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  • Elements of the Theory of Functions (Dover Books on Mathematics)

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Elements of the Theory of Functions (Dover Books on Mathematics)

by Konrad Knopp (Author), Bagemihl Frederick (Translator)
This well-known book provides a clear and concise review of general function theory via complex variables. Suitable for undergraduate math majors, the treatment explores only those topics that are simplest but are also most important for the development of the theory. Prerequisites include a knowledge of the foundations of real analysis and of the elements of analytic geometry.
The text begins with an introduction to the system of complex numbers and their operations. Then the concept of sets of numbers, the limit concept, and closely related matters are extended to complex quantities. Final chapters examine the elementary functions, including rational and linear functions, exponential and trigonometric functions, and several others as well as their inverses, including the logarithm and the cyclometric functions. Numerous examples clarify the essential ideas, and proofs are expressed in a direct manner without sacrifice of completeness or rigor.
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  1. ISBN-10
    0486601544
  2. ISBN-13
    978-0486601540
  3. Publisher
    Dover Publications
  4. Publication date
    October 19, 2016
  5. Language
    English
  6. Dimensions
    5.5 x 0.5 x 8 inches
  7. Print length
    160 pages
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About the Author

German mathematician Konrad Knopp (1882–1957) taught at the University of Königsberg from 1915-26 and at Tübingen University from 1926 until his retirement in 1950. His other Dover books include Infinite Sequences and Series, Theory and Applications of Infinite Series, Theory of Functions, and Problem Book in the Theory of Functions.

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Konrad Knopp

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Customer reviews

4.7 out of 5 stars
13 global ratings

Top reviews from the United States

  • Kevin Kiersky
    5.0 out of 5 stars Very Clear and Sharp Mentor of Math +++
    Reviewed in the United States on April 3, 2010
    Format: PaperbackVerified Purchase
    Recently, I dug into my collection of "old-school" math books looking for a good review of general function theory via complex variables. I [somehow] recalled this author as having a very good approach to this area. This topic is so wide and deep as to allow for many approaches. The whole presentation of this author via his little series of math works follows a very clear and sharp path from complex variables to general function theory. It seems many authors delay starting at the start with complex numbers and variables -- yet the "complex way" is a very streamlined way into general function theory and even infinite series -- as this Mentor shows -- starting with this very great little gem of an introduction. Even complex numbers can be approached from various angles -- one of the best being that of "Elements of the Theory of Functions" by Konrad Knopp +++
    14 people found this helpful
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  • john
    4.0 out of 5 stars an introduction to functions whose domain includes complex variables
    Reviewed in the United States on September 5, 2019
    Format: PaperbackVerified Purchase
    this is a small and well-written book which seems like it should be an introduction to the larger, two-volume work, "the theory of functions", by knopp. but in my opinion, it is a smaller book, without problem sets, that emphasizes somewhat different topics. there are five sections. I. complex numbers and their geometric representation (41 pages). II. linear functions and circular transformations (23 pages). III. sets and sequences. power series (23 pages). IV. analytic functions and conformal mapping (17 pages). V. elementary functions (30 pages).
    volume 1 of "the theory of functions" alone has approximately the same number of pages (about 140), nearly ALL of which are devoted to analytic functions of complex variables. while one could argue about the "meaning" of a theory of functions, the main "applications" of such a theory appear to be in the area of analytic functions of a complex variable.
    the "elements" covers this material in 17 pages and without a problem set. so there are no questions, problems or demonstrations of the power of conformal mapping and cauchy's integral theorem in solving problems involving, say, conservative fields in physics.
    so this little introductory book (with no problem sets) outlines a stimulating "theory of functions", but it does not explore the breadth and power of analytic functions of complex variables. these are covered in much greater depth
    in knopp's "theory of functions, vols. 1 & 2", as well as in the accompanying problem book.
    4 people found this helpful
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  • robert bonneau
    5.0 out of 5 stars Read this book the summer before engineering grad school. ...
    Reviewed in the United States on April 5, 2017
    Format: Paperback
    Read this book the summer before engineering grad school. I thought I knew a thing or 2 about applied math.
    Wrong. This little book changed everything. But it & read it.
    2 people found this helpful
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  • Roger Bagula
    4.0 out of 5 stars A Classic with outdated language
    Reviewed in the United States on August 5, 2001
    Format: Paperback
    This book goes with the series of books written by this author:" Theory of Functions". Together with the other parts it gives a good introduction to the theory of complex functional analysis. Although the language is in places outdated, the mathematics covered is solid and necessary. It is a starting point in study for subjects like chaos and fractals as well. One of the best points is that is a cheap Dover book!
    17 people found this helpful
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Top reviews from other countries

  • julien jung
    5.0 out of 5 stars Five Stars
    Reviewed in the United Kingdom on July 16, 2014
    Format: PaperbackVerified Purchase
    prompt delivery an correct description
    Report
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