Calculus book for specific topics

In summary, there is a need for a book with a large number of exercises and solutions for improper integrals, but no such book has been found. The closest options are Apostol's Calculus Volume 1 and Volume 2, which cover most of the topics mentioned and have some exercises with solutions. However, they do not have as many exercises on improper integrals as desired.
  • #1
Parhs
6
0
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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  • #2
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.
 

1. What is calculus and why is it important?

Calculus is a branch of mathematics that studies continuous change and is used to solve problems involving rates of change. It is important because it provides a framework for understanding and analyzing real-world phenomena such as motion, growth, and optimization.

2. What specific topics are typically covered in a calculus book?

A calculus book usually covers topics such as limits, derivatives, integrals, differential equations, and multivariable calculus. Some books may also include applications of calculus in physics, engineering, and economics.

3. How is a calculus book organized?

A calculus book is typically organized into chapters that cover different topics. Each chapter may begin with an introduction and then present concepts, definitions, theorems, and examples. Practice problems and exercises are usually included at the end of each chapter.

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Yes, there are calculus books available for different levels of students. Introductory calculus books are usually aimed at high school or college students who are new to the subject. Advanced calculus books are geared towards students who have already completed introductory calculus courses and are looking to deepen their understanding of the subject.

5. How can I choose the best calculus book for my needs?

Choosing the best calculus book depends on your level of understanding and the topics you need to study. Look for a book that is well-organized, has clear explanations and examples, and includes practice problems and exercises. It is also helpful to read reviews and ask for recommendations from teachers or other students.

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