Complex analysis jump to navigation jump to search in this chapter, we examine the behavior of elementary functions and introduce exponential, logarithmic, and trigonometric functions. Some elementary complex functions, complex analysis. Some elementary complex functions, complex analysis youtube. The purpose of this book is to prescnt a straightforward introduction to complex numbers and their properties. The book visual complex analysis by tristan needham is a great introduction to complex analysis that does not skip the fundamentals that you mentioned.
Elementary real and complex analysis dover books on mathematics. The book is the result of a complete rewriting and revision of a translation of the second 1957 russian edition. Functions of a complex variable and some of their applications, volume 1, discusses the fundamental ideas of the theory of functions of a complex variable. Numerous changes and additions have been made, both in the text and in the.
Khan academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their. The emphasis is on disentangling and explaining all the necessary concepts. Bicomplex numbers and their elementary functions 63 show in the next sections, such an algebra enjoys most of the properties one would expect from a good generalization of the. To have the courage to think outside the square, we need to be intrigued by a problem. There is another equally interesting way of introducing bicomplex numbers. We describe how to define elementary functions in such an algebra polynomials. The system of complex numbers and the gaussian plane of numbers 4. Complex analysiselementary functions wikibooks, open. Numerous examples have been given throughout the book, and there is also a. Complex numbers and their elementary properties functions of.
The purpose of this book is to develop the foundations of the theory of holomorphicity on the ring of bicomplex numbers. There is a book by yaglom called complex numbers in geometry. Professor 19872008 university of warsaw 19681980 instytute of informatics university of botswana 19802008 department of mathematics. Good books on complex numbers mathematics stack exchange.
In his elementary algebra text book, elements of algebra, he introduces these numbers almost at once and then uses them in a natural way. Theory of functions, parts i and ii dover books on mathematics konrad knopp. Pdf bicomplex numbers and their elementary functions. Books on complex analysis definitely use the topics that you mentioned, but usually assume that the reader is already familiar with some algebra and geometry of complex numbers. Continued usage for this purpose gradually endowed them with some degree of conceptual existence. Bicomplex holomorphic functions the algebra, geometry and. Teachers using these notes would enhance the quality of their teaching and by implication, students success. Download complex variables pdf download free online book chm pdf.
Theory of functions, parts i and ii dover books on. The set of real numbers is a subset of the complex numbers. The result of adding, subtracting, multiplying, and dividing complex numbers is a complex number. Volume 1 elements of the theory of functions table of contents. Complex numbers, complex functions, elementary functions, integration. Elementary functions and complex numbers digital book, pp. Power series and elementary analytic functions, complex integration and cauchy s. In this paper we introduce the algebra of bicomplex numbers as a generalization of the field of complex numbers. The material on complex numbers and equations occupies roughly the first half of the book. Lecture notes in elementary complex functions with computer.
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