Partial Differential Equations for Scientists and Engineers

Partial Differential Equations & BeyondStanley J. Farlow's Partial Differential Equations for Scientists and Engineers is one of the most widely used textbooks that Dover has ever published. Readers of the many Amazon reviews will easily find out why. Jerry, as Professor Farlow is known to the mathematical community, has written many other fine texts — on calculus, finite mathematics, modeling, and other topics. We followed up the 1993 Dover edition of the partial differential equations title in 2006 with a new edition of his An Introduction to Differential Equations and Their Applications. Readers who wonder if mathematicians have a sense of humor might search the internet for a copy of Jerry's The Girl Who Ate Equations for Breakfast (Aardvark Press, 1998). Critical Acclaim for Partial Differential Equations for Scientists and Engineers:"This book is primarily intended for students in areas other than mathematics who are studying partial differential equations at the undergraduate level. The book is unusual in that the material is organized into 47 semi-independent lessonsrather than the more usual chapter-by-chapter approach. "An appealing feature of the book is the way in which the purpose of each lesson is clearly stated at the outset while the student will find the problems placed at the end of each lesson particularly helpful. The first appendix consists of integral transform tables whereas the second is in the form of a crossword puzzle which the diligent student should be able to complete after a thorough reading of the text. "Students (and teachers) in this area will find the book useful as the subject matter is clearly explained. The author and publishers are to be complimented for the quality of presentation of the material." — K. Morgan, University College, Swansea

• 1. IntroductionLesson 1. Introduction to Partial Differential Equations2. Diffusion-Type ProblemsLesson 2. Diffusion-Type Problems (Parabolic Equations)Lesson 3. Boundary Conditions for Diffusion-Type ProblemsLesson 4. Derivation of the Heat EquationLesson 5. Separation of VariablesLesson 6. Transforming Nonhomogeneous BCs into Homogeneous OnesLesson 7. Solving More Complicated Problems by Separation of VariablesLesson 8. Transforming Hard Equations into Easier OnesLesson 9. Solving Nonhomogeneous PDEs (Eigenfunction Expansions)Lesson 10. Integral Transforms (Sine and Cosine Transforms)Lesson 11. The Fourier Series and TransformLesson 12. The Fourier Transform and its Application to PDEsLesson 13. The Laplace TransformLesson 14. Duhamel's PrincipleLesson 15. The Convection Term u subscript x in Diffusion Problems3. Hyperbolic-Type ProblemsLesson 16. The One Dimensional Wave Equation (Hyperbolic Equations)Lesson 17. The D'Alembert Solution of the Wave EquationLesson 18. More on the D'Alembert SolutionLesson 19. Boundary Conditions Associated with the Wave EquationLesson 20. The Finite Vibrating String (Standing Waves)Lesson 21. The Vibrating Beam (Fourth-Order PDE)Lesson 22. Dimensionless ProblemsLesson 23. Classification of PDEs (Canonical Form of the Hyperbolic Equation)Lesson 24. The Wave Equation in Two and Three Dimensions (Free Space)Lesson 25. The Finite Fourier Transforms (Sine and Cosine Transforms)Lesson 26. Superposition (The Backbone of Linear Systems)Lesson 27. First-Order Equations (Method of Characteristics)Lesson 28. Nonlinear First-Order Equations (Conservation Equations)Lesson 29. Systems of PDEsLesson 30. The Vibrating Drumhead (Wave Equation in Polar Coordinates)4. Elliptic-Type ProblemsLesson 31. The Laplacian (an intuitive description)Lesson 32. General Nature of Boundary-Value ProblemsLesson 33. Interior Dirichlet Problem for a CircleLesson 34. The Dirichlet Problem in an AnnulusLesson 35. Laplace's Equation in Spherical Coordinates (Spherical Harmonics)Lesson 36. A Nonhomogeneous Dirichlet Problem (Green's Functions)5. Numerical and Approximate MethodsLesson 37. Numerical Solutions (Elliptic Problems)Lesson 38. An Explicit Finite-Difference MethodLesson 39. An Implicit Finite-Difference Method (Crank-Nicolson Method)Lesson 40. Analytic versus Numerical SolutionsLesson 41. Classification of PDEs (Parabolic and Elliptic Equations)Lesson 42. Monte Carlo Methods (An Introduction)Lesson 43. Monte Carlo Solutions of Partial Differential Equations)Lesson 44. Calculus of Variations (Euler-Lagrange Equations)Lesson 45. Variational Methods for Solving PDEs (Method of Ritz)Lesson 46. Perturbation method for Solving PDEsLesson 47. Conformal-Mapping Solution of PDEsAnswers to Selected ProblemsAppendix 1. Integral Transform TablesAppendix 2. PDE Crossword PuzzleAppendix 3. Laplacian in Different Coordinate SystemsAppendix 4. Types of Partial Differential EquationsIndex