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 * <<color("Corrections, Addition:")>> Right after Eq 4.14, $\omega$ was missing in the definition $r \equiv A/\omega_c$. Right before Eq 4.15,$t$ was missing in $\sin (\omega_c t + \theta_0)$. Both corrected (thanks ZA!). Also, footnote 4 is added.&mdash;~-''<<DateTime(2014-10-18T18:21:02-0700)>>''-~

Lecture Notes

  • Lecture 6, Oct 21: SHO, free or damped

  • Lecture 5, Oct 16: Conservation theorems, 1D motion

    • Addition, Correction: Footnotes 4 and 6 are new, and they reflect what we discussed in class. In the last bullet point of page 6, the last sentence was mathematically incorrect (while physically still very meaningful, if qualified a bit), and is removed. In principle, a saddle point can exist in one dimension in a mathematical sense, as we exemplified in class! At the end of the paragraph just after that bullet point “a saddle point” is added.—12:43PM, Oct 16, 2014

  • Lecture 4, Oct 14: UCM and SHM

    • Corrections, Addition: Right after Eq 4.14, $\omega$ was missing in the definition $r \equiv A/\omega_c$. Right before Eq 4.15,$t$ was missing in $\sin (\omega_c t + \theta_0)$. Both corrected (thanks ZA!). Also, footnote 4 is added.—6:21PM, Oct 18, 2014

    • Correction: Four lines below 4.12, at the end: $\ddot x$ → $\ddot y$. (Thanks, ZA!)—9:05AM, Oct 14, 2014

  • Lecture 3, Oct 9: Air resistance, Non-linear oscillator

    • Addition: Eq. 3.6 is actually integrable, rather easily by hand, and the result is now added (Eq. 3.9).—9:41PM, Oct 09, 2014

    • Correction: Eqs. 3.25 (and Eq. 3.27) missed $t_a$ in the middle term. Now, this is fixed, thanks to KD (!), whose question led to this correction. Equation numbers in page 9 are cleaned up as well.—7:27AM, Oct 09, 2014

  • Lecture 2, Oct 7: Newton’s laws, air resistance

    • Change: The end of page 4: references to sections and examples are removed.—12:15PM, Oct 07, 2014

    • Correction: Page 3: Marge box, near the end: last year → 2010.—9:32AM, Oct 07, 2014

    • Change: The end of page 2: “the textbook” → “various books.”—6:38PM, Oct 06, 2014

  • Lecture 1, Oct 2: Intro: particles, dimensions, vectors, scalars, matrices…

    • Addition: A new footnote (1) regarding real and complex numbers.—12:31PM, Oct 17, 2014

    • Addition, change: A new footnote (3). $L \rightarrow O$ in line 2 of page 7.—12:52PM, Oct 02, 2014

    • Correction: Pages 6,7, in definition boxes of vector, scalar: linear → orthogonal.—9:38AM, Oct 02, 2014

Appendices

  • A1: Perturbation

    • Correction At the end, the case when $v_0$ is non-zero was discussed incorrectly in the Oct 3 version. Now, corrected.—9:25AM, Oct 05, 2014

    • Addition: Page 8, more physics discussion added at the end.—10:28AM, Oct 03, 2014

    • Correction, addition: Page 7, the last term in the third order solution had a wrong sign—now corrected. Page 8, discussion added about the exact solution.—9:30PM, Oct 02, 2014

    • Change: page 6, the first sentence and the equations of the example (A.2) were arranged in a slightly different way.—12:42PM, Oct 02, 2014

  • A2: Essential trig identities