This book presents topics of science and engineering which occur in nature or are part of daily life.This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation, epidemic wave fronts, and advection-diffusion processes.
The student who reads through this book and solves many of the exercises will have a sound knowledge base for upper division mathematics, science, and engineering courses where detailed models and applications are introduced.--BOOK JACKET. Partial differential equations are used in mathematical models of a huge range of real-world phenomena, from electromagnetism to financial markets. Partial Differential Equation Free Surface FlowsThis new edition of Applied PDEs contains many new sections and exercises Including, American options, transform methods, free surface flows, linear elasticity and complex characteristics. Pearson Modern Classics are acclaimed titles at a value price. Applied Partial Differential Equations with Fourier Series and Boundary Value Problems emphasizes the physical interpretation of mathematical solutions and introduces applied mathematics while presenting differential equations. Coverage includes Fourier series, orthogonal functions, boundary value problems, Greens functions, and transform methods. This text is ideal for readers interested in science, engineering, and applied mathematics. It is a more modern, comprehensive treatment intended for students who need more than the purely numerical solutions provided by programs like the MATLAB PDE Toolbox, and those obtained by the method of separation of variables, which is usually the only theoretical approach found in the majority of elementary textbooks. This will fill a need in the market for a more modern text for future working engineers, and one that students can read and understand much more easily than those currently on the market. Includes new and important materials necessary to meet current demands made by diverse applications Very detailed solutions to odd numbered problems to help students Instructors Manual Available. This textbook is for the standard, one-semester, junior-senior course that often goes by the title Elementary Partial Differential Equations or Boundary Value Problems. The audience consists of students in mathematics, engineering, and the sciences. The topics include derivations of some of the standard models of mathematical physics and methods for solving those equations on unbounded and bounded domains, and applications of PDEs to biology. The text differs from other texts in its brevity; yet it provides coverage of the main topics usually studied in the standard course, as well as an introduction to using computer algebra packages to solve and understand partial differential equations. For the 3rd edition the section on numerical methods has been considerably expanded to reflect their central role in PDEs. Partial Differential Equation Code For NumericalA treatment of the finite element method has been included and the code for numerical calculations is now written for MATLAB. To further aid the reader in mastering the material and using the book, the clarity of the exercises has been improved, more routine exercises have been included, and the entire text has been visually reformatted to improve readability. Partial differential equations are a central concept in mathematics. They arise in mathematical models whose dependent variables vary continuously as functions of several independent variables (usually space and time). Their power lies in their universality: there is a huge and ever- growingrange of real-world problems to which they can be applied, from fluid mechanics and electromagnetism to probability and finance. This is an enthusiastic and clear guide to the theory and applications of PDEs. Partial Differential Equation Software To ProduceIt deals with questions such as the well-posedness of a PDE problem: when is there aunique solution that changes only slightly when the input data is slightly changed This is connected to the problem of establishing the accuracy of a numerical solution to a PDE, a problem that become increasingly important as the power of computer software to produce numerical solutionsgrows.
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