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In http://calculuswithjulia.github.io/precalc/exp_log_functions.html

Typo related to the following line:
The amount of time to double an investment that grows according...

The logarithm base should be e:

The amount of time to double an investment that grows according to $P_0 e^{rt}$ solves $P_0 e^{rt}=2P_0$, or $rt=\ln^{(2)}$. So we get $t=\ln^{(2)}/r$. As $\ln^{(2)}$ is

log(2)

h \cdot(a + n(n+1)/2) is accepted as true but it seems the correct one is (n+1)(a+h \cdot n/2) so the answer should be No, this is false. Am I wrong?

https://calculuswithjulia.github.io/precalc/polynomial.html#Factoringpolynomials

For example, the polynomial (x−1)1000 can be compactly represented using the factored form, but would require 1001 coefficients to store in expanded form. (As well, due to floating point differences, the two would evaluate quite differently as one would require over a 1000 operations to compute, the other just two.)

I don't think exponentiation is one operation, except where the base is a power of two. If the implementation does use the x86 floating point exponentiation instruction (which I don't think Julia does), then it's worth noting that that operation takes a lot longer than a single multiply and introduces rounding error (maybe more than the multiplies), so this isn't quite right.

Just for fun:

using BenchmarkTools

f(a, b) = a^b

# Exponentiate by squaring.
# Other algorithms are available
g(a, b) = let acc = a
    for _ in 1:b-1
        acc *= a
    end
    acc
end

@assert f(10.0, 50) == g(10.0, 50)
@assert f(.9, 100) == g(.9, 100)

# Same speed
@benchmark f(10.0, 50)
@benchmark g(10.0, 50)

# f is 50x faster, but that's because there's a better algorithm available for these smaller numbers that llvm is picking for us, I think.
@benchmark f(.9, 100)
@benchmark g(.9, 100)

Hi,
In the guide for Getting started (https://calculuswithjulia.github.io/getting-started-with-julia.html) there needs to be added "using Pkg" directive, so the newcomers won't wonder why the first command they are asked to input does not work :)
Thanks for putting it together!

julia> 2^(-1)
0.5

@jverzani

in http://calculuswithjulia.github.io/getting-started-with-julia.html :
Bindar and Julia Box are great and convenient, -> Binder

in http://calculuswithjulia.github.io/julia_interfaces.html# :
Notebooks can be saved (as *.ipynb files) for sharing or reused. -> reuse
programming withing the language. -> within

should fix into
$$~
\sqrt{h(t)} = \sqrt{h_0} -\frac{1}{2}\frac{a}{A}\sqrt{2g} t.
~$$
https://github.com/CalculusWithJulia/CalculusWithJulia.github.io/blob/master/ODEs/odes.mmd#L225

As I'm sure you know, return is not a function and doesn't need the brackets. You also mention a "return call".

By this point you've introduced other keywords (if, else, function, end), so one more shouldn't be too scary, right?

These break tags are visible when they probably should not be. https://calculuswithjulia.github.io/precalc/numbers_types.html#Complexnumbers (scroll up slightly)

I believe this line https://github.com/CalculusWithJulia/CalculusWithJulia.github.io/blob/master/integrals/improper_integrals.mmd#L355 should have one f(x) as an integrand