“…The exposition is at the undergraduate level, building on basic principles of advanced calculus without appeal to more sophisticated techniques of complex analysis and Lebesgue integration. Among the topics covered are Fourier series and integrals, approximation theory, Stirling's formula, the gamma function, Bernoulli numbers and polynomials, the Riemann zeta function, Tauberian theorems, elliptic integrals, ramifications of the Cantor set, and a theoretical discussion of differ…”
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“…These topics are applicable to the study of problems in complex analysis, stochastic and evolution processes and approximation theory.…”
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“…Introducing those areas of mathematics which are most important to practical problem solving in the field, this book pays particular attention to ordinary differential equations, linear algebra and vector analysis, complex analysis, and numerical methods. Fourier series and partial differential equations are also covered thoroughly. …”
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“…We then develop certain prerequisites from complex analysis such as power series, multivalued functions (including the concepts of branch points and branch cuts), and the all-important gamma function. …”
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“…Separate chapters discuss the fundamentals of complex analysis; the concept of conformal transformations; the most important of the elementary fun…”
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“…Real numbers, inequalities and intervalsFunction, domain and rangeBasic coordinate geometryPolar coordinatesMathematical inductionBinomial theoremCombination of functionsSymmetry in functions and graphsInverse functionsComplex numbers; real and imaginary formsGeometry of complex analysisModulus-argument form of a complex numberRoots of complex numbersLimitsOne-sided limitsDerivativesLeibniz's formulaDifferentialsDifferentiation of inverse trigonometric functionsImplicit differentiationParametrically defined curves and parametric differentiationThe exponential functionThe logarithmic functionHy…”
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“…Spencer, MathSciNet The book under review is the faithful reprint of the original edition of one of the most influential textbooks in modern complex analysis and geometry. The classic …”
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“…It aims at being a tribute to the excellent achievements of Heinrich Begehr in complex analysis and complex differential equations, and especially to his prominent role as one of the creators and long-time leader of the International Society for Analysis, its Applications and Computation (ISAAC).…”
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“…As experiments construct more complex analysis techniques with several analysis dimensions, approximating results for alternate signal models can become more difficult. …”
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“…The modern singularity theory for smooth mappings, which is currently undergoing intensive development, can be thought of as a crossroad where the most abstract topics (such as algebraic and differential geometry and topology, complex analysis, invariant theory, and Lie group theory) meet the most applied topics (such as dynamical systems, mathematical physics, geometrical optics, mathematical economics, and control theory). …”
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“…Pluripotential theory is a very powerful tool in geometry, complex analysis and dynamics. This volume brings together the lectures held at the 2011 CIME session on "pluripotential theory" in Cetraro, Italy. …”
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“…The topic of this bookis located at the intersection of complex analysis, operator theory and partial differential equations. …”
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“…Numerous well-presented and important papers from the conference are gathered in the proceedings for the purpose of pointing directions for useful future research in diverse areas of mathematics including algebraic geometry, analysis, commutative algebra, complex analysis, discrete mathematics, dynamical systems, number theory and topology. …”
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“…It captures the essence of his mathematics, a development and transition from applied mathematics to complex analysis-quasiconformal mappings and moduli of Riemann surfaces-and the essence of his personality, a progression from a young revolutionary refugee to an elder statesman in the world of mathematics and a fighter for global h…”
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“…The book emphasizes the geometric approach as well as classical and semi-classical results which Lars Ahlfors felt every student of complex analysis should know before embarking on independent research. …”
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“…This volume is the third of three in a series surveying the theory of theta functions which play a central role in the fields of complex analysis, algebraic geometry, number theory and most recently particle physics. …”
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“…This book presents the extensions to the quaternionic setting of some of the main approximation results in complex analysis. It also includes the main inequalities regarding the behavior of the derivatives of polynomials with quaternionic cofficients. …”
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“…Different aspects of harmonic analysis, complex analysis, sampling theory, approximation theory and related topics are covered in this volume. …”
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“…The prerequisite requirements are modest: only some familiarity with basic ideas of real and complex analysis is expected.…”
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