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I read here all the recommendations but looking at tables of contents of each book none satisfies what I need.I am given a book series that has 4 volumes and 2800 pages but it is very hard to follow.I am looking for something that helps me learn how to proof and little easier to follow. The topics i need are (

  • Improper Integrals(type 1-3,converage tests Gamma and Β functions)
  • Laplace transform(properties,bessel,inverse laplace transform,convolution)
  • Double Integrals
  • Functions of two variables(derivatives...etc)
  • Multiple variable functions

However all analysis and calculus advanced calculus dont have these stuff. Spivak doesnt even have converage test etc ..

Any reccomendation?

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up vote 1 down vote accepted

It sounds like what you're looking for is what used to be covered in advanced calculus courses. Typically, these were 2-semester length courses that followed the elementary calculus sequence and, in the U.S., taken by 3rd and 4th year undergraduate mathematics majors. There are quite a few standard texts for these courses (which in many universities have been "replaced" by an expansion of the undergraduate real analysis course), many of which have the title Advanced Calculus, such as the texts by Angus E. Taylor and W. Robert Mann, by David V. Widder, by Robert Creighton Buck, and by Wilfred Kaplan. For more extensive coverage of classical analysis topics such as the gamma function, Laplace transform, differentiating under the integral sign, etc., look for an older text, one from before the early 1950s (when things rapidly started to get more abstract and less applied in the undergraduate mathematics curriculum), such as Advanced Calculus by Frederick S. Woods, the book that many here will recognize as the book that Richard Feynman worked through on his own while in high school.

If there is a university within driving distance of where you live, the simplest way of finding what you want is to simply look on the library shelves. According to the on-line card catalog for the university near where I live, their library has over 30 books with the title Advanced Calculus. If I include the likely number of very similar books without this exact same title that are shelved in roughly the same location as these books, the total is probably over 100 books.

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Thank you. I'll search again advanced calc books.however even apostols book didnt have 90 excercises for improper integrals.i wonder where my book author found them – GorillaApe Mar 5 '12 at 17:01

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