3 ms·

I'm trying to find a calculus book that goes incredibly deep into integration techniques Still searching, so if anyone has any tips I'd love to hear

cevi 2y ago
Have you tried to read any of the literature on the Risch algorithm? If you haven't, you might want to get started by taking a look at the paper "Integration in Finite Terms" by Rosenlicht [1] and chasing down some of the references mentioned in [2]. Of course, in the real world we don't give up on integrals just because they can't be expressed in terms of elementary functions. Usually we also check if the result happens to be a hypergeometric function, such as a Bessel function. If you want to get started on understanding hypergeometric functions, maybe try reading [3] (as well as the tangentially related book "A = B" [4]). [1] https://www.cs.ru.nl/~freek/courses/mfocs-2012/risch/Integration%20in%20Finite%20Terms--Maxwell%20Rosenlicht.pdf https://www.cs.ru.nl/~freek/courses/mfocs-2012/risch/Integra... [2] https://mathoverflow.net/questions/374089/does-there-exist-a-complete-implementation-of-the-risch-algorithm https://mathoverflow.net/questions/374089/does-there-exist-a... [3] https://www.math.ru.nl/~heckman/tsinghua.pdf https://www.math.ru.nl/~heckman/tsinghua.pdf [4] https://www2.math.upenn.edu/~wilf/AeqB.html https://www2.math.upenn.edu/~wilf/AeqB.html
ExciteByte 2y ago
These might of interest to you: https://link.springer.com/book/10.1007/978-3-030-43788-6 https://link.springer.com/book/10.1007/978-3-030-43788-6 https://link.springer.com/book/10.1007/978-3-031-24228-1 https://link.springer.com/book/10.1007/978-3-031-24228-1 https://link.springer.com/book/10.1007/978-3-030-02462-8 https://link.springer.com/book/10.1007/978-3-030-02462-8 https://link.springer.com/book/10.1007/978-3-031-21262-8 https://link.springer.com/book/10.1007/978-3-031-21262-8

cevi 2y ago

Have you tried to read any of the literature on the Risch algorithm? If you haven't, you might want to get started by taking a look at the paper "Integration in Finite Terms" by Rosenlicht [1] and chasing down some of the references mentioned in [2]. Of course, in the real world we don't give up on integrals just because they can't be expressed in terms of elementary functions. Usually we also check if the result happens to be a hypergeometric function, such as a Bessel function. If you want to get started on understanding hypergeometric functions, maybe try reading [3] (as well as the tangentially related book "A = B" [4]). [1] https://www.cs.ru.nl/~freek/courses/mfocs-2012/risch/Integration%20in%20Finite%20Terms--Maxwell%20Rosenlicht.pdf https://www.cs.ru.nl/~freek/courses/mfocs-2012/risch/Integra... [2] https://mathoverflow.net/questions/374089/does-there-exist-a-complete-implementation-of-the-risch-algorithm https://mathoverflow.net/questions/374089/does-there-exist-a... [3] https://www.math.ru.nl/~heckman/tsinghua.pdf https://www.math.ru.nl/~heckman/tsinghua.pdf [4] https://www2.math.upenn.edu/~wilf/AeqB.html https://www2.math.upenn.edu/~wilf/AeqB.html

ExciteByte 2y ago

These might of interest to you: https://link.springer.com/book/10.1007/978-3-030-43788-6 https://link.springer.com/book/10.1007/978-3-030-43788-6 https://link.springer.com/book/10.1007/978-3-031-24228-1 https://link.springer.com/book/10.1007/978-3-031-24228-1 https://link.springer.com/book/10.1007/978-3-030-02462-8 https://link.springer.com/book/10.1007/978-3-030-02462-8 https://link.springer.com/book/10.1007/978-3-031-21262-8 https://link.springer.com/book/10.1007/978-3-031-21262-8