Handbook of Differential Equations
1st Edition
Published on 12. May 2014
694 pages
978-1-4832-2096-3 (ISBN)
Description
Handbook of Differential Equations is a handy reference to many popular techniques for solving and approximating differential equations, including exact analytical methods, approximate analytical methods, and numerical methods. Topics covered range from transformations and constant coefficient linear equations to finite and infinite intervals, along with conformal mappings and the perturbation method. Comprised of 180 chapters, this book begins with an introduction to transformations as well as general ideas about differential equations and how they are solved, together with the techniques needed to determine if a partial differential equation is well-posed or what the "natural" boundary conditions are. Subsequent sections focus on exact and approximate analytical solution techniques for differential equations, along with numerical methods for ordinary and partial differential equations. This monograph is intended for students taking courses in differential equations at either the undergraduate or graduate level, and should also be useful for practicing engineers or scientists who solve differential equations on an occasional basis.
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Handbook of Differential Equations
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Person
Dr. Daniel Zwillinger is a Senior Principal Systems Engineer for the Raytheon Company. He was a systems requirements "book boss for the Cobra Judy Replacement (CJR) ship and was a requirements and test lead for tracking on the Ungraded Early Warning Radars (UEWR). He has improved the Zumwalt destroyer's software accreditation process and he was test lead on an Active Electronically Scanned Array (AESA) radar. Dan is a subject matter expert (SME) in Design for Six Sigma (DFSS) and is a DFSS SME in Test Optimization, Critical Chain Program Management, and Voice of the Customer. He is currently leading a project creating Trust in Autonomous Systems. At Raytheon, he twice won the President's award for best Six Sigma project of the year: on converting planning packages to work packages for the Patriot missile, and for revising Raytheon's timecard system. He has managed the Six Sigma white belt training program. Prior to Raytheon, Dan worked at Sandia Labs, JPL, Exxon, MITRE, IDA, BBN, and The Mathworks (where he developed an early version of their Statistics Toolbox).
For ten years, Zwillinger was owner and president of Aztec Corporation. As a small business, Aztec won several Small Business Innovation Research (SBIR) contracts. The company also created several software packages for publishing companies. Prior to Aztec, Zwillinger was a college professor at Rensselaer Polytechnic Institute in the department of mathematics.
Dan has written several books on mathematics on the topics of differential equations, integration, statistics, and general mathematics. He is editor-in-chief of the Chemical Rubber Company's (CRC's) "Standard Mathematical Tables and Formulae, and is on the editorial board for CRC's "Handbook of Chemistry and Physics. Zwillinger holds a bachelor's degree in mathematics from the Massachusetts Institute of Technology (MIT). He earned his doctorate in applied mathematics from the California Institute of Technology (Caltech). Zwillinger is a certified Raytheon Six Sigma Expert and an ASQ certified Six Sigma Black Belt. He also holds a pilot's license.
Content
PrefaceIntroductionHow to Use This BookI.A Definitions and Concepts 1 Definition of Terms 2 Alternative Theorems 3 Bifurcation Theory 4 A Caveat for Partial Differential Equations 5 Classification of Partial Differential Equations 6 Compatible Systems 7 Conservation Laws 8 Differential Resultants 9 Fixed Point Existence Theorems 10 Hamilton-Jacobi Theory 11 Limit Cycles 12 Natural Boundary Conditions for a PDE 13 Self-Adjoint Eigenfunction Problems 14 Sturm-Liouville Theory 15 Variational Equations 16 Well-Posedness of Differential Equations 17 Wronskians and Fundamental SolutionsI.B Transformations 18 Canonical Forms 19 Canonical Transformations 20 Darboux Transformation 21 An Involutory Transformation 22 Liouville Transformation - 1 23 Liouville Transformation - 2 24 Reduction of Linear ODEs to a First Order System 25 Transformations of Second Order Linear ODEs - 1 26 Transformations of Second Order Linear ODEs - 2 27 Transformation of an ODE to an Integral Equation 28 Miscellaneous ODE Transformations 29 Reduction of PDEs to a First Order System 30 Transforming Partial DifFerential Equations 31 Transformations of Partial DifFerential EquationsII Exact Analytical Methods 32 Introduction to Exact Analytical Methods 33 Look Up TechniqueII.A Exact Methods for ODEs 34 An N-th Order Equation 35 Use of the Adjoint Equation* 36 Autonomous Equations 37 Bernoulli Equation 38 Clairaut's Equation 39 Computer-Aided Solution 40 Constant Coefficient Linear Equations 41 Contact Transformation 42 Delay Equations 43 Dependent Variable Missing 44 Differentiation Method 45 Differential Equations with Discontinuities* 46 Eigenfunction Expansions* 47 Equidimensional-in-x Equations 48 Equidimensional-in-y Equations 49 Euler Equations 50 Exact First Order Equations 51 Exact Second Order Equations 52 Exact N-th Order Equations 53 Factoring Equations* 54 Factoring Operators* 55 Factorization Method 56 Fokker-Planck Equation 57 Fractional Differential Equations* 58 Free Boundary Problems* 59 Generating Functions* 60 Green's Functions* 61 Homogeneous Equations 62 Method of Images* 63 Integrable Combinations 64 Integral Representations: Laplace's Method* 65 Integral Transforms: Finite Intervals* 66 Integral Transforms: Infinite Intervals* 67 Integrating Factors* 68 Interchanging Dependent and Independent Variables 69 Lagrange's Equation 70 Lie Groups: ODEs 71 Operational Calculus* 72 PfafSan Differential Equations 73 Prüfer Substitution 74 Reduction of Order 75 Riccati Equation - 1 76 Riccati Equation - 2 77 Matrix Riccati Equations 78 Scale Invariant Equations 79 Separable Equations 80 Series Solution* 81 Equations Solvable for x 82 Equations Solvable for y 83 Superposition* 84 Method of Undetermined Coefficients* 85 Variation of Parameters 86 Vector Ordinary Differential EquationsII.
