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517.91 --- Integral equations --- Inverse problems (Differential equations) --- Numerical solutions --- Congresses
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ISBN: 9780387770369 Year: 2008 Publisher: New York NY Springer New York Imprint Springer
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This book presents first-year calculus roughly in the order in which it first was discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers. From the reviews: The aim of this interesting new contribution to the series Readings in Mathematics is an attempt to restore the historical order in the presentation of basic mathematical analysis...such a historical approach can provide a very fruitful and interesting approach to mathematical analysis. - Jean Mawhin, Zentralblatt The authors include a large number of once-traditional subjects which have now vanished from the analysis curriculum, at least in the standard American courses. Thus we find continued fractions, elliptic integrals, the Euler-MacLaurin summation formula, etc., most of which are found only in more compendious works. Many of the exercises are inspired by original papers, with the bibliographic references sometimes given. The work is very well illustrated. The book is definitely an analysis text, rather than a history, but a great deal of reliable historical material is included. For those seeking an alternative to the traditional approach, it seems to me to be of great interest. - Thomas Archibald, Mathematical Reviews The authors...have assembled an impressive array of annotated results, quotations, tables, charts, figures and drawings, many copied from original documents....they write with great enthusiasm and with evident affection for both analysis and history. - John Troutman, American Mathematical Monthly
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ISBN: 9781139107136 9780521134439 9781139116923 1139116924 9781139127585 1139127586 1139107135 0521134439 9781139114752 1139114751 110718861X 1139112562 128329589X 9786613295897 1139122665 Year: 2009 Publisher: Cambridge
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The first book to approach high oscillation as a subject of its own, Highly Oscillatory Problems begins a new dialogue and lays the groundwork for future research. It ensues from the six-month programme held at the Newton Institute of Mathematical Sciences, which was the first time that different specialists in highly oscillatory research, from diverse areas of mathematics and applications, had been brought together for a single intellectual agenda. This ground-breaking volume consists of eight review papers by leading experts in subject areas of active research, with an emphasis on computation: numerical Hamiltonian problems, highly oscillatory quadrature, rapid approximation of functions, high frequency wave propagation, numerical homogenization, discretization of the wave equation, high frequency scattering and the solution of elliptic boundary value problems.
Oscillations --- 519.63 --- 519.64 --- 681.3*G17 --- Cycles --- Fluctuations (Physics) --- Vibration --- 681.3*G17 Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- 519.64 Numerical methods for solution of integral equations. Quadrature formulae --- Numerical methods for solution of integral equations. Quadrature formulae --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- Oscillations.
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