Calculus book for specific topics

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SUMMARY

The discussion focuses on the search for a calculus book that provides extensive exercises on improper integrals, specifically seeking a resource with around 75 pages dedicated to this topic. The user mentions existing books like Thomas' Calculus and Apostol's Calculus but finds them lacking in the specific exercise content required. Recommendations include Apostol's Calculus Volume 1 and Volume 2, which, while not containing the exact number of exercises, cover the necessary theory comprehensively and include solutions for many computational problems.

PREREQUISITES
  • Understanding of improper integrals and their types
  • Familiarity with Laplace transforms
  • Knowledge of series of functions and double integrals
  • Basic concepts of multivariable calculus
NEXT STEPS
  • Explore Apostol's Calculus Volume 1 and Volume 2 for foundational theory
  • Research additional resources on improper integrals with extensive exercises
  • Investigate online platforms offering calculus exercises with solutions
  • Look into specialized analysis books that cover advanced calculus topics
USEFUL FOR

Students and educators in mathematics, particularly those focusing on calculus and analysis, as well as anyone seeking comprehensive resources for practicing improper integrals and related topics.

Parhs
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I have searched the mainstream books thomas calculus, steward and lots other like apostols,rudin etc.
I was given two books in my college called analysis and applications but it is in greek written by an old local proffessor . It is 1600 pages total 2 volumes..

However the second book has these topics.

Arithmetical Methods

Improper integrals (30 pages theory + 75 pages excercises)
-first,second,third type
-convergence tests
-parametrical improper integrals
-gamma and betta functions

Laplace transform

Series of functions

Two variable functions

Double integrals

Multiple variable functions

However i didnt find any book that has 75 pages with excersices for improper integrals only! Each chapter has tons of excercises.The problem is that most of them don't have solutions.

But couldn't find another book. Searched analysis books but they didnt even mentioned these stuff.Searched calculus and advanced calculus but no luck..

Is there any reccomendation that has lots of excercises with solutions ?
 
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You should reconsider Apostol's Calculus Volume 1 and Volume 2. They cover most of the topics you listed in depth. Although they don't contain 75 pages of exercises on improper integrals, they build up the theory so that you can apply the theory to any suitable problem. There are some computational exercises too, though, most of which contain solutions in the back of the book.
 

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