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After getting to the last part of complex analysis, our teacher had mentioned that to solve harder, more intricate looking complex analysis problems, there are usually “cookbook” methods for solving these problems, for example splitting up multiple piecewise contours with different function definitions based on their shapes or using special functions that transform into another function. Most research articles and even math stack exchange is good enough for these types of problems, but i was wondering if anyone knows of a cookbook, or a book with a set of methods specifically targeting complex valued functions (similar to how physicists have mathematical methods for physicists but broader), usually solving a complex integral? If this question is a duplicate, which i couldn’t find, please specifically note the book itself, thanks.
I am an engineering student at the polytechnic university of turin.My first mathematics course is basically real analysis and calculus together and the book is called analysis 1 by claudio cannuto.
Even though it is a pretty good book I feel I need something that explains stuff a little more thoroughly.The problem that I am facing is that I cant really find many books that contain both the computational side of calculus but also the analysis side while also explaining stuff pretty well.
Would books like the first volume of zorich or understanding analysis by paul zorn be a good fit?Also since I have minimal calculus experience from high school the course is kicking my ass, so any advice would be welcome.
Thanks in advance for your answers.