picture should be -x+y=2

p. 611, equation (C.30): The "R_2" should be "2R_2"

p. 617, equation (C.53): The "==" in the 2nd eqn should be "="

p. 631, answer to 1.2#27: The answer should be y=Cx^2-x

p. 631, answer to 1.2#29: The x should be in the numerator and the square root term in the denominator:
(+/- x)/sqrt(ln(x)+C)

p. 632, answer to 1.4#8: It IS exact, with answer (2cos x -1)y^2-2x = C

p. 632, answer to 1.4#16: The solution is for #15 (not #16 as given).

p. 632, answer to 1.5#48: Corrected answer is sqrt(y) = x^2 * ln|x| + C*x^2

p. 634, answer to 2.2#2a(ii):Corrected statement: "Solutions are unique everywhere except possibly y=-2."

p. 634, answer to 2.2#4: The "2"s should not be there. Correct answer is
y(x)=(x-1+sqrt(3))^2

p. 635, answer to 2.3#5: The "-2" is each of the pictures should be "-3" instead.

p. 643, answer to 4.5#5: The solution should be yp=Ax*e^(2x)sin(x)+Bx*e^(2x)cos(x)+Ce^(2x)sin(x)+Ee^(2x)cos(x)+F sin(x)+G cos(x).

p. 643, answer to 4.5#11: The solution should be A=11/17, B=-7/17.

p. 643, answer to 4.6#5: The solution should be yp=Ax*e^(2x)sin(x)+Bx*e^(2x)cos(x)+Ce^(2x)sin(x)+Ee^(2x)cos(x)+F sin(x)+G cos(x).

p. 643, answer to 4.6#11: The solution should be A=11/17, B=-7/17.

p. 644, answer to 4.7#3: The solution should be y(x)=-1+cos(x)+sin(x)+ln(sec(x)+tan(x))*sin(x).

p. 653, answer to C.2#6b (multiple errors): The 3rd column should be "4", "0", "6". The determinant of the coefficient matrix is -14. The answers are x=-84/(-14)=6, y=-42/(-14)=3, z=14/(-14)=-1.

## Typos from Second/Third Printing

p. 19. use "[ ]" instead of "{ }" in the implicitplot line in Maple code:
implicitplot([eq2,eq3,eq4,eq5,eq6,eq7,eq8,eq9], x=...rest is okay);

The code will run fine with "{ }" but you cannot use the "color" option with it.

p. 62, Computer Code 1.9 for Matlab: M-file is called Example5.m. Thus we need to change the call to it (first line on p. 63) to 'Example5.m'.

p. 161, Computer Code 3.1 for Maple: Remove "diff" from 3rd line, 4th line, and 5th line in order to have example match up with that of Matlab and Mathematica.

p. 231. The appropriate change of variables is "x=e^t".

p. 240. Right-hand-side of problem #3 should be cos(3x) for the first ODE and 12 cos(3x) for the second ODE.

p. 252, Computer Code 4.4 for Maple: Need "eval" around rhs of 3rd line. Code should read
eq1:=eval(simplify(subs(eqyp, eqODE)));

p. 315. Formula (3.15) is wrong and should be corrected in ALL corresponding places (for example, both equations before it, the one after it, etc.) as:
int((1/f^2)*exp(int(-a1/a0)dx)dx)
That is, the f^2 in the denominator needs to be outside of the exponential. The c does not need to be there.

p. 330. Delete "and eigenvalues" from the third sentence. It should read
However, students often prefer to have "nicer looking" eigenvectors.
p. 367. Insert the following sentences immediately preceding Remark 1:
"Important note: we point out that the above method won't work for any arbitrary basis of eigenvectors but will always work for some basis of eigenvectors. That is, in certain situations we may not be able to get past step (a) and the problem is that we need to choose a different basis from which to start. Starting from a "good" basis allows the above algorithm to work and we mention the following: Remark 1..."

p. 430. Second equation (integral of exp(-st)*sin(bt)dt...). Insert a minue sign between the two fractions on the rhs.

p. 444. In Theorem 7.3.1, remove from the 2nd part of piecewise definition the ">". That part should read:
f(t-a), t "greater than or equal to" a.
p. 451. In Problem #5, last inequality should read:
0, t>5.
p. 572. Rewrite the function on the rhs of ans1:
ans1=nthroot(x^2+y^2,4);

p. 644, answer to 4.7#3: The solution should be y(x)=-1+cos(x)+sin(x)+ln(sec(x)+tan(x))*sin(x).

Thank you for reporting the above typos and errata. We appreciate your support!!

Send additional ones to:
Randall Swift (e-mail: rjswift "at" csupomona "dot" edu)
or
Stephen Wirkus (e-mail: swirkus "at" asu "dot" edu)