Kategoria BISAC: Mathematics >> Complex Analysis

Dieses Buch fuhrt anschaulich in die Arithmetik komplexer Zahlen ein und behandelt umfassend ihre Rolle sowohl beim Losen von Gleichungen wie auch in der Geometrie der Ebene. Ubungsaufgaben mit Losungen sowie ein Anhang zum Rechnen mit komplexen Zahlen und konformen Abbildungen in MAPLE komplettieren das Lehrbuch.

This textbook introduces the theory of complex variables at undergraduate level. A good collection of problems is provided in the second part of the book. The book is written in a user-friendly style that presents important fundamentals a beginner needs to master the technical details of the subject. The organization of problems into focused sets is an important feature of the book and the teachers may adopt this book for a course on complex variables and for mining problems.

What are the random-like phenomena that can be found everywhere in real-life world? When carrying out a random sampling survey on the traffic situation, we often obtain some descriptive results such as approximately expedite, a little crowded and so on, therefore, the average level should be regarded as the random fuzzy phenomenon, which is one of the random-like phenomena. Decision makers usually need to make the decision for these problems with random-like phenomena. Which model should be constructed for them? How should we handle these models to find the optimal strategy? How can we apply...

This monograph strives to introduce a solid foundation on the usage of Gröbner bases in ring theory by focusing on noncommutative associative algebras defined by relations over a field K. It also reveals the intrinsic structural properties of Gröbner bases, presents a constructive PBW theory in a quite extensive context and, along the routes built via the PBW theory, the book demonstrates novel methods of using Gröbner bases in determining and recognizing many more structural properties of algebras, such as the Gelfand-Kirillov dimension, Noetherianity, (semi-)primeness,...

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...

A powerful, unified approach to mathematical and computational modeling in science and engineering

Mathematical and computational modeling makes it possible to predict the behavior of a broad range of systems across a broad range of disciplines. This text guides students and professionals through the axiomatic approach, a powerful method that will enable them to easily master the principle types of mathematical and computational models used in engineering and science. Readers will discover that this axiomatic approach not only enables them to systematically construct effective...

PAMIR (Parameterized Adaptive Multidimensional Integration Routines) is a suite of Fortran programs for multidimensional numerical integration over hypercubes, simplexes, and hyper-rectangles in general dimension p, intended for use by physicists, applied mathematicians, computer scientists, and engineers. The programs, which are available on the internet at website and are free for non-profit research use, are capable of following localized peaks and valleys of the integrand. Each program comes with a Message-Passing Interface (MPI) parallel version for cluster use as well as serial...

PAMIR (Parameterized Adaptive Multidimensional Integration Routines) is a suite of Fortran programs for multidimensional numerical integration over hypercubes, simplexes, and hyper-rectangles in general dimension p, intended for use by physicists, applied mathematicians, computer scientists, and engineers. The programs, which are available on the internet at website and are free for non-profit research use, are capable of following localized peaks and valleys of the integrand. Each program comes with a Message-Passing Interface (MPI) parallel version for cluster use as well as serial...

The principle of local activity explains the emergence of complex patterns in a homogeneous medium. At first defined in the theory of nonlinear electronic circuits in a mathematically rigorous way, it can be generalized and proven at least for the class of nonlinear reaction-diffusion systems in physics, chemistry, biology, and brain research. Recently, it was realized by memristors for nanoelectronic device applications. In general, the emergence of complex patterns and structures is explained by symmetry breaking in homogeneous media, which is caused by local activity. This book argues that...

String theory says we live in a ten-dimensional universe, but that only four are accessible to our everyday senses. According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe.

Time and again, where Yau has gone, physics has followed. Now for the first time, readers will follow Yau's penetrating thinking on where...

Spin glasses are disordered magnetic systems that have led to the development of mathematical tools with an array of real-world applications, from airline scheduling to neural networks. Spin Glasses and Complexity offers the most concise, engaging, and accessible introduction to the subject, fully explaining what spin glasses are, why they are important, and how they are opening up new ways of thinking about complexity.

This one-of-a-kind guide to spin glasses begins by explaining the fundamentals of order and symmetry in condensed matter physics and how spin glasses fit...

This carefully written textbook is an introduction to the beautiful concepts and results of complex analysis. It is intended for international bachelor and master programmes in Germany and throughout Europe; in the Anglo-American system of university education the content corresponds to a beginning graduate course. The book presents the fundamental results and methods of complex analysis and applies them to a study of elementary and non-elementary functions (elliptic functions, Gamma- and Zeta function including a proof of the prime number theorem ) and a new feature in this context to...

This textbook introduces the theory of complex variables at undergraduate level. A good collection of problems is provided in the second part of the book. The book is written in a user-friendly style that presents important fundamentals a beginner needs to master the technical details of the subject. The organization of problems into focused sets is an important feature of the book and the teachers may adopt this book for a course on complex variables and for mining problems.

This review volume, co-edited by Nobel laureate G Ertl, provides a broad overview on current studies in the understanding of design and control of complex chemical systems of various origins, on scales ranging from single molecules and nano-phenomena to macroscopic chemical reactors. Self-organizational behavior and the emergence of coherent collective dynamics in reaction-diffusion systems, reactive soft matter and chemical networks are covered. Special attention is paid to the applications in molecular cell biology and to the problems of biological evolution, synthetic biology and design of...

The field of computational sciences has seen a considerable development in mathematics, engineering sciences, and economic equilibrium theory. Researchers in this field are faced with the problem of solving a variety of equations or variational inequalities. We note that in computational sciences, the practice of numerical analysis for finding such solutions is essentially connected to variants of Newton's method. The efficient computational methods for finding the solutions of fixed point problems, nonlinear equations and variational inclusions are the first goal of the present book. The...

This volume consists of one expository paper and two research papers: T Hirai, A Hora and E Hirai, Introductory expositions on projective representations of groups (referred as E])T Hirai, E Hirai and A Hora, Projective representations and spin characters of complex reflection groups G(m,p,n) and G(m,p,∞), I;T Hirai, A Hora and E Hirai, Projective representations and spin characters of complex reflection groups G(m,p,n) and G(m,p,∞), II, Case of generalized symmetric groups.Since Schur's trilogy on...

Reliability of Large and Complex Systems, previously titled Reliability of Large Systems, is an innovative guide to the current state and reliability of large and complex systems.

In addition to revised and updated content on the complexity and safety of large and complex mechanisms, this new edition looks at the reliability of nanosystems, a key research topic in nanotechnology science. The author discusses the importance of safety investigation of critical infrastructures that have aged or have been exposed to varying operational conditions. This reference provides...

Geo-mathematical modelling: models from complexity science

Sir Alan Wilson, Centre for Advanced Spatial Analysis, University College London

Mathematical and computer models for a complexity science tool kit

Geographical systems are characterised by locations, activities at locations, interactions between them and the infrastructures that carry these activities and flows. They can be described at a great variety of scales, from individuals and organisations to countries. Our understanding, often...

The book constitutes a basic, concise, yet rigorous course in complex analysis, for students who have studied calculus in one and several variables, but have not previously been exposed to complex analysis. The textbook should be particularly useful and relevant for undergraduate students in joint programmes with mathematics, as well as engineering students. The aim of the book is to cover the bare bones of the subject with minimal prerequisites. The core content of the book is the three main pillars of complex analysis: the Cauchy-Riemann equations, the Cauchy Integral Theorem, and Taylor...

The book constitutes a basic, concise, yet rigorous course in complex analysis, for students who have studied calculus in one and several variables, but have not previously been exposed to complex analysis. The textbook should be particularly useful and relevant for undergraduate students in joint programmes with mathematics, as well as engineering students. The aim of the book is to cover the bare bones of the subject with minimal prerequisites. The core content of the book is the three main pillars of complex analysis: the Cauchy-Riemann equations, the Cauchy Integral Theorem, and Taylor...