Need a really advanced Calculus book

In summary, a really advanced Calculus book should cover topics such as multivariable calculus, vector calculus, differential equations, complex analysis, and advanced integration techniques. It is necessary to have a strong foundation in basic calculus before using a really advanced Calculus book, and it can be used for self-study but a background in advanced mathematics and access to resources is recommended. Prerequisites for using a really advanced Calculus book may vary, but typically include a strong understanding of basic calculus, linear algebra, and possibly differential equations. Some highly recommended authors and publishers for really advanced Calculus books include Michael Spivak, Tom M. Apostol, and Springer Publishing.
  • #1
AdrianZ
319
0
I'm looking for an advanced Calculus book that explains special (non-elementary) functions and their properties and applications (like Lambert W function, elliptic functions, error function, Ei and other special functions). I'd also like it to contain different methods of integration like contour integration and differentiation under the integral sign.
 
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  • #2
Much of what you are looking for is covered in Whittaker and Watson's Modern Analysis.
 
  • #3
i don't know if it has all this but i suggest you look at apostol's mathematical analysis.
 

1. What topics should be covered in a really advanced Calculus book?

A really advanced Calculus book should cover topics such as multivariable calculus, vector calculus, differential equations, complex analysis, and advanced integration techniques.

2. Is it necessary to have a strong foundation in basic calculus before using a really advanced Calculus book?

Yes, a strong foundation in basic calculus is essential for understanding the advanced concepts and techniques covered in a really advanced Calculus book.

3. Can a really advanced Calculus book be used for self-study or is it better suited for a classroom setting?

A really advanced Calculus book can be used for self-study, but it is recommended to have a background in advanced mathematics and access to resources such as online lectures or a tutor for assistance.

4. Are there any specific prerequisites for using a really advanced Calculus book?

Prerequisites for using a really advanced Calculus book may vary, but typically include a strong understanding of basic calculus, linear algebra, and possibly differential equations.

5. Are there any recommended authors or publishers for really advanced Calculus books?

Some highly recommended authors and publishers for really advanced Calculus books include Michael Spivak, Tom M. Apostol, and Springer Publishing.

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