Partial Differential Equations and Mathematica
This new book on partial differential equations provides a more accessible treatment of this demanding subject. There is a need to introduce technology into math courses; therefore, the authors integrate the use of Mathematica throughout the book, rather than just providing a few sample problems at the ends of chapters.
Although the text is rich in theory and develops the underlying mathematical analysis, it emphasizes the development of methods. Numerous examples in every chapter present the techniques that are representative of virtually every concept in the book. And unlike other textbooks, the answers, hints, and solutions to all exercises are provided on the spot.
Partial Differential Equations and Mathematica provides both the basic concepts and the methods for beginners, while also providing training and encouragement for those who plan to continue their studies in the subject itself or in applied areas. This is a textbook that is challenging and instructive, but at the same time, reasonable in its demands.
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Method of Characteristics
Linear Equations with Constant Coefficients
10 other sections not shown
apply approximate arbitrary assume auxiliary becomes boundary conditions boundary value problems bounded called Chapter characteristic coefficients complete condition u(x,0 Consider constant continuous corresponding curve defined DEFINITION denote derivatives determine difference domain dx dy element EXAMPLE Exercise expansion expr expressed finite formula Fourier Fourier transform function f given gives Green's function heat Hence homogeneous independent initial condition integral interval inverse known Laplace transform linear Mathematica method Note obtained operator ordinary differential equations orthogonal partial differential equation particular period plots positive prescribed problem reduces region represents respect result satisfies scheme Show side sinh solution Solve substitution temperature THEOREM tion transform variables variation wave yields zero