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Scientific computing is a fast growing and fast changing area whose applications to various branches of science, engineering, medicine, economics (and others) are increasing in number and relevance every day. There are two main reasons (among others) that make scientific computing change so rapidly. One is the increasing number of different research areas beginning to make use of numerical simulation: from nanotechnology to genomics, from computer­ aided diagnosis and operations in medical applications (which involve often com­ plete simulations of parts of the human body) to economics and finance. Each new application, and each new aspect of earlier applications, draws heavily on the know­ how that has been acquired on other problems with similar mathematical features. It has to be pointed out that the lofty perspective of mathematics succeeds quite often in finding connections among very different phenomena, that tum out in the end to share the same mathematical and numerical structure. In tum, new applica­ tions contribute to the cross-fertilization by "sending back" new interpretations and suggestions which are often useful in more classical applications. All this creates a resonance effect that contributes greatly to the growth rate of the whole field.

519.6 <063> --- 519.62 <063> --- 519.63 <063> --- 681.3*G17 <063> --- 681.3*G18 <063> --- 681.3*G18 <063> Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis)--Congressen --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis)--Congressen --- 681.3*G17 <063> Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis)--Congressen --- Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis)--Congressen --- 519.63 <063> Numerical methods for solution of partial differential equations--Congressen --- Numerical methods for solution of partial differential equations--Congressen --- 519.62 <063> Numerical methods for solution of ordinary differential equations--Congressen --- Numerical methods for solution of ordinary differential equations--Congressen --- 519.6 <063> Computational mathematics. Numerical analysis. Computer programming--Congressen --- Computational mathematics. Numerical analysis. Computer programming--Congressen --- Mathematical analysis. --- Analysis (Mathematics). --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Analysis. --- Applications of Mathematics. --- Computational Mathematics and Numerical Analysis. --- Computer mathematics --- Electronic data processing --- Mathematics --- Engineering --- Engineering analysis --- Mathematical analysis --- 517.1 Mathematical analysis

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Mathematics

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This volume contains contributed survey papers from the main speakers at the LMS/EPSRC Symposium “Building bridges: connections and challenges in modern approaches to numerical partial differential equations”. This meeting took place in July 8-16, 2014, and its main purpose was to gather specialists in emerging areas of numerical PDEs, and explore the connections between the different approaches. The type of contributions ranges from the theoretical foundations of these new techniques, to the applications of them, to new general frameworks and unified approaches that can cover one, or more than one, of these emerging techniques.

Computer mathematics. --- Partial differential equations. --- Computational Science and Engineering. --- Partial Differential Equations.

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Il testo intende essere di supporto ad un primo insegnamento di Analisi Matematica secondo i principi dei nuovi Ordinamenti Didattici. È in particolare pensato per Ingegneria, Informatica, Fisica. Il testo presenta tre diversi livelli di lettura. Un livello essenziale permette allo studente di cogliere i concetti indispensabili della materia e di familiarizzarsi con le relative tecniche di calcolo. Un livello intermedio fornisce le giustificazioni dei principali risultati e arricchisce l'esposizione mediante utili osservazioni e complementi. Un terzo livello di lettura, basato su numerosi riferimenti ad un testo virtuale disponibile in rete, permette all'allievo più motivato ed interessato di approfondire la sua preparazione sulla materia. Completano il testo numerosi esempi ed esercizi con soluzioni. La grafica accattivante, a 2 colori, fa di questo testo un punto di riferimento fondamentale per lo studio della disciplina.

Harmonic analysis. Fourier analysis --- Partial differential equations --- Differential equations --- Mathematical analysis --- Mathematics --- Fourieranalyse --- differentiaalvergelijkingen --- analyse (wiskunde) --- wiskunde