Partial Differential Equations for Scientists and EngineersMost physical phenomena, whether in the domain of fluid dynamics, electricity, magnetism, mechanics, optics, or heat flow, can be described in general by partial differential equations. Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations. This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing the mathematical model) and how to solve the equation (along with initial and boundary conditions). Written for advanced undergraduate and graduate students, as well as professionals working in the applied sciences, this clearly written book offers realistic, practical coverage of diffusiontype problems, hyperbolictype problems, elliptictype problems, and numerical and approximate methods. Each chapter contains a selection of relevant problems (answers are provided) and suggestions for further reading. 
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This is an excellent text not for those who want to learn how to solve PDE (as there are many, many books on that topic,) But more for those who want to understand PDE. The mix of rigor and intuition is nice, and in my opinion Farlow is a good textbook writer. For covering such a broad number of topics in PDE, I am impressed
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good book
Contents
II  3 
III  9 
IV  11 
V  19 
VI  27 
VII  33 
VIII  43 
IX  49 
XXXI  213 
XXXII  223 
XXXIII  232 
XXXIV  243 
XXXV  245 
XXXVI  253 
XXXVII  262 
XXXVIII  270 
X  58 
XI  64 
XII  72 
XIII  81 
XIV  89 
XV  97 
XVI  106 
XVII  112 
XVIII  121 
XIX  123 
XX  129 
XXI  137 
XXII  146 
XXIII  153 
XXIV  161 
XXV  168 
XXVI  174 
XXVII  183 
XXVIII  191 
XXIX  198 
XXX  205 
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Common terms and phrases
algebraic apply approximation basic boundary conditions boundaryvalue problems calculus canonical form circle conformal mappings convection cosine transform curve D'Alembert solution depends diagram diffusion Dirichlet problem discussed drumhead eigenfunctions eigenvalues elliptic EulerLagrange equation example Figure find the solution finite sine finitedifference flux formula Fourier series Fourier transform frequency given gives graph Green's function grid points heat equation heat flow hence homogeneous hyperbolic IBVP illustrate initial conditions initialboundaryvalue problem initialvalue problem inside integral transforms interior Dirichlet problem interpretation introduce inverse Laplace transform Laplace's equation Laplacian linear mathematical minimizing function Monte Carlo method nonhomogeneous nonlinear Note onedimensional original problem parabolic partial derivatives Partial Differential Equations PDE V2u physical potential PURPOSE OF LESSON random reader separation of variables simple sine and cosine sine transform solution u(x,t solve PDE steadystate STEP substitute Suppose technique theory velocity wave equation zplane zero