09-04-08 Note that the url given for the textbook is currently a broken link. Instead, the information is temporarily posted here.
09-04-08 There are many formatting issues, especially in the table of contents and figures. There are also a few coloring errors. I'm sorry for these, but please ignore them.
Most of the errors won't hurt your understanding. Major ones are highlighted in red.
09-04-08 p. x: "meant be" should be "meant to be".
09-04-08 p. 28: In the first line of Sec. 2.3, "a a Monte" should be "a Monte".
09-06-08 p. 41: In (b), "the the" should be "the".
09-06-08 p. 92: In the fourth bullet, change ". and" to ", and".
09-08-08 p. 10: The footnote should read, "The solutions to challenges, except those marked "Extra", can be found on the book's website."
09-08-08 p. 16: In "Use an alternate formula", add a footnote to say, "This is true since x^2 - 56 x + 1 = (x-x_1)(x-x_2)."
09-08-08 p. 21: In the figure caption, insert "equation" before "(1.1)".
09-08-08 p. 29: In the pointer, "Unit III" should be "in Unit III".
09-08-08 p. 30: The equation for phi^lo should end in a comma, and that for phi^up should end with a period.
09-08-08 p. 44: The first sentence after the bullets should begin, "In addition to using a testing program,".
09-08-08 p. 20: The last sentence should begin, "If we use Gauss elimination ...".
09-09-08 p. 45: In Pointer 4.1, "See, for example [33]." should be "See, for example, [33]."
09-09-08 p. 59: In Pointer 5.4, "inspection,we" should be "inspection, we"
09-09-08 p. 78: In Section 5.6.1, the first sentence of the second paragraph ("In MATLAB we compute...") is missing a period.
09-09-08 p. 84: In Pointer 5.10, the last sentence is missing a period.
09-09-08 p. 108: In Pointer 8.1, second paragraph: "The generalized eigenvalue problem, used in Challenge 8.1 is discussed...": delete the comma.
09-11-08 p. 33: Remove space between "..." and the comma that follows it.
09-11-08 p. 59: In Pointer 5.4, "if it is defines" should be "if it defines".
09-13-08 p. 55: Let delta = machine-epsilon / 2.
09-13-08 p. 57: Fig. 5.1: "To" should be "to".
09-13-08 p. 59: In Challenge 5.4, insert the (2,2) element of L after the (3,1) element in the list.
09-13-08 p. 62: In Alg 5.1, change the arrow to an equal sign.
09-13-08 p. 64: In Alg 5.2, change "k=1,....n-1" to "k=1,...,n-1" and remove period at end of next line.
09-13-08 p. 65: In the first sentence of Section 5.3.3, remove the first occurence of the word "matrix".
09-13-08 p. 68: Insert a period after the last displayed equation.
09-13-08 p. 69: Remove the period after the first displayed equation in Pointer 5.5.
09-13-08 p. 75: change "a system" to "the system" in the 2nd bullet.
09-13-08 p. 79: Insert two plus signs in the 3rd displayed equation in the section, one after each set of dots.
09-13-08 p. 80: Insert a plus sign in the 1st displayed equation in Challenge 5.19, after the dots.
09-14-08 p. 69: Change "plot(t,b',g*')" to "plot(t,b,'g*')".
09-15-08 p. 76: In Challenge 5.14, change "form" to "contains" and insert comma after dots.
09-15-08 p. 80: In Challenge 5.19, insert comma before v_n in the definition of V, and change "+r" to "-r" three times.
09-15-08 p. 81: Explain that the horizontal and vertical axes correspond to perturbations in the 1st and 2nd component of the solution.
09-15-08 p. 81: In Algorithm 5.5, last line, square each of the c components.
09-15-08 p. 81: Change "+r" to "-r" in the matrix inverse bullet.
09-15-08 For consistency throughout the book, change all occurrences of "full rank matrix" to "full-rank matrix", and all other occurrences of "full-rank" to "full rank".
09-15-08 For consistency throughout the book, change all occurrences of "nullspace" and "null-space" to "null space".
09-15-08 p. 107: In Challenge 8.6 (b) and (c), insert a plus sign after the three dots.
09-15-08 p. 53: Change "Examples of Level 1 BLAS operation" to "Examples of Level 1 BLAS operations".
09-16-08 p. 66: In Challenge 5.11, change "The norm of the vector" to "The norm of a vector".
