Calculus Made Easy by Silvanus P. Thompson (1910)
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Calculus Made Easy by Silvanus P. Thompson (1910)
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Re: Calculus Made Easy by Silvanus P. Thompson (1910)
#2My biggest mistake as a SWE (now in my 30s) was not learning higher level mathematics and allowing what knowledge I did possess to wither on the vine.
Re: Calculus Made Easy by Silvanus P. Thompson (1910)
#3Silvanus' book makes calculus simple by adopting an infinitesimal approach, like Newton and Leibniz did when they invented calculus. But that approach was shunned by mathematicians for a long time, because it was only made rigorous in the 60s. After Silvanus' book, I also recommend Elementary Calculus: An Infinitesimal Approach, by professor Jerome Keisler, for those interested in this alternative pathway to calculus. It can be freely downloaded at https://people.math.wisc.edu/~hkeisler/calc.html
Relevant wikipedia entry: https://en.m.wikipedia.org/wiki/Nonstandard_analysis
Re: Calculus Made Easy by Silvanus P. Thompson (1910)
#4My biggest mistake as a SWE (now in my 30s) was not learning higher level mathematics and allowing what knowledge I did possess to wither on the vine.
What better hobby to pick for those cold winter evenings, than to do some integrals!
Edit: I can recommend this book for a self-guided study
https://archive.org/details/zeldovich-higher-mathematics-for...
The author was a Soviet nuclear physicist (who participated in the creation of the H-bomb), so his main point isn't rigor. It can be a nice change of perspective from standard American texts.
Re: Calculus Made Easy by Silvanus P. Thompson (1910)
#5My biggest mistake as a SWE (now in my 30s) was not learning higher level mathematics and allowing what knowledge I did possess to wither on the vine.
What better hobby to pick for those cold winter evenings, than to do some integrals! Edit: I can recommend this book for a self-guided study https://archive.org/details/zeldovich-higher-mathematics-for... The author was a Soviet nuclear physicist (who participated in the creation of the H-bomb), so his main point isn't rigor. It can be a nice change of perspective from standard American texts.
Although Soviet-era books were notoriously terse & difficult to digest, they had some very aesthetic typesetting. I have owned a few (Problems in Physics by Irodov, & another by Krotov) and they all share similar design aesthetics.
Re: Calculus Made Easy by Silvanus P. Thompson (1910)
#6I think it would be fun to go through all of these books in a group, but to also do worksheets with something like XCas, Maxima, Fricas, etc.
Re: Calculus Made Easy by Silvanus P. Thompson (1910)
#7Silvanus' book makes calculus simple by adopting an infinitesimal approach, like Newton and Leibniz did when they invented calculus. But that approach was shunned by mathematicians for a long time, because it was only made rigorous in the 60s. After Silvanus' book, I also recommend Elementary Calculus: An Infinitesimal Approach, by professor Jerome Keisler, for those interested in this alternative pathway to calculus…
I have mixed feelings about this. I've been through nonstandard analysis. My response was, "We shouldn't need the axiom of choice to define the derivative."
But I think that it is extremely important to understand that the infinitesimal notation really MEANS something. Here is some Python to demonstrate.
# d is a functor. It takes a function and returns a second function.
# The second function captures the change in f over a small distance.
# The dx/2 business reduces artefacts of it being a finite distance.
def d (f, dx=0.001):
return lambda t: (f(t + dx/2) - f(t - dx/2))
# d²x / dx²
def second_derivative (f):
return lambda t: d(d(f))(t) / (d(x)(t) * d(x)(t))
def x (t):
return t
def cubed (t):
return t*t*t
print("The second derivative of cubed at 1 is near", second_derivative(cubed)(1))Re: Calculus Made Easy by Silvanus P. Thompson (1910)
#8My biggest mistake as a SWE (now in my 30s) was not learning higher level mathematics and allowing what knowledge I did possess to wither on the vine.
Late 30s here. I keep feeling like I should learn math better, but damn, I just never need it. It’s much easier to learn stuff I need. As it is, I’ve lost everything back to about 8th grade math because I’ve never used any of it, so it’s just as gone as all the French I used to know but never found an excuse to use.
[edit] and I’m dreading my kids getting past elementary school math because they’re gonna be like “why the hell am I spending months of my life on quadratic equations?” and I’m not gonna have an answer, because IDK why we did that either. At least I have answers for calculus, even if they’re not much good (“so you can do physics stuff”, “right, but will I ever need to do physics stuff?”, “uhhh… unless you really want to, no.”)
Re: Calculus Made Easy by Silvanus P. Thompson (1910)
#9[deleted]
Re: Calculus Made Easy by Silvanus P. Thompson (1910)
#10Silvanus' book makes calculus simple by adopting an infinitesimal approach, like Newton and Leibniz did when they invented calculus. But that approach was shunned by mathematicians for a long time, because it was only made rigorous in the 60s. After Silvanus' book, I also recommend Elementary Calculus: An Infinitesimal Approach, by professor Jerome Keisler, for those interested in this alternative pathway to calculus…
I have mixed feelings about this. I've been through nonstandard analysis. My response was, "We shouldn't need the axiom of choice to define the derivative." But I think that it is extremely important to understand that the infinitesimal notation really MEANS something. Here is some Python to demonstrate. # d is a functor. It takes a function and returns a second function. # The second function captures the change in…
Dang it! I hate re-reading after the time for editing is over and finding a stupid mistake.
The Python is correct, but the comment is not. The formula for the second derivative should be, of course:
# d²y / dx²