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Theory and Application of Infinite Series
Unusually clear and interesting classic covers real numbers and sequences, foundations of the theory of infinite series and development of the theory (series of valuable terms, Euler's summation formula, asymptotic expansions, other topics). Exercises throughout. Ideal for self-study.
592 pages, Paperback
First published January 1, 1964
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July 5, 2021
The book Theory and Application of Infinite Series by Konrad Knopp is an excellent teaching guide and a thorough exploration of the subject. Well, although I say that, the book touches on a great many things but does not go into depth with some other parts. For instance, the book does not go too deeply into Continued Fractions. Originally published in the German language in 1921, this book is a classic of mathematical clarity.
As with most books on higher mathematics that I possess, the book contains theorems, proofs, definitions, workable problems, detailed examples, and so on. While most of the book is text, it does contain plenty of formulas and some graphs. The book is pretty long, but it is not the longest mathematical treatise that I have.
The pros of the book are that it is an in-depth approach to the subject, it has the aforementioned positives, it has plenty of footnotes, and the work states the mathematics quite clearly throughout. Sometimes when people get really far into higher mathematics, they forget that not everyone knows what they are talking about. However, since the book is generally written for people studying that subject, it is a forgivable error.
The cons of the book are more difficult to list. I can’t say the subject is outdated or somewhat useless since Infinite Series come up a lot in mathematics and the subject hasn’t changed all that much. Also, since the book is quite thorough and has practice problems it makes it even more useful.
The book has a detailed Bibliography with such luminaries as Isaac Newton, Leonhard Euler, Karl Gauss, John Wallis, Augustin-Louis Cauchy and so on. If you are looking for a specific portion of the book, there is an index organized by subject name.
All in all, this book was really well done. If you are a fan of reading old mathematical texts, this book might be worth your time.
As with most books on higher mathematics that I possess, the book contains theorems, proofs, definitions, workable problems, detailed examples, and so on. While most of the book is text, it does contain plenty of formulas and some graphs. The book is pretty long, but it is not the longest mathematical treatise that I have.
The pros of the book are that it is an in-depth approach to the subject, it has the aforementioned positives, it has plenty of footnotes, and the work states the mathematics quite clearly throughout. Sometimes when people get really far into higher mathematics, they forget that not everyone knows what they are talking about. However, since the book is generally written for people studying that subject, it is a forgivable error.
The cons of the book are more difficult to list. I can’t say the subject is outdated or somewhat useless since Infinite Series come up a lot in mathematics and the subject hasn’t changed all that much. Also, since the book is quite thorough and has practice problems it makes it even more useful.
The book has a detailed Bibliography with such luminaries as Isaac Newton, Leonhard Euler, Karl Gauss, John Wallis, Augustin-Louis Cauchy and so on. If you are looking for a specific portion of the book, there is an index organized by subject name.
All in all, this book was really well done. If you are a fan of reading old mathematical texts, this book might be worth your time.
Displaying 1 of 1 review