This discussion centers on recommended books for learning integral solving techniques. Key titles mentioned include "Handbook of Mathematical Formulas and Integrals" by Alan Jeffrey and "Inside Interesting Integrals" by Andrei D. Polyanin and Alexander V. Manzhirov. The latter book offers a collection of clever methods for computing complex definite integrals, along with challenge problems and detailed solutions. Additionally, the discussion highlights the importance of complex analysis knowledge for understanding certain integral techniques, particularly those involving contour integration.
PREREQUISITESMathematics students, engineering students, and educators seeking to deepen their understanding of integral techniques and complex analysis applications.
Dragon27 said:You might like this one:
https://www.amazon.com/dp/1493912763/?tag=pfamazon01-20
just look at the title!
"Inside Interesting Integrals: A Collection of Sneaky Tricks, Sly Substitutions, and Numerous Other Stupendously Clever, Awesomely Wicked, and Devilishly Seductive Maneuvers for Computing Nearly 200 Perplexing Definite Integrals From Physics, Engineering, and Mathematics (Plus 60 Challenge Problems with Complete, Detailed Solutions)"
Here's an excerpt from the Preface:Buffu said:Does it assumes me to know complex analysis ?
For a modern undergraduate math major not to have ever had a course in complex analysis seems to me to be shocking. As an electrical engineering major, 50 years ago, I took complex analysis up through contour integration (from Stanford’s math department) at the start of my junior year using R.V. Churchill’s famous book Complex Variables and Applications. (I still have my beat-up, coffee-stained copy.) I think contour integration is just too beautiful and powerful to be left out of this book but, recognizing that my assumed reader may not have prior knowledge of complex analysis, all the integrals done in this book by contour integration are gathered together in their own chapter at the end of the book. Further, in that chapter I’ve included a ‘crash mini-course’ in the theoretical complex analysis required to understand the technique (assuming only that the reader has already encountered complex numbers and their manipulation).