Where can I learn advanced calculus?

I am immensely interested in calculus.I am aware of both integration & differenciation and their respective application.But I see a lot of problems on this involving certain special functions.

Can someone just inform me about certain websites,PDF or videos so that I can learn these new stuff.

Some of the topics I found interesting and I want to learn about are:

Gamma ,Beta,Digamma,Poly gamma, functions,Poly logarithms ,Harmonic numbers,Riemann Zeta function,Walli's Integral, Binomial Series and their summations , Catalan's constant , Glaisher-Kinkelin constant, Dirichlet Eta & Beta Functions , etc.

#Calculus

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Comments

riemann zeta function

catalan's constant

glaisher–kinkelin constant

Pi Han Goh - 4 years, 9 months ago

@Aditya Sharma

A Former Brilliant Member - 4 years, 9 months ago

@Pi Han Goh

A Former Brilliant Member - 4 years, 9 months ago

http://classicalrealanalysis.info/documents/TBB-AllChapters-Landscape.pdf

Try the textbook above. Its free and contains analysis - usually studied by mathematicians after Calculus. It puts Calculus on a rigorous foundation and has a lot of proofs.

On the other hand, if you are looking for more "applied maths", you can look up subjects like differential equations, multi-variable calculus and partial differential equations. There is also complex analysis - calculus in complex variables.

You can get some of this from: khanacademy.org http://www.mecmath.net/calc3book.pdf (little short for me on practice, but does cover the concepts)

Star Light - 4 years, 8 months ago

Thanks

A Former Brilliant Member - 4 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$