09-18-08 p. 66: In the paragraph that starts with "Therefore", insert an equal sign after the three dots.
09-18-08 p. 26 In Pointer 2.1, in the expression for ||x||_2, put absolute value signs around the x's. (Otherwise it is incorrect for complex values.)
09-18-08 For consistency throughout the book, always put a comma before "where" in sentences like, "A, where A = ..." or "A, where A is".
09-22-08 p. 26 In Pointer 2.1, the matrix norms can be generalized to mxn matrices by changing the upper limit on the summations over i from "n" to "m".
09-24-08 p. 114: Change "curve" to "surface" twice.
09-24-08 p. 115: In the definition of H(x), i,j=1,...,n.
09-24-08 p. 122: Change the boldface header from "Modified Cholesky Strategies" to "Modified Cholesky Strategy".
09-24-08 p. 128: Insert comma after 2nd equation for p.
09-24-08 p. 129: Define g^{(k+1)} = g(x^{k+1}).
09-24-08 Caption to Figure 9.6: Change "positive bases" to "spanning sets".
09-24-08 Challenge 9.13: Change "convergence" to "Convergence" in table.
09-24-08 p. 141: In the constrained optimization problem, c_i is a function from S into R, i=1,...,m.
09-24-08 p. 141: The sentence below the two bullets should not be a new paragraph.
09-24-08 p. 143: Insert a comma after the displayed equation with epsilon on the right-hand side.
09-24-08 p. 137: The last line should end in a comma.
09-24-08 p. 149: In the definition of the barrier method, "f(x)" should have x in boldface. (It is a vector, not a scalar.)
09-24-08 Table 10.1: The constraint for 2nd order cone programming should have a >= sign, not <.
09-24-08 Chapter 12: "gymbal" should be "gimbal".
09-24-08 p. 163: Insert comma after three dots.
09-24-08 Challenge 13.3: Insert period after 2nd displayed equation.
09-24-08 Equation (15.3): Insert comma.
09-25-08 p. 111: Each bullet should end with a period.
09-25-08 "Linesearch" should be one word, throughout the book.
09-25-08 p. 117: Eliminate comma before "and is given in Algorithm 9.1".
09-25-08 p. 121: Insert comma before "and it is remarkably fast".
09-25-08 p. 125: In caption to Fig 9.4, remove comma before "but".
09-25-08 p. 130: Remove period in equation (9.5).
09-25-08 p. 152: Insert commas after each of the first 3 displayed equations.
09-25-08 p. 166: Remove comma before "but has not translated".
09-25-08 p. 170: Capitalize "is" in the subsection header.
09-25-08 p. 177: Insert comma after displayed equation "K = ".
09-25-08 p. 183: Insert comma after equation (15.3).
09-26-08 p. 9: Replace "1.70" by "almost 3.40". Replace "8.98 x 10^307" by "almost 1.80 x 10^308"
09-26-08 p. 18: Insert comma after "Ax=b" displayed equation.
09-26-08 p. 22: Remove comma after "graphically".
09-26-08 p. 24: Change the derivative "d" to roman font (twice).
09-26-08 p. 26: Note that x is an nx1 vector.
09-26-08 p. 28: In Pointer 1, "data that needs" should be "data that need".
10-02-08 p. 126: In Pointer 9.3, insert a space between "Schnabel" and "[42]".
10-02-08 p. 118: Insert period after reference to Figure 9.3.
10-02-08 p. 120: In Challenge 9.3, insert period after "i.e".
10-02-08 p. 70: After Algorithm 5.4, change "[Q, R, P] = qr(A,0)" to "[Q, R, P] = qr(A)".
10-02-08 In references like "[111, p.304]", there should always be a space before the page number: "[111, p. 304]". Make this change wherever appropriate.
10-03-08 p. 86: In Pointer 6.1, "pehaps" should be "perhaps".
10-07-08 There are some inconsistencies in numbers such as "1" vs. "one". Please ignore.
10-07-08 The formatting of algorithms is also inconsistent, sometimes beginning "Take" and sometimes "Given". Punctuation is also inconsistent. Please ignore.
10-07-08 p. 299, In Pointer 24.2, in F_2, the exponent on x_2 should be a 2.
10-07-08 p. 299, last paragraph: remove the 2nd "then".
