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"Asymptotic methods are frequently used in many branches of both pure and applied mathematics, and this classic text remains the most up-to-date book dealing with one important aspect of this area, namely, asymptotic approximations of integrals. In Asymptotic Approximations of Integrals, all results are proved rigorously, and many of the approximation formulas are accompanied by error bounds. A thorough discussion on multidimensional integrals is given, and references are provided. Asymptotic Approximations of Integrals contains the "distributional method," which is not available elsewhere. Most of the examples in this text come from concrete applications.Since its publication twelve years ago, significant developments have occurred in the general theory of asymptotic expansions, including smoothing of the Stokes phenomenon, uniform exponentially improved asymptotic expansions, and hyperasymptotics. These new concepts belong to the area now known as "exponential asymptotics." Expositions of these new theories are available in papers published in various journals, but not yet in book form."

"Transonic aerodynamics, the study of the aerodynamics of flight at speeds near the speed of sound, warrants a great deal of attention from industry and science. As an airplane approaches Mach one, the drag steeply increases. This has prompted scientists to study transonic range of flight and to design reduced wing drag. Asymptotic theory of transonic aerodynamics forms the basis for this monograph. The equations governing transonic flow are inherently nonlinear and must ultimately be solved numerically. Asymptotic analysis simplifies and enriches both the theory and the computations of these flows. It reduces the number of parameters involved, can simplify the geometry, and clarifies near and fluid conditions. Transonic Aerodynamics: Problems in Asymptotic Theory offers exciting results, perspectives, and case studies for the treatment of problems arising in transonic aerodynamics. New advances including triple deck theory, analysis of stagnation at the nose of a body, transonic choked flow, and the transonic area rule are presented. Interest in analyzing the transonic range of flight, its stability properties, and especially the question of designing reduced drag (shockless or weak shock) airfoils keeps growing. Present day commercial aircraft cruise in the transonic range. Mechanical and aeronautical engineers interested in compressible fluid flows, design of optimal wings, and an understanding of transonic flow held about wings and airfoils will find the book invaluable. This book is understandable to those with a knowledge of continuum mechanics (fluids) and asymptotic methods. It is appropriate for graduate courses in aerodynamics and mathematical methods."

"This book provides the latest and most comprehensive research on asymptotic and hybrid methods in electromagnetics, and offers guidance on how to apply multipole and asymptotic methods to solve diffraction problems."

"The papers in this volume attest to how Louis Chen’s cutting-edge ideas influenced and continue to influence such areas as molecular biology and computer science. He has developed applications of his work on Poisson approximation to problems of signal detection in computational biology. The original papers contained in this book provide historical context for Chen’s work alongside commentary on some of his major contributions by noteworthy statisticians and mathematicians working today. "

"The first part of the book (basic methods) covers convergent and divergent series, Chebyshev expansions, numerical quadrature, and recurrence relations. Its focus is on the computation of special functions; however, it is suitable for general numerical courses. Pseudoalgorithms are given to help students write their own algorithms. In addition to these basic tools, the authors discuss other useful and efficient methods, such as methods for computing zeros of special functions, uniform asymptotic expansions, Pad approximations, and sequence transformations. The book also provides specific algorithms for computing several special functions (like Airy functions and parabolic cylinder functions, among others)."

"This research monograph deals with a modeling theory of the system of Navier-stokes-fourier equations for a newtonian fluid governing a compressible viscous and heat conducting flows. The main objective is threefold. First , to 'deconstruct' this Navier-Stokes-Fourier system in order to unify the puzzle of the various partial simplified approximate models used in Newtonian Classical Fluid Dynamics and this, first facet, have obviously a challenging approach and a very important pedagogic impact on the university education. The second facet of the main objective is to outline a rational consistent asymptotic/mathematical theory of the of fluid flows modeling on the basis of a typical Navier-Stokes-Fourier initial and boundary value problem. The third facet is devoted to an illustration of our rational asymptotic/mathematical modeling theory for various technological and geophysical stiff problems from, aerodynamics, thermal and thermocapillary convections and also meteofluid dynamics."

"Pada skripsi ini dibahas pembuktian Teorema Perubahan Variabel untuk menyelesaikan integral lipat tiga. Fungsi integrannya adalah yang kontinu dan mempunyai support yang kompak. Dengan menggunakan substitusi fungsi ( ), dimana adalah fungsi yang terturunkan sekali dan ( ) , untuk ‖ ‖ , diperoleh ∫ ( ( ))| ( )| ∫ ( ) . Pada setiap tahap pengintegralan digunakan Teorema Dasar Kalkulus dan suatu fungsi yang didefinisikan sebagai anti turunan dari fungsi terhadap satu peubah yaitu ( ) ( ) ∫ ( ) . Proses ini dilakukan berulang kali sebanyak jumlah variabel dari fungsi integrannya.

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In this skripsi, the proof of The Theorem of Change of Variables in triple integrals is explored. The integrand is a continuous function with a compact support. With a substitution ( ), where is once differentiable, ( ) , for ‖ ‖ , we prove ∫ ( ( ))| ( )| ∫ ( ) . At every stage of integration, we use Fundamental Theorem of Calculus and a function which is defined as an antiderivative of with respect to one variable, that is ( ) ( ) ∫ ( ) . This process is carried out repeatedly as many as the number of the variables of the integrand."

"There has been a growing interest in the use of Fourier analysis to examine questions of accuracy and stability of numerical methods for solving partial differential equations. This kind of analysis can produce particularly attractive and useful results for hyperbolic equations. This book provides useful reference material for those concerned with computational fluid dynamics: for physicists and engineers who work with computers in the analysis of problems in such diverse fields as hydraulics, gas dynamics, plasma physics, numerical weather prediction, and transport processes in engineering, and who need to understand the implications of the approximations they use; and for applied mathematicians concerned with the more theoretical aspects of these computations."