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 Craig, Walter, 1953 author.
 Providence, Rhode Island : American Mathematical Society, [2018]
 Description
 Book — ix, 205 pages : illustrations ; 27 cm.
 Summary

 Introduction Wave equations The heat equation Laplace's equation Properties of the Fourier transform Wave equations on $\mathbb{R}^n$ Dispersion Conservation laws and shocks Bibliography Index.
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QA377 .C85 2018  Unknown 
 Erdogan, M. Burak.
 Cambridge, United Kingdom : Cambridge University Press, 2016.
 Description
 Book — xvi, 186 pages ; 24 cm.
 Summary

 Preface Notation
 1. Preliminaries and tools
 2. Linear dispersive equations
 3. Methods for establishing wellposedness
 4. Global dynamics of nonlinear dispersive PDEs
 5. Applications of smoothing estimates References Index.
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QA377 .E73 2016  Unknown 
3. Inside finite elements [2016]
 Weiser, Martin, author.
 Berlin ; Boston : Walter de Gruyter GmbH, [2016]
 Description
 Book — xi, 146 pages : illustrations ; 25 cm.
 Summary

All relevant implementation aspects of finite element methods are discussed in this book. The focus is on algorithms and data structures as well as on their concrete implementation. Theory is covered as far as it gives insight into the construction of algorithms. Throughout the exercises complete FEsolver for scalar 2D problems will be implemented in Matlab/Octave.
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All relevant implementation aspects of finite element methods are discussed in this book. The focus is on algorithms and data structures as well as on their concrete implementation. Theory is covered only as far as it gives insight into the construction of algorithms. In the exercises, a complete FEsolver for stationary 2D problems is implemented in Matlab/Octave. Contents: Finite Element Fundamentals Grids and Finite Elements Assembly Solvers Error Estimation Mesh Refinement Multigrid Elastomechanics Fluid Mechanics Grid Data Structure Function Reference.
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QC20.7 .F56 W45 2016  Unknown 
 Dobrushkin, V. A. (Vladimir Andreevich), author.
 Boca Raton : CRC Press, Taylor & Francis, [2015]
 Description
 Book — xvi, 672 pages : illustrations ; 26 cm.
 Summary

 FirstOrder Equations Introduction Separable Equations Equations with Homogeneous Coefficients Exact Differential Equations Integrating Factors FirstOrder Linear Differential Equations Equations Reducible to first Order Existence and Uniqueness Review Questions for
 Chapter 1 Applications of First Order ODE Applications in Mathematics Curves of Pursuit Chemical Reactions Population Models Mechanics Electricity Applications in Physics Thermodynamics Flow Problems Review Questions for
 Chapter 2 Mathematical Modeling and Numerical Methods Mathematical Modeling Compartment Analysis Difference Equations Euler's Methods Error Estimates The RungeKutta Methods Multistep Methods Error Analysis and Stability Review Questions for
 Chapter 3 Secondorder Equations Second and Higher Order Linear Equations Linear Independence and Wronskians The Fundamental Set of Solutions Equations with Constant Coefficients Complex Roots Repeated Roots. Reduction of Order Nonhomogenous Equations Variation of Parameters Operator Method Review Questions for
 Chapter 4 Laplace Transforms The Laplace Transform Properties of the Laplace Transform Convolution Discontinuous and Impulse Functions The Inverse Laplace Transform Applications to Homogenous Equations Applications to Nonhomogenous Equations Internal Equations Review Questions for
 Chapter 5 Series of Solutions Review of Power Series The Recurrence Power Solutions about an Ordinary Point Euler Equations Series Solutions Near a Regular Singular Point Equations of Hypergeometric Type Bessel's Equations Legendre's Equation Orthogonal Polynomials Review Questions for
 Chapter 6 Applications of Higher Order Differential Equations Boundary Value Problems Some Numerical Methods Dynamics Dynamics of Rotational Motion Harmonic Motion Modeling: Forced Oscillations Modeling of Electric Circuits Some Variational Problems Review Questions for
 Chapter 7 Appendix: Software Packages Answers to Problems Bibliography Index.
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QA372 .D63 2015  Unknown 
 Vasy, András, author.
 Providence, Rhode Island : American Mathematical Society, [2015]
 Description
 Book — x, 281 pages : illustrations ; 27 cm.
 Summary

 * Introduction* Where do PDE come from* First order scalar semilinear equations* First order scalar quasilinear equations* Distributions and weak derivatives* Second order constant coefficient PDE: Types and d'Alembert's solution of the wave equation* Properties of solutions of second order PDE: Propagation, energy estimates and the maximