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An Invitation To Applied Mathematics

Author: Carmen Chicone
Publisher: Academic Press
ISBN: 0128041544
Size: 29.94 MB
Format: PDF
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An Invitation to Applied Mathematics: Differential Equations, Modeling, and Computation introduces the reader to the methodology of modern applied mathematics in modeling, analysis, and scientific computing with emphasis on the use of ordinary and partial differential equations. Each topic is introduced with an attractive physical problem, where a mathematical model is constructed using physical and constitutive laws arising from the conservation of mass, conservation of momentum, or Maxwell's electrodynamics. Relevant mathematical analysis (which might employ vector calculus, Fourier series, nonlinear ODEs, bifurcation theory, perturbation theory, potential theory, control theory, or probability theory) or scientific computing (which might include Newton's method, the method of lines, finite differences, finite elements, finite volumes, boundary elements, projection methods, smoothed particle hydrodynamics, or Lagrangian methods) is developed in context and used to make physically significant predictions. The target audience is advanced undergraduates (who have at least a working knowledge of vector calculus and linear ordinary differential equations) or beginning graduate students. Readers will gain a solid and exciting introduction to modeling, mathematical analysis, and computation that provides the key ideas and skills needed to enter the wider world of modern applied mathematics. Presents an integrated wealth of modeling, analysis, and numerical methods in one volume Provides practical and comprehensible introductions to complex subjects, for example, conservation laws, CFD, SPH, BEM, and FEM Includes a rich set of applications, with more appealing problems and projects suggested

Nonlocal Modeling Analysis And Computation

Author: Qiang Du
Publisher: SIAM
ISBN: 161197562X
Size: 51.60 MB
Format: PDF
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Studies of complexity, singularity, and anomaly using nonlocal continuum models are steadily gaining popularity. This monograph provides an introduction to basic analytical, computational, and modeling issues and to some of the latest developments in these areas. Nonlocal Modeling, Analysis, and Computation includes motivational examples of nonlocal models, basic building blocks of nonlocal vector calculus, elements of theory for well-posedness and nonlocal spaces, connections to and coupling with local models, convergence and compatibility of numerical approximations, and various applications, such as nonlocal dynamics of anomalous diffusion and nonlocal peridynamic models of elasticity and fracture mechanics. A particular focus is on nonlocal systems with a finite range of interaction to illustrate their connection to local partial differential equations and fractional PDEs. These models are designed to represent nonlocal interactions explicitly and to remain valid for complex systems involving possible singular solutions and they have the potential to be alternatives for as well as bridges to existing models. The author discusses ongoing studies of nonlocal models to encourage the discovery of new mathematical theory for nonlocal continuum models and offer new perspectives on traditional models, analytical techniques, and algorithms.

A Practical Course In Differential Equations And Mathematical Modelling

Author: Nail H. Ibragimov
Publisher: World Scientific
ISBN: 9814291951
Size: 50.42 MB
Format: PDF, Kindle
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A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author?s own theoretical developments. The book ? which aims to present new mathematical curricula based on symmetry and invariance principles ? is tailored to develop analytic skills and ?working knowledge? in both classical and Lie?s methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundamental solution, etc. easy to follow and interesting for students. The book is based on the author?s extensive teaching experience at Novosibirsk and Moscow universities in Russia, CollŠge de France, Georgia Tech and Stanford University in the United States, universities in South Africa, Cyprus, Turkey, and Blekinge Institute of Technology (BTH) in Sweden. The new curriculum prepares students for solving modern nonlinear problems and will essentially be more appealing to students compared to the traditional way of teaching mathematics.

Mathematical Modeling

Author: Mark M. Meerschaert
ISBN: 9780124876521
Size: 78.10 MB
Format: PDF, Mobi
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Mathematical Modeling, Second Edition, offers a unique approach to mathematical modeling by providing an inviting overview, and applying problem-solving methodology throughout concerning three major areas: optimization, dynamical systems, and stochastic processes. Providing a thorough revision, the author takes a practical approach toward the solution of a variety of real problems such as docking two vehicles in space, growth rate of an infectious disease, and wildlife management. Rigorous mathematical techniques required for reasonable solutions are introduced as necessary. * A large collection of real-world problems * An integration of computer outputs from the latest versions of Mathematica, Maple, Lindo, Minitab * A systematic five-step modeling method * Applies calculus, differential equations, linear algebra, and probability New To This Edition: * Material on discrete modeling, including integer programming * Extended treatment on chaos and fractals * Additional material on linear programming, including the use of spreadsheet tools * More applications in probability and statistics