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The emphasis of this work is on constructing 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.

Nonlinear partial differential operators --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Data processing --- Differential equations, Partial. --- Maple (Computer file) --- Mathematica (Computer file) --- Partial differential equations --- Mathematics. --- Partial differential equations. --- Statistical physics. --- Applied mathematics. --- Engineering mathematics. --- Partial Differential Equations. --- Nonlinear Dynamics. --- Appl.Mathematics/Computational Methods of Engineering. --- Differential equations, partial. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Mathematical and Computational Engineering. --- Engineering --- Engineering analysis --- Mathematical analysis --- Physics --- Mathematical statistics --- Statistical methods

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Partial differential equations --- Engineering sciences. Technology --- differentiaalvergelijkingen --- ingenieurswetenschappen

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It is well known that computer algebra systems have revolutionized teaching and the learning processes in mathematics, science, and - gineering, allowing students to computationally investigate complicated problems to ?nd exact or approximate analytic solutions, numeric so- tions, and illustrative two- and three-dimensional graphics. Since the 1960s there has existed individual packages for solving s- ci?c analytic, numerical, graphical and other problems. The need to solve all those problems with the aid of a single system, has led to the idea of construction of a modern general purpose computer algebra s- tem. The ?rst two papers describing analytic calculations realized on a computer were published in 1953 [7]. In the early 1970s, systems of - alytic computations (SAC),or computer algebra systems (CAS), began to appear. Computer algebra systems are computational interactive programs that facilitate symbolic mathematics and can handle other type of pr- lems. The ?rst popular systems were Reduce, Derive, and Macsyma, which are still commercially available. Macsyma was one of the ?rst and most mature systems. It was developed at the Massachusetts - stitute of Technology (MIT), but practically its evolution has stopped since thesummer of 1999. Afree software version of Macsyma, Maxima, is actively being maintained. To the present day, there have been developed more than a hundred computer algebra systems [7], [18]. Among these we can ?nd Axiom, Derive, Maxima, Maple, Mathematica, Matlab, MuMATH, MuPAD, Reduce, etc. All these systems can be subdivided into specialized and general-purpose computer algebra systems ([7], [18], [2]).

Mathematical control systems --- Computer science --- Computer. Automation --- informatica --- wiskunde --- informaticaonderzoek

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The first book to compare the main two computer algebra systems (CAS), Maple and Mathematica used by students, mathematicians, scientists, and engineers. Both systems are presented in parallel so that Mathematica users can learn Maple quickly by finding the Maple equivalent to Mathematica functions, and vice versa. This student reference handbook consists of core material for incorporating Maple and Mathematica as a working tool into different undergraduate mathematical courses (abstract and linear algebra, geometry, calculus and analysis, complex functions, special functions, integral and discrete transforms, algebraic and transcendental equations, ordinary and partial differential equations, integral equations, numerical analysis and scientific computing). The book also contains applications from various areas of mathematics, physics, and music theory and can be useful for graduate students, professors, and researchers in science and engineering. One of the goals of this book is to develop problem-solving skills (that are most useful for solving sophisticated research problems) finding solutions with Maple and Mathematica and not to depend on a specific version of both systems (Maple 12 and Mathematica 6 and 7 are considered). Part I, describes the foundations of Maple and Mathematica (with equivalent problems and solutions). Part II, describes Mathematics with Maple and Mathematica by using equivalent problems. Finally, this book is ideal for scientists who want to corroborate their Maple and Mathematica work with independent verification provided by another CAS. J. Carter, SIAM Review 50: 149-152 (2008).