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Solving Nonlinear Partial Differential Equations with Maple and Mathematica

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The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple and Mathematica, facilitates a deeper understanding of the subject. Among a big number of CAS, we choose the two systems, Maple and Mathematica, that are used worldwide by students, research mathematicians, scientists, and engineers. As in the our previous books, we propose the idea to use in parallel both systems, Maple and Mathematica, since in many research problems frequently it is required to compare independent results obtained by using different computer algebra systems, Maple and/or Mathematica, at all stages of the solution process. One of the main points (related to CAS) is based on the implementation of a whole solution method (e.g. starting from an analytical derivation of exact governing equations, constructing discretizations and analytical formulas of a numerical method, performing numerical procedure, obtaining various visualizations, and comparing the numerical solution obtained with other types of solutions considered in the book, e.g. with asymptotic solution).

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Partial Differential Equations: Vol. 1 Foundations and Integral Representations (Universitext)
Partial Differential Equations: Vol. 1 Foundations and Integral Representations (Universitext)
From the reviews:

"Friedrich Sauvigny's remarkable two-volume opus constitutes the author's attempt to treat the beautiful and difficult subject of PDEs in a thorough and instructive way. is a fine place to learn PDEs with the goal of doing serious work in the field. Friedrich Sauvigny's scholarship is exemplary and thorough; at the same...

Linear Algebra and Geometry
Linear Algebra and Geometry

This book is the result of a series of lectures on linear algebra and the geometry of multidimensional spaces given in the 1950s through 1970s by Igor R. Shafarevich at the Faculty of Mechanics and Mathematics of Moscow State University.

Notes for some of these lectures were preserved in the faculty library, and these were used...
Numerical Methods in Finance with C++ (Mastering Mathematical Finance)
Numerical Methods in Finance with C++ (Mastering Mathematical Finance)

Driven by concrete computational problems in quantitative finance, this book provides aspiring quant developers with the numerical techniques and programming skills they need. The authors start from scratch, so the reader does not need any previous experience of C++. Beginning with straightforward option pricing on binomial trees, the book...


Partial Differential Equations 2: Functional Analytic Methods (Universitext)
Partial Differential Equations 2: Functional Analytic Methods (Universitext)
This comprehensive two-volume textbook presents the whole area of Partial Differential Equations - of the elliptic, parabolic, and hyperbolic type - in two and several variables. Special emphasis is put on the connection of PDEs and complex variable methods.

In this second volume the following topics are treated: Solvability of...

Introduction to Differential Calculus: Systematic Studies with Engineering Applications for Beginners
Introduction to Differential Calculus: Systematic Studies with Engineering Applications for Beginners

Enables readers to apply the fundamentals of differential calculus to solve real-life problems in engineering and the physical sciences

Introduction to Differential Calculus fully engages readers by presenting the fundamental theories and methods of differential calculus and then showcasing how the discussed concepts can be...

An Introduction to Partial Differential Equations
An Introduction to Partial Differential Equations
"This is an introductory book on the subject of partial differential equations which is suitable for a large variety of basic courses on this topic. In particular, it can be used as a textbook or self-study book for large classes of readers with interests in mathematics, engineering, and related fields. Its usefulness stems from its clarity,...
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