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

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.

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.