The writing of some formulas in Mathcad differs from the writing of these formulas in textbooks in mathematics.
My students have learned to partially correct this.
One example is in the picture.
Three questions.
1. Guess how my students do it! What is written in the hidden area.
2. Show other examples of such a mismatch of operators in Mathcad and textbooks.
3. What needs to be changed - Mathcad or textbooks?
It goes without saying that its not the textbooks which should be changed, of course.
And Mathcads way of showing the square of the sine and cosine is perfectly compliant with the ISO80000-2. Omitting the parentheses and putting the exponent right after the functions name is allowed for named functions which also have a named inverse (and also preferred by me in that case) but its not mandatory.
The standards would also allow something like
BTW, try your workaround in Prime where we don't have the comfort of the Prefix Operator 😉
To conform with the standards we would of course have to change the standard Prime display to use an upright font without serifs.
And as you ask for other examples: The usage of "log" for the decadic logarithm "lg" is wrong! According to the standards "log" is neither the decadic nor the natural logarithm but should only be used to represent a generic logarithm, e.g. to demonstrate a log rule.
So instead of writing
you may simply write
but thats it. There is nothing like log(100)=2.
BTW, quite some lecture notes and even some textbooks use "log" for the natural logarithm "ln" which of course is incorrect, too.
>Mathematica is famous for using non-standard own notations.
Boltzmann used Mathematica for calculations, not Mathcad.
Boltzmann died 1906, ISO was founded 1947 in London. Boltzmann didn't even have the opportunity to adhere to international standards because there simply weren't any. 😉
By the way, the tomb and the bust were cleaned in the meantime 🙂
https://upload.wikimedia.org/wikipedia/commons/5/58/Ludwig_Boltzmann_Grave_Zentralfriedhof_Vienna_2022.jpg
Nowadays we would write the equation (which actually stems from Max Planck based on ideas from Boltzmann) like
And here is Boltzmann, resurrected, studying the current standards online and being fascinated by the possibilities offered by today's technology
And if you are a fan, you sure need this: SKLOGW
From my book "Leo Tolstoy and Math" " (mpei.ac.ru)
Leo Tolstoy and Ludwig Boltzmann are similar externally and internally. Both in their young and not very young years were revelers, both married young people, both gave birth to a bunch of kids, both wore bushy beards in their mature years, and both, alas, ended their lives tragically. Boltzmann committed suicide. Tolstoy, as many believe, also actually carried out an act of suicide, but not instantaneous, but stretched out for a week. Both have unusual graves. Tolstoy has a modest mound in the forest. Boltzmann has his famous formula S = k lnW engraved on his gravestone, relating the entropy S of a thermodynamic state to the number of corresponding microstates W (log (decimal logarithm) is engraved on the monument instead of ln (natural logarithm), since the second spelling appeared only 13 years after Boltzmann's death). In addition, many mathematicians quite reasonably believe that there is only one natural logarithm, and the decimal logarithm is some kind of temporary construction designed to facilitate manual calculations (think of the slide rule, which we already mentioned). The parameter k in the Boltzmann formula is the Boltzmann constant, one of several fundamental constants (Planck's constant, Avogadro's number, etc.) on which modern physics is based. Boltzmann's forerunner in the discovery of molecular kinetic theory was Maxwell (1831–1879). You will laugh, but he also wore a bushy beard with a shovel. Maybe it's all about the beard?!
