Changelog `1^(st)` edition to `2^(nd)` (last updated 2022 Jul 14)
Introduced in the second edition
- Default typesize decreased from 12pt to 10pt
- Free, complete course management at MyOpenMath including randomly generated versions of most exercises now available. Course shell fully aligned to textbook available from the course browser. Request an instructor account to access.
Changes (do not appear in the `1^(st)` edition print version or previous version download)
Chapter 1
- P 10: "matrix" changed to "block"
- P 11: lower case letters for entries capitalized in definition of matrix subtraction
- P 20: exercise 1, column matrix times row matrix examples removed
- P 21: exercise 8, added clarification that `mathbf(u)` and `mathbf(v)` have the same number of entries
- P 22: added exercises on computing dot product in SageMath
- Section 1.4: "length" changed to "magnitude" (also modified throughout the text)
- P 25: clarification of the calculation
- P 29: exercise 6d, `mathbf(u)` and `mathbf(v)` swapped
- P 44: added questions about existence of inverses; TODO move exercise 4
- P 45: hint added to exercise 7; exercise 10 moved to section 1.5
- P 48: demonstration of the unusualness of eigenvectors added
Chapter 2
- P 57: shorthand provided in summary of elementary row operations
- P 59: clarification added to instructions of exercise 2
- P 60: exercises on elementary matrices added
- P 69: exercise 5, `a,b,c` specified as arbitrary real numbers
- P 73: paragraphs one and two adjusted
- P 74: crumpet 15, last sentence corrected
- P 76: synchronized the matrix and the code
- P 78: clarification of instructions for exercises 7 and 10
Chapter 3
- P 84: added "and all scalars `r,s` to theorem 3
- P 85: theorem 4 part 3 inserted: `(rA)^-1=1/r A^-1`; justification for theorem 4 claim 6 now requested in exercises
- P 86: "rule" changed to "property"
- P 87: several "calculate this without calculating that" exercises added
- P 90: removed spurious "as well"
- P 94: exercises 12 and 13 reworded
- P 101: solution reference in exercise 4 fixed
- P 102: exercise 17 and the preamble to exercises 20-21 reworded
- P 104: parts (vi) and (vii) of theorem 6 swapped
- P 109: added explanation of the "trick"
- P 120: `ME` changed to `EM`
- P 122: "both" removed from crumpet
- P 129: parentheses added to `det(MB)` in exercise 3
- P 130: claim in exercise 6 slanted
Chapter 4
- P 139 list of vector spaces trimmed down by 2 that were never used (one because it was not a vector space!); instructions in exercise 2 clarified
- P 142 instructions for exercises 21, 23, and 26 corrected
- P 143 order of equalities reversed
- P 144 preliminary discussion clarified
- P 147 "proper" inserted in exercise 4; `t^2` inserted in exercise 7
- P 152 definition of kernel generalized
- P 154 ordered pair added to exercise 1c; "the" changed to "a" in exercise 11
- P 155 `n` and `m` swapped in exercise 14; "linear" changed to "a linear transformation" in exercise 17
- P 163 brown line clarified
- P 164-167 collected all exercises involving rotation into a section at the end of the exercises
- P 167 added an exercise on reflection about a line other than the axes
- P 169 bolded "isomorphism" and "isomorphic"; inserted "corresponds" in penultimate paragraph
- P 171 added an exercise on identifying one-to-one functions; added an exercise on identifying onto functions; rephrased exercises 1 and 2; added "linear?" to exercises 3 and 4; added a third exercise like 3 and 4
- P 176 fixed refrence in footnote
- P 177 changed `1/(2pi)` to `1/pi` in exercise 1f; simplified wording of exercises 2-13
- P 179 eliminated exercise 15c
Chapter 5
- P 184 added a sentence to the explanation that row operation do not affect linear dependence relationships
- P 185 renamed parameters in the parametric form
- P 188-191 clarified the statements of 6 exercises
- P 195 added four exercises on calculating a vector given a coordinate vector
- P 195-197 removed a redundant exercise and clarified another
- P 202-204 much of the discussion moved to a crumpet
- P 206-207 several exercises clarified
- P 217 exercise 4 modified, part b added to exercise 6
Chapter 6
- P 226-227 clarified exercises
- P 232 reworded list item (iii) to use eigenspace dimension
- P 232-233 clarified notation for the dominant eigenvalue and associated quantities by subscripting with `d` instead of `j`
- P 234 replaced `M` by `mathbf(v)_6` in exercise 3 and reworded the instructions
- P 235 minor revisions to exercises 6 and 8
- P 236 rewrote exercise 14
- P 243 clarified exercises 2,4,5
- P 244 added exercise 13
- P 250 corrected definition of orthogonal projection in lise of key concepts
- P 252 replaced exercise 3h
- P 253 minor revision to exercise 7
Chapter 7
- P 257 minor rewording
- P 258 minor rewording; changed "theorem" to "corollary"
- P 260 added explanation of linear variation of parameters
- P 263 clarified crumpet 29 bullet point 1
- P 264 clarifications to exercise 1
- P 265-266 swapped method requested in exercises 3 and 4 and fixed solutions and answers
- P 276 changed "sector" to "industry" in exercise 9 and clarified
- P 277 changed numbers in exercise 11
- P 281 removed special treatment of case `m=0`
- P 285-287 corrected formula for Fourier coefficients
- P 288 added two parts to exercise 7; added "the first" to exercises 8-10; replaced `V_([0,L])` notation in Answers
- P 289 replaced `V_([0,L])` notation
- P 290 simplified explanation of brownie experiment
- P 292 clarified the role of Newton's law of cooling
- P 294 vocabulary correction
- P 295 added the term "long run behavior"
- P 298 clarified analogy between geometric series and discrete dynamical systems
- P 299 added some explanation of asymptotic periodicity
- P 300 added several parts to exercise 1 and modified existing parts
- P 301 fixed equations in exercises 10 and 11
- P 302 clarified linearization
- P 310 changed 50 to 60 in footnote
- P 312 extended the hint in exercise 12
Answers and Solutions
- P 315-413 corrected, supplemented, and synchronized many answers and solutions
PDF with revisions
A PDF with these revisions and numerous bug fixes is available for download here. This version will always be the most up-to-date revision and will change regularly. You might consider this a preview of the next edition. Suggestions welcome at brinl1@southernct.edu!