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knopp k elements theory functions 2016

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Textbook in PDF format 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. Complex numbers and their geometric representation Foundations The System of Complex Numbers and the Gaussian Plane of Numbers The Riemann Sphere of Numbers Linear functions and circular transformations Mapping by Means of Linear Functions Normal Forms and Particular Linear Mappings Sets and sequences. Power series Point Sets and Sets of Numbers Sequences of Numbers. Infinite Series Power Series Analytic functions and conformai, mapping Functions of a Complex Variable Analytic Functions and Conformal Mapping The elementary functions Power and Root. The Rational Functions The Exponential, Trigonometric, and Hyperbolic Functions The Logarithm, the Cyclometric Functions, and the Binomial Series

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Knopp K. Elements of the Theory of Functions 2016.pdf 7.2 MB

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knopp k elements theory functions 2016

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