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Notes on Diffy Qs: Differential Equations for Engineers: Changes

March 7th 2010 edition:

Pagination and numbering is kept as constant as possible. The following changes were made:

  1. Exercise 2.4.5 was not possible. Replace 0.8 with 1.1 and 0.39 with 0.8. Also add a note that you always get two possibilities for the mass in the formulas.
  2. Fix the formula for the complex roots on page 54, that is the discriminant should be negated under the square root sign if we take out an i.
  3. Fix theorem 4.1.2. There was an unneeded hypothesis about p and q which do not appear in the theorem.
  4. On page 60, fix the solution corresponding to complex roots.
  5. On page 60, fix the factorization of the characteristic equation in example 2.3.5.
  6. Also on page 60, relabel the arbitrary constants to be more consistent and make them all upper case.
  7. IODE Project III has changed (there was always some confusion about what was Project III) and now fits more after section 2.3, rather than before 2.6.
  8. On page 75 on top, there was a typo in the expression for u1', the x should be an argument to the cosine.
  9. In example 2.6.1, when stating the parameters, it should say m=0.5 (the example was computed correctly, so no other changes).
  10. Add exercise 2.4.6.
  11. Add hint to exercise 2.4.1.
  12. Theorem 2.5.1 holds for any order, so simply drop the words "second order"
  13. In exercise 2.5.1, also explicitly state that the initial conditions must be satisfied.
  14. Remove unneeded reference to [EP] on page 73.
  15. Put a box around the formula for the practical resonance frequency on page 81.
  16. Minor clarifications in places.
  17. Add a few more words to the index.
  18. Fixed other minor typos and mistakes.

February 17th 2010 edition:

Pagination and numbering is kept as constant as possible. The following changes were made:

  1. Fix solution to example 1.3.4. The solution should end up being . Thanks to Leonardo Gomes for noticing.
  2. Fix the computation of the constants in Example 2.4.1. Also fix the discussion right after the example, and fix Figure 2.2.
  3. Fix examples on page 72 and 73.
  4. Fix example 6.1.7 (page 234), the inverse transform was off by an extra 1/2.
  5. Fix Example 6.3.3 (page 243), the convolution was not computed correctly.
  6. Figure on page 37 (bottom of page) should have x=5 and x=0. Thanks to Jeff Winegar for pointing it out.
  7. Add Theorem 2.1.3 to highlight the fact that the superposition of two linearly independent solutions is the general solution to the homogeneous equation.
  8. Add Theorem 2.5.1, to give the solution to highlight how nonhomogeneous equations are solved.
  9. Add k to the examples on top of page 49 to make them less trivial.
  10. Exercise 2.3.4 was hard to read correctly, reformulate.
  11. Due to minor changes in the text, Figure 4.12 moved up a page resulting in a much more logical pagination.
  12. Many small clarifications.
  13. Many minor typo and grammar fixes.

You can get the LaTeX source of this old version if your really want to, but I suggest just using the newest version.

February 8th 2010 edition:

Pagination and numbering is kept as constant as possible. The following changes were made:

  1. Fix error in example on page 34. The integrating factor is off by a constant. Instead rework the example to be done by substituting into formula (1.4). Thanks to Sean Raleigh for noticing.
  2. Integrate in a different way in Example 1.1.3 to get rid of an extra k. Also fixup the constant in front. Finally rename C' to D and add assumption that k > 0.
  3. Fix the derivation in example 1.3.3, there was a negative sign mistake in the middle, though it made no difference in the solution. Also consistently keep time in minutes for the example.
  4. Fix example 1.4.1, there was a missing minus sign in the solution. Thanks to Ian Simon for pointing it out.
  5. Fix example on page 103. The expression for x1 in the middle of the page should have etcos(t) -i etsin(t). The rest of the example also needed to have the signs fixed. Thanks to Sean Raleigh for noticing.
  6. Exercise 1.1.7 had a typo making the solution very hard (without a computer algebra system). The right hand side should be a not .
  7. Exercise 1.3.7 was impossible (typo in the equation) replace with a different exercise.
  8. Add forgotten initial condition to Exercise 0.2.9 (x'(0)=0).
  9. Exercise 1.5.6 was way too difficult. Replace with an easier exercise.
  10. Add "then find x(10)" to exercise 1.1.1.
  11. Fix caption on Figure 1.
  12. Fix captions on Figure 1.7-1.10 (replace -0.1 by 0.1), replace Figures 1.6-1.10 with new versions which have the correct vertical scale.
  13. In example 1.2.2, use for an example solution.
  14. Add exercises 0.2.11, 1.1.9-10, 1.2.5, 1.3.8-12, 1.4.11-12, 1.7.5
  15. Exercise 1.5.1 was already worked out as an example. Replace.
  16. Regenerate some of the figures for better looking output using better parameters and newer version of genius.
  17. Clarify exposition somewhat in many places, and clarify some exercises.
  18. Fix some other minor grammar mistakes or simply awkward english in places.

You can get the LaTeX source of this old version if your really want to, but I suggest just using the newest version.

January 10th 2010 edition:

Pagination, numbering, everything is the same except for very minor edits as follows.

  1. Fixed examples on the first page of section 2.1. The k in the equations should be k2. Thanks to Thomas Wicklund for noticing.
  2. Got rid of the version with the EP sections in the titles. So there is now only one PDF version of the notes. If you like you can make any version you want from the latex source.
  3. Restructured the initial "notes about these notes" section a little.
  4. Fix some other minor grammar mistakes or simply awkward english in places.

You can get the LaTeX source of this old version if your really want to, but I suggest just using the newest version.

November 25th 2009 edition:

Pagination, numbering, everything is the same except for very minor edits as follows.

  1. Exercise 2.1.8 was missing a minus sign (thanks to Eliot Brenner for spotting thigs). It should look like:
    Exercise 2.1.8: Suppose is a solution to . Show that

    is also a solution.
  2. Minor english, grammar, spelling, and punctuation fixes all over.
  3. Minor clarifications, and some cosmetic changes.

You can get the LaTeX source of this old version if your really want to, but I suggest just using the newest version.

October 23rd 2009 edition:

Pagination, numbering, everything is the same except for very minor edits as follows.

  1. Exercise 4.6.4 on page 188 is fixed. While theoretically the exercise is possible, it is not what was intended. The last side condition should be u(x,0) = 3 cos x + cos 3x.
  2. Minor english, grammar, spelling, and punctuation fixes all over.
  3. The license in the book now explicitly specifies that printing course packs is permitted. Plus other minor updates in the introductory section.

You can get the LaTeX source of this old version if your really want to, but I suggest just using the newest version.

September 29th 2009 edition:

Pagination, numbering, everything is the same except for very minor edits as follows.

  1. Example 1.4.2 is fixed. There was an error with integration and there is a factor of 2 missing in the 5th line of the computation on page 30. If you do not wish to get the whole new pdf file, here is an updated page 29 and 30. Thanks to Thomas Wicklund for spotting this error.
  2. Minor english, grammar, and punctuation fixes all over chapter 1.
  3. Website added to notes (chapter 0).

You can get the LaTeX source of this old version if your really want to, but I suggest just using the newest version.

May 12th 2009 edition:

First version. You can get the LaTeX source of this old version if your really want to, but I suggest just using the newest version.

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