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An Invitation To Applied Mathematics

Author: Carmen Chicone
Publisher: Academic Press
ISBN: 0128041544
Size: 60.91 MB
Format: PDF, Kindle
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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

A First Course In The Numerical Analysis Of Differential Equations

Author: A. Iserles
Publisher: Cambridge University Press
ISBN: 0521734908
Size: 41.35 MB
Format: PDF
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lead the reader to a theoretical understanding of the subject without neglecting its practical aspects. The outcome is a textbook that is mathematically honest and rigorous and provides its target audience with a wide range of skills in both ordinary and partial differential equations." --Book Jacket.

A First Course In Differential Equations Modeling And Simulation

Author: Carlos A. Smith
Publisher: CRC Press
ISBN: 1439850887
Size: 23.49 MB
Format: PDF, Mobi
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Emphasizing a practical approach for engineers and scientists, A First Course in Differential Equations, Modeling, and Simulation avoids overly theoretical explanations and shows readers how differential equations arise from applying basic physical principles and experimental observations to engineering systems. It also covers classical methods for obtaining the analytical solution of differential equations and Laplace transforms. In addition, the authors discuss how these equations describe mathematical systems and how to use software to solve sets of equations where analytical solutions cannot be obtained. Using simple physics, the book introduces dynamic modeling, the definition of differential equations, two simple methods for obtaining their analytical solution, and a method to follow when modeling. It then presents classical methods for solving differential equations, discusses the engineering importance of the roots of a characteristic equation, and describes the response of first- and second-order differential equations. A study of the Laplace transform method follows with explanations of the transfer function and the power of Laplace transform for obtaining the analytical solution of coupled differential equations. The next several chapters present the modeling of translational and rotational mechanical systems, fluid systems, thermal systems, and electrical systems. The final chapter explores many simulation examples using a typical software package for the solution of the models developed in previous chapters. Providing the necessary tools to apply differential equations in engineering and science, this text helps readers understand differential equations, their meaning, and their analytical and computer solutions. It illustrates how and where differential equations develop, how they describe engineering systems, how to obtain the analytical solution, and how to use software to simulate the systems.

Partial Differential Equations Of Applied Mathematics

Author: Erich Zauderer
Publisher: Wiley-Interscience
ISBN: 9780471315162
Size: 40.42 MB
Format: PDF, Docs
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The only comprehensive guide to modeling, characterizing, and solving partial differential equations This classic text by Erich Zauderer provides a comprehensive account of partial differential equations and their applications. Dr. Zauderer develops mathematical models that give rise to partial differential equations and describes classical and modern solution techniques. With an emphasis on practical applications, he makes liberal use of real-world examples, explores both linear and nonlinear problems, and provides approximate as well as exact solutions. He also describes approximation methods for simplifying complicated solutions and for solving linear and nonlinear problems not readily solved by standard methods. The book begins with a demonstration of how the three basic types of equations (parabolic, hyperbolic, and elliptic) can be derived from random walk models. It continues in a less statistical vein to cover an exceptionally broad range of topics, including stabilities, singularities, transform methods, the use of Green's functions, and perturbation and asymptotic treatments. Features that set Partial Differential Equations of Applied Mathematics, Second Edition above all other texts in the field include: Coverage of random walk problems, discontinuous and singular solutions, and perturbation and asymptotic methods More than 800 practice exercises, many of which are fully worked out Numerous up-to-date examples from engineering and the physical sciences Partial Differential Equations of Applied Mathematics, Second Edition is a superior advanced-undergraduate to graduate-level text for students in engineering, the sciences, and applied mathematics. The title is also a valuable working resource for professionals in these fields. Dr. Zauderer received his doctorate in mathematics from the New York University-Courant Institute. Prior to joining the staff of Polytechnic University, he was a Senior Weitzmann Fellow of the Weitzmann Institute of Science in Rehovot, Israel.

Elementary Calculus Of Financial Mathematics

Author: A. J. Roberts
Publisher: SIAM
ISBN: 9780898718225
Size: 63.37 MB
Format: PDF, ePub
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Financial mathematics and its calculus introduced in an accessible manner for undergraduate students. Topics covered include financial indices as stochastic processes, Ito's stochastic calculus, the Fokker-Planck Equation and extra MATLAB/SCILAB code.

Scientific Computing And Differential Equations

Author: Gene H. Golub
Publisher: Elsevier
ISBN: 0080516696
Size: 80.65 MB
Format: PDF, Mobi
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Scientific Computing and Differential Equations: An Introduction to Numerical Methods, is an excellent complement to Introduction to Numerical Methods by Ortega and Poole. The book emphasizes the importance of solving differential equations on a computer, which comprises a large part of what has come to be called scientific computing. It reviews modern scientific computing, outlines its applications, and places the subject in a larger context. This book is appropriate for upper undergraduate courses in mathematics, electrical engineering, and computer science; it is also well-suited to serve as a textbook for numerical differential equations courses at the graduate level. An introductory chapter gives an overview of scientific computing, indicating its important role in solving differential equations, and placing the subject in the larger environment Contains an introduction to numerical methods for both ordinary and partial differential equations Concentrates on ordinary differential equations, especially boundary-value problems Contains most of the main topics for a first course in numerical methods, and can serve as a text for this course Uses material for junior/senior level undergraduate courses in math and computer science plus material for numerical differential equations courses for engineering/science students at the graduate level

Computational Partial Differential Equations Using Matlab

Author: Jichun Li
Publisher: CRC Press
ISBN: 9781420089059
Size: 23.23 MB
Format: PDF, Mobi
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This textbook introduces several major numerical methods for solving various partial differential equations (PDEs) in science and engineering, including elliptic, parabolic, and hyperbolic equations. It covers traditional techniques that include the classic finite difference method and the finite element method as well as state-of-the-art numerical methods, such as the high-order compact difference method and the radial basis function meshless method. Helps Students Better Understand Numerical Methods through Use of MATLAB® The authors uniquely emphasize both theoretical numerical analysis and practical implementation of the algorithms in MATLAB, making the book useful for students in computational science and engineering. They provide students with simple, clear implementations instead of sophisticated usages of MATLAB functions. All the Material Needed for a Numerical Analysis Course Based on the authors’ own courses, the text only requires some knowledge of computer programming, advanced calculus, and difference equations. It includes practical examples, exercises, references, and problems, along with a solutions manual for qualifying instructors. Students can download MATLAB code from www.crcpress.com, enabling them to easily modify or improve the codes to solve their own problems.

An Introduction To Mathematical Modeling

Author: Edward A. Bender
Publisher: Courier Corporation
ISBN: 0486137120
Size: 41.56 MB
Format: PDF, ePub, Mobi
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Accessible text features over 100 reality-based examples pulled from the science, engineering, and operations research fields. Prerequisites: ordinary differential equations, continuous probability. Numerous references. Includes 27 black-and-white figures. 1978 edition.