Introduction To Analysis With Complex Numbers PDF Download
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| Author | : Irena Swanson |
| Publisher | : World Scientific |
| Total Pages | : 455 |
| Release | : 2021-02-18 |
| Genre | : Mathematics |
| ISBN | : 9811225877 |
Download Introduction To Analysis With Complex Numbers Book in PDF, ePub and Kindle
This is a self-contained book that covers the standard topics in introductory analysis and that in addition constructs the natural, rational, real and complex numbers, and also handles complex-valued functions, sequences, and series.The book teaches how to write proofs. Fundamental proof-writing logic is covered in Chapter 1 and is repeated and enhanced in two appendices. Many examples of proofs appear with words in a different font for what should be going on in the proof writer's head.The book contains many examples and exercises to solidify the understanding. The material is presented rigorously with proofs and with many worked-out examples. Exercises are varied, many involve proofs, and some provide additional learning materials.
| Author | : Ravi P. Agarwal |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 345 |
| Release | : 2011-07-01 |
| Genre | : Mathematics |
| ISBN | : 146140195X |
Download An Introduction to Complex Analysis Book in PDF, ePub and Kindle
This textbook introduces the subject of complex analysis to advanced undergraduate and graduate students in a clear and concise manner. Key features of this textbook: effectively organizes the subject into easily manageable sections in the form of 50 class-tested lectures, uses detailed examples to drive the presentation, includes numerous exercise sets that encourage pursuing extensions of the material, each with an “Answers or Hints” section, covers an array of advanced topics which allow for flexibility in developing the subject beyond the basics, provides a concise history of complex numbers. An Introduction to Complex Analysis will be valuable to students in mathematics, engineering and other applied sciences. Prerequisites include a course in calculus.
| Author | : John P. D'Angelo |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 177 |
| Release | : 2010 |
| Genre | : Functions of complex variables |
| ISBN | : 0821852744 |
Download An Introduction to Complex Analysis and Geometry Book in PDF, ePub and Kindle
Provides the reader with a deep appreciation of complex analysis and how this subject fits into mathematics. The first four chapters provide an introduction to complex analysis with many elementary and unusual applications. Chapters 5 to 7 develop the Cauchy theory and include some striking applications to calculus. Chapter 8 glimpses several appealing topics, simultaneously unifying the book and opening the door to further study.
| Author | : H. A. Priestley |
| Publisher | : OUP Oxford |
| Total Pages | : 344 |
| Release | : 2003-08-28 |
| Genre | : Mathematics |
| ISBN | : 0191037206 |
Download Introduction to Complex Analysis Book in PDF, ePub and Kindle
Complex analysis is a classic and central area of mathematics, which is studied and exploited in a range of important fields, from number theory to engineering. Introduction to Complex Analysis was first published in 1985, and for this much awaited second edition the text has been considerably expanded, while retaining the style of the original. More detailed presentation is given of elementary topics, to reflect the knowledge base of current students. Exercise sets have been substantially revised and enlarged, with carefully graded exercises at the end of each chapter. This is the latest addition to the growing list of Oxford undergraduate textbooks in mathematics, which includes: Biggs: Discrete Mathematics 2nd Edition, Cameron: Introduction to Algebra, Needham: Visual Complex Analysis, Kaye and Wilson: Linear Algebra, Acheson: Elementary Fluid Dynamics, Jordan and Smith: Nonlinear Ordinary Differential Equations, Smith: Numerical Solution of Partial Differential Equations, Wilson: Graphs, Colourings and the Four-Colour Theorem, Bishop: Neural Networks for Pattern Recognition, Gelman and Nolan: Teaching Statistics.
| Author | : Maxwell Rosenlicht |
| Publisher | : Courier Corporation |
| Total Pages | : 270 |
| Release | : 2012-05-04 |
| Genre | : Mathematics |
| ISBN | : 0486134687 |
Download Introduction to Analysis Book in PDF, ePub and Kindle
Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition.
| Author | : Vladimir Eiderman |
| Publisher | : CRC Press |
| Total Pages | : 383 |
| Release | : 2021-12-20 |
| Genre | : Mathematics |
| ISBN | : 100051112X |
Download An Introduction to Complex Analysis and the Laplace Transform Book in PDF, ePub and Kindle
The aim of this comparatively short textbook is a sufficiently full exposition of the fundamentals of the theory of functions of a complex variable to prepare the student for various applications. Several important applications in physics and engineering are considered in the book. This thorough presentation includes all theorems (with a few exceptions) presented with proofs. No previous exposure to complex numbers is assumed. The textbook can be used in one-semester or two-semester courses. In one respect this book is larger than usual, namely in the number of detailed solutions of typical problems. This, together with various problems, makes the book useful both for self- study and for the instructor as well. A specific point of the book is the inclusion of the Laplace transform. These two topics are closely related. Concepts in complex analysis are needed to formulate and prove basic theorems in Laplace transforms, such as the inverse Laplace transform formula. Methods of complex analysis provide solutions for problems involving Laplace transforms. Complex numbers lend clarity and completion to some areas of classical analysis. These numbers found important applications not only in the mathematical theory, but in the mathematical descriptions of processes in physics and engineering.
| Author | : Sanford L. Segal |
| Publisher | : Elsevier |
| Total Pages | : 733 |
| Release | : 2011-08-18 |
| Genre | : Mathematics |
| ISBN | : 008087164X |
Download Nine Introductions in Complex Analysis Book in PDF, ePub and Kindle
Nine Introductions in Complex Analysis
| Author | : Kevin Houston |
| Publisher | : |
| Total Pages | : 264 |
| Release | : 2017-07-21 |
| Genre | : Mathematics |
| ISBN | : 9781999795207 |
Download Complex Analysis Book in PDF, ePub and Kindle
Dr Kevin Houston follows up his best-selling book How to Think Like a Mathematician with Complex Analysis: An Introduction. Complex Analysis is a central subject in mathematics with applications in engineering, physics, and even the study of prime numbers. It has been said that often the shortest route in the solution of a real problem is to take a shortcut through the complex numbers. Unlike other texts this book gets quickly to the heart of Complex Analysis: the concept of complex contour integration. This means that students get much more practice in the fundamental concept than they normally would. The central method of proof - use of the Estimation Lemma - is emphasised throughout because students then have a unifying principle to help understand and remember those proofs. The book contains all you will need for an introductory course in Complex Analysis and includes a short and sweet proof of Cauchy's Theorem - one which the majority of students can grasp not only the outline but the details as well. The book contains copious examples and exercises tested on students arising from Dr. Houston's 20 years plus experience of teaching the subject
| Author | : Sergei Ovchinnikov |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 154 |
| Release | : 2015-02-26 |
| Genre | : Mathematics |
| ISBN | : 147042018X |
Download Number Systems Book in PDF, ePub and Kindle
This book offers a rigorous and coherent introduction to the five basic number systems of mathematics, namely natural numbers, integers, rational numbers, real numbers, and complex numbers. It is a subject that many mathematicians believe should be learned by any student of mathematics including future teachers. The book starts with the development of Peano arithmetic in the first chapter which includes mathematical induction and elements of recursion theory. It proceeds to an examination of integers that also covers rings and ordered integral domains. The presentation of rational numbers includes material on ordered fields and convergence of sequences in these fields. Cauchy and Dedekind completeness properties of the field of real numbers are established, together with some properties of real continuous functions. An elementary proof of the Fundamental Theorem of Algebra is the highest point of the chapter on complex numbers. The great merit of the book lies in its extensive list of exercises following each chapter. These exercises are designed to assist the instructor and to enhance the learning experience of the students.
| Author | : R.B. Burckel |
| Publisher | : Birkhäuser |
| Total Pages | : 572 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034893744 |
Download An Introduction to Classical Complex Analysis Book in PDF, ePub and Kindle
This book is an attempt to cover some of the salient features of classical, one variable complex function theory. The approach is analytic, as opposed to geometric, but the methods of all three of the principal schools (those of Cauchy, Riemann and Weierstrass) are developed and exploited. The book goes deeply into several topics (e.g. convergence theory and plane topology), more than is customary in introductory texts, and extensive chapter notes give the sources of the results, trace lines of subsequent development, make connections with other topics, and offer suggestions for further reading. These are keyed to a bibliography of over 1,300 books and papers, for each of which volume and page numbers of a review in one of the major reviewing journals is cited. These notes and bibliography should be of considerable value to the expert as well as to the novice. For the latter there are many references to such thoroughly accessible journals as the American Mathematical Monthly and L'Enseignement Mathématique. Moreover, the actual prerequisites for reading the book are quite modest; for example, the exposition assumes no prior knowledge of manifold theory, and continuity of the Riemann map on the boundary is treated without measure theory.