10-07-08 p. 304, In Algorithm 24.3, when increasing lambda, always keep it <= 1. Initialize x-hat to the solution to F_a(x) = 0.
10-07-08 p. 306, In Challenge 24.4(c), "[x,lambda]" should be "[lambda,x]".
10-07-08 p. 306, In the parameterized Sard theorem, let a have n components, not m.
10-07-08 p. 308: Change the sentence before the challenge to, "When the ode solver passes the value lambda=1, use inverse interpolation, discussed in the next challenge, to compute ..."
10-07-08 Chapter 25: My terminology is bad:
"truss" should be "member" or "beam.
"triangle" should be "triangular truss".
"vertex" of a truss should be "node".
10-07-08 p. 311: Insert period after displayed equation.
10-07-08 p. 313: In the displayed equation above the challenge, remove the "*".
10-07-08 p. 313, In Challenge 25.2, change "Solve the four problems from" to "Solve each of the four problems".
10-07-08 p. 317, In Challenge 26.1, "100 days" should be "100 time units".
10-07-08 p. 317: In the last line, "J(x_t)" should be "J(x_{fixed})".
10-07-08 p. 318: In Challenge 26.3(a), "cycles" should be "time units".
10-07-08 p. 320: In Pointer 26.1 and in the bibliography, "Constantino" should be "Costantino".
10-09-08 p. 115: In the "First-Order" section, note that h is a small positive scalar.
10-09-08 p. 138: In the table of Challenge 9.13, remove the space before "itn".
10-09-08 p. 142: Replace the comma at the end of the last full paragraph by a period.
10-09-08 pp. 146-147: Make punctuation in bulleted list consistent.
10-09-08 p. 162: In Pointer 11.1, change "Challenge 11.5 11.6" to "Challenges 11.5 and 11.6".
10-09-08 p. 168: Change "Quaternions are a common choice, and the Pointer 12.1" to "Quaternions are a common choice, and Pointer 12.1".
10-09-08 p. 170: Insert period after "where t = [0, 0.01, . . . , 6.00]".
10-09-08 p. 173: In the caption to Fig. 13.2, change "time(sec)" to "time (sec)".
10-09-08 p. 177, In Section "Model 1: Least Squares (E = 0)", make the punctuation in bulleted list consistent.
10-09-08 p. 316: In the fourth bullet, change "a adult" to "an adult".
10-10-08 p. 121: Insert a comma before "k" in the 2nd displayed equation.
10-13-08 p. 123: In Algorithm 9.2, change the "<" in the termination test to "<=".
10-14-08 p. 126: In the bullet for Lipschitz continuous, remove "for all x,".
10-23-08 p. 191: In the first sentence, put a comma before "and" and insert "is" after "it".
10-23-08 Throughout: Be consistent about hyphenation in "pseudorandom" and "quasi-random".
10-23-08 p. 196: In the first sentence, insert "nonnegative" before "probability".
10-23-08 p. 203: change "gives an increase" to "gives a large increase"
10-23-08 p. 208: In Pointer 17.3, change "But they" to "But the samples".
10-23-08 p. 209: Insert a comma before "where alpha is a constant".
10-23-08 p. 210: Insert a comma after the 4th displayed equation.
10-23-08 p. 211: In Algorithm 18.2, x should be made boldface (twice) in the last line.
10-23-08 p. 213: In the first displayed equation, the last x should be made boldface.
10-23-08 p. 214: In Algorithm 18.3:
10-23-08 p. 215: In the paragraph after Challenge 18.4, change "times the variance" to "times the square root of the variance".
10-23-08 p. 221: In the 2nd paragraph, change "a (overly!)" to "an overly".
10-23-08 p. 233-234:
10-23-08 p. 234: In the first line of the first displayed equation of Section 20.1.1, "(t)" should not be a subscript.
10-23-08 p. 237: In the table, under Example 1, replace "e^{-t}" by "e^t" (twice). In the last column of the table, the figures should be listed in order (1,2,3).
10-23-08 p. 242: In Approach 2, change "derivative" to "derivative of y".
10-23-08 p. 243: In Algorithm 20.1, capitalize "method" and format the algorithm so that it is consistent with other algorithms. (Other algorithms in this chapter also need some reformatting.)
10-23-08 p. 252: In Figure 20.9, the stars should be on top of the tick marks.
10-23-08 p. 260: Remove the empty equation labeled (20.22) and fix references to the 4 equations around it.
10-23-08 p. 261: Insert comma after 1st displayed equation.
10-23-08 p. 263: In Challenge 20.21, insert comma before "where".
10-23-08 p. 265:
10-23-08 p. 266: In Pointer 20.8, change "solution exists" to "solution exists (with two continuous derivatives)". In the 2nd bullet, remove "- b'(t)/2".
10-23-08 p. 271: In paragraph 3, line 4, "t <= 0" should be "t >= 0".
10-23-08 p. 274: In Challenge 21.4(a), the notation "I(t)_{ij}" means "I(t, x_i, y_j)", and similarly for the other terms.
10-23-08 p. 275: In the 3 displayed equations midpage, change "t+1" to "t + delta", 3 times.
10-23-08 p. 275: In the line above Challenge 21.5, change "problem" to "challenge".
10-23-08 p. 279: In Challenge 22.2, the "d theta" in the last term has the wrong typeface for "d".
10-23-08 p. 279: In the line after the challenge, insert a comma before "where".
10-23-08 p. 286: In Pointer 23.2, use "Sec." instead of the symbol (twice).
10-23-08 p. 291: In Challenge 23.7, insert a comma before "where".
10-24-08 p. 298: In Pointer 24.1, insert a comma after "considered in Challenge 24.5".
10-27-08 p. 300: In the 2nd paragraph, change "some model" to "a model".
10-27-08 p. 300: In the third paragraph, change "the gradient of F" to "the gradient of f".
10-27-08 p. 305: The vertical axis in the figure should be labeled "x(lambda)", where x(lambda) denotes the solution curve for rho(lambda,x)=0.
10-27-08 p. 307: Change "junp" to "jump" and "sysems" to "systems".
10-30-08 p. 298: In Figure 24.1, the label for the point "b" in the right-hand picture has been cut off.
11-11-08 In Challenge 17.1, the Lipschitz constant is 98.5.
11-13-08 p. 199, 5th line from bottom: "the the" should be "the".
11-13-08 p. 192: The third bullet is missing a period.
11-13-08 p. 211: first paragraph: "We illustrate this method Pointer 18.1" should be "We illustrate this method in Pointer 18.1".
11-17-08 p. 226: "Challenge" should not be capitalized in the text following the challenge.
11-17-08 p. 227: Change p^{k+2} to (k+3)^p.
11-21-08 p. 243: Change "the difference between y(t+h) and y_{n+1}" to "the difference between y(t_n+h) and y_{n+1}".
11-21-08 p. 247: in Algorithm 20.2 change "t0, t1,...tN," to "t0, t1,...,tN," (add comma)
11-24-08 p. 201: "A convex function f(x) has a unique minimum that can be found" should be "A minimizer of a convex function that is bounded below on a compact set can be found"
11-25-08 p. 246: In Challenge 20.6, the superscripts "n+1" and "n" should be subscripts.
11-25-08 p. 244: In the backward Euler displayed equation, "h" should be "h_n".
11-25-08 p. 246: In the displayed equation in Challenge 20.6, "h" should be "h_n".
11-25-08 p. 245: When the mean value theorem is used, set eta = (t_n, yhat), where yhat is between y_n and y(t_n).
12-01-08 p. 222: In the last sentence in the paragraph before Challenge 19.2 "[r_2 n + 1]" should be "[r_1 n + 1]".
12-01-08 p. 234: Remove comma after "(20.1)" in the first line of Section 20.1.1.
12-01-08 p. 242: In Challenge 20.3, "point data" should be "data point".
12-01-08 p. 251: Insert a period at the end of the 2nd paragraph.
12-01-08 p. 252: In the caption of Figure 20.9, change "factor of two" to "a factor of two".
12-01-08 p. 253: Two lines above Section 20.2.6, change "it is usually" to "it usually".
12-01-08 p. 266: In the Sundials link, change the period after "gov" to "/". The link to Genda should be http://www.math.tu-berlin.de/numerik/mt/NumMat/Software .
12-01-08 p. 281: Change "integrate equation (1)" to "integrate equation (22.1)". Change "problem (1)" to "(22.1)".
12-01-08 p. 286: In Pointer 23.1, change "Challenge 23.5 and 23.6" to "Challenges 23.5 and 23.6".
12-01-08 Leading zeros should be inserted in many locations: e.g., "h=.1" should be "h=0.1". Please ignore all of these.