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.

Note by A Former Brilliant Member
4 years, 1 month ago

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@Pi Han Goh

A Former Brilliant Member - 4 years, 1 month ago

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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 ago

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