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Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the cl- sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Ma- ematical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs. Preface "It is impossible to exaggerate the extent to which modern applied mathematics has been shaped and fueled by the g- eral availability of fast computers with large memories. Their impact on mathematics, both applied and pure, is comparable to the role of the telescopes in astronomy and microscopes in biology." — Peter Lax, Siam Rev. Vol. 31 No. 4 Congratulations! You have chosen to study partial differential equations.

Differential equations, Partial. --- Partial differential equations --- Global analysis (Mathematics). --- Differential equations, partial. --- Computer science. --- Analysis. --- Partial Differential Equations. --- Computational Science and Engineering. --- Informatics --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematical analysis. --- Analysis (Mathematics). --- Partial differential equations. --- Computer mathematics. --- Computer mathematics --- Electronic data processing --- Mathematics --- 517.1 Mathematical analysis --- Mathematical analysis --- Computer science --- Mathematics.

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Engineering mathematics --- Industrial engineering --- 519.6 --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- Management engineering --- Simplification in industry --- Engineering --- Value analysis (Cost control) --- Engineering analysis --- Mathematical analysis --- Industrial applications --- Mathematics&delete& --- Computer programs --- Mathematics --- Programming

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Since the dawn of computing, the quest for a better understanding of Nature has been a driving force for technological development. Groundbreaking achievements by great scientists have paved the way from the abacus to the supercomputing power of today. When trying to replicate Nature in the computer’s silicon test tube, there is need for precise and computable process descriptions. The scienti?c ?elds of Ma- ematics and Physics provide a powerful vehicle for such descriptions in terms of Partial Differential Equations (PDEs). Formulated as such equations, physical laws can become subject to computational and analytical studies. In the computational setting, the equations can be discreti ed for ef?cient solution on a computer, leading to valuable tools for simulation of natural and man-made processes. Numerical so- tion of PDE-based mathematical models has been an important research topic over centuries, and will remain so for centuries to come. In the context of computer-based simulations, the quality of the computed results is directly connected to the model’s complexity and the number of data points used for the computations. Therefore, computational scientists tend to ?ll even the largest and most powerful computers they can get access to, either by increasing the si e of the data sets, or by introducing new model terms that make the simulations more realistic, or a combination of both. Today, many important simulation problems can not be solved by one single computer, but calls for parallel computing.

Differential equations, Partial --- Parallel processing (Electronic computers) --- Numerical solutions --- Data processing. --- 519.63 --- 681.3 *G18 --- Partial differential equations --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- High performance computing --- Multiprocessors --- Parallel programming (Computer science) --- Supercomputers --- Numerical solutions&delete& --- Data processing --- Global analysis (Mathematics). --- Computer science. --- Computer science --- Differential equations, partial. --- Analysis. --- Computational Science and Engineering. --- Computational Mathematics and Numerical Analysis. --- Mathematics of Computing. --- Theoretical, Mathematical and Computational Physics. --- Partial Differential Equations. --- Mathematics. --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Informatics --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematics --- Mathematical analysis. --- Analysis (Mathematics). --- Computer mathematics. --- Computer science—Mathematics. --- Mathematical physics. --- Partial differential equations. --- 517.1 Mathematical analysis --- Mathematical analysis --- Physical mathematics --- Physics

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This text sheds light on how mathematical models and computing can help understanding and prediction of complicated physical processes; how communication networks should be designed and implemented to meet the increasingly challenging requirements from users; and how modern engineering principles can lead to better and more robust software systems.   Through interviews with 12 internationally recognized researchers within these fields, conducted by the well-known science writer Dana Mackenzie and the science journalist Kathrine Aspaas, the reader gets views on recent achievements and future challenges.  .

Mathematics --- Physical Sciences & Mathematics --- Mathematics - General --- Computer science. --- Software engineering. --- Computers. --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer software engineering --- Informatics --- Mathematics. --- Computer organization. --- User interfaces (Computer systems). --- Partial differential equations. --- Computer mathematics. --- Mathematical models. --- Biomathematics. --- Computational Science and Engineering. --- Partial Differential Equations. --- Mathematical Modeling and Industrial Mathematics. --- Physiological, Cellular and Medical Topics. --- Computer Systems Organization and Communication Networks. --- User Interfaces and Human Computer Interaction. --- Computer systems --- Cybernetics --- Machine theory --- Calculators --- Cyberspace --- Engineering --- Science --- Differential equations, partial. --- Physiology --- Computer network architectures. --- Architectures, Computer network --- Network architectures, Computer --- Computer architecture --- Animal physiology --- Animals --- Biology --- Anatomy --- Partial differential equations --- Interfaces, User (Computer systems) --- Human-machine systems --- Human-computer interaction --- Organization, Computer --- Electronic digital computers --- Models, Mathematical --- Simulation methods --- Computer mathematics --- Electronic data processing

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Partial differential equations --- Mathematical physics --- Engineering sciences. Technology --- Computer science --- Computer. Automation --- differentiaalvergelijkingen --- analyse (wiskunde) --- informatica --- wiskunde --- informaticaonderzoek --- ingenieurswetenschappen --- fysica