apexNotes.txt

Instead of “Note: these are the same functions as in Exercises ##—##”, should we just combine them into a single problem with multiple parts?

13.5: Multi-v chain rule: Example 1 rewrites dz/dt as only a function of the independent variable t.  Examples 2 through 5 leave dz/dt as functions of the independent and intermediate variables.  Exercises 19-22 do this as well.



html could do:
http://aimath.org/knowlepedia/
ebook (epub?) (https://www.amazon.com/gp/education-publishing ?)
ET version
js to enable highlighting
use xslt to remove need for js when possible?
asymptote fonts?
	(https://sourceforge.net/p/asymptote/discussion/409349/thread/f4013b12/)
	(https://sourceforge.net/p/asymptote/discussion/409349/thread/29822c2b/)
convert figs.asy to javascript
3d images
	mine: https://sourceforge.net/p/asymptote/discussion/409349/thread/920f9769/
	svg: https://sourceforge.net/p/asymptote/discussion/409349/thread/27b15a6b/
	jpg: FAQ9.2
	mpg: examples/animations/earthmoon.asy


All
Transitions into and out of each section.
remove all !?


possible examples:
4.4 Fast Inverse Square Root
8.2 Fourier series
8.6 Gamma function?
8.7 required n to achieve desired level of accuracy
9.2 rationalizing a repeating decimal
9.2 Riemann Zeta function?
9.10 examples from numerical integration
swing jump distance


Should the notebook be distributed with the text?  Eventually.  CC-BY-NC, same as Apex.



My to do:
  kill [over|under]full hboxes
  spellcheck - aspell

  | to norm/abs
  Watch out for extra !
  unitfrac (or at least spaces before units). search:
	egrep -c '\dft\W' text/*tex | grep -v ':0$'
  vspace to addvspace, [small|med|big]skip to [small|med|big]break ?


Typos:

10.1#19: The solution is $x^2+z^2=\frac1{(1+y^2)^2}$.
10.3 p586 Definition 59: Should specify $v\ne0$.
10.5#31b “allows one to the use the formula.”
11.2 p637 Theorem 94: $\int\vec r$ isn’t defined.  We could take this to be a definition instead of a theorem.  The alternative would be to define $\int\vec r$ as the inverse operation of $\vec r’$, but I’m having trouble seeing how that would extend to definite integrals.
11.2#13: The function is not a vector (on the other hand, one could argue part of the problem is that realization).
12.4 Definition 88 p710: The dz on the left should be dw.
12.6#25-28(b): Should probably specify that $\vec u$ is the unit vector in the direction of $\vec v$.
12.8#17: The solution should have $f(x)=\dots\pm2\sqrt{4-x^2}$ instead of $f(x)=\dots\pm\sqrt{4-x^2}$ (three locations).  The absolute maximum is at $(\sqrt2,\sqrt2,4+4\sqrt2)$ (I forget if I’ve told you that one).
13.5#17,18: “compare you result with the known formula.”