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The second edition of this comprehensive and accessible text continues to offer students a challenging and enjoyable study of complex variables that is infused with perfect balanced coverage of mathematical theory and applied topics. The author explains fundamental concepts and techniques with precision and introduces the students to complex variable theory through conceptual develop-ment of analysis that enables them to develop a thorough understanding of the topics discussed. Geometric interpretation of the results, wherever necessary, has been inducted for making the analysis more accessible. The level of the text assumes that the reader is acquainted with elementary real analysis. Beginning with the revision of the algebra of complex variables, the book moves on to deal with analytic functions, elementary functions, complex integration, sequences, series and infinite products, series expansions, singularities and residues. The application-oriented chapters on sums and integrals, conformal mappings, Laplace transform, and some special topics, provide a practical-use perspective. Enriched with many numerical examples and exercises designed to test the student's comprehension of the topics covered, this book is written for a one-semester course in complex variables for students in the science and engineering disciplines.
This work is an introduction to the theory and practice of Business Statistics, a core course in business colleges, 4-year institutions, and MBA programmes. This updated edition includes more focus on Excel to reflect upon the change in the curriculum.
Covers complex numbers, analytic functions, integration, residue theory, conformal mapping, and Fourier and Laplace transforms.
Complex Analysis with Applications to Flows and Fields presents the theory of functions of a complex variable, from the complex plane to the calculus of residues to power series to conformal mapping. The book explores numerous physical and engineering applications concerning potential flows, the gravity field, electro- and magnetostatics, steady heat conduction, and other problems. It provides the mathematical results to sufficiently justify the solution of these problems, eliminating the need to consult external references. The book is conveniently divided into four parts. In each part, the mathematical theory appears in odd-numbered chapters while the physical and engineering applications can be found in even-numbered chapters. Each chapter begins with an introduction or summary and concludes with related topics. The last chapter in each section offers a collection of many detailed examples. This self-contained book gives the necessary mathematical background and physical principles to build models for technological and scientific purposes. It shows how to formulate problems, justify the solutions, and interpret the results.
This book presents holomorphic operator functions of a single variable and applications, which are focused on the relations between local and global theories. It is based on methods and technics of complex analysis of several variables.
This inter-disciplinary work covering the continuum mechanics of novel materials, condensed matter physics and partial differential equations discusses the mathematical theory of elasticity of quasicrystals (a new condensed matter) and its applications by setting up new partial differential equations of higher order and their solutions under complicated boundary value and initial value conditions. The new theories developed here dramatically simplify the solving of complicated elasticity equation systems. Large numbers of complicated equations involving elasticity are reduced to a single or a few partial differential equations of higher order. Systematical and direct methods of mathematical physics and complex variable functions are developed to solve the equations under appropriate boundary value and initial value conditions, and many exact analytical solutions are constructed. The dynamic and non-linear analysis of deformation and fracture of quasicrystals in this volume presents an innovative approach. It gives a clear-cut, strict and systematic mathematical overview of the field. Comprehensive and detailed mathematical derivations guide readers through the work. By combining mathematical calculations and experimental data, theoretical analysis and practical applications, and analytical and numerical studies, readers will gain systematic, comprehensive and in-depth knowledge on continuum mechanics, condensed matter physics and applied mathematics.

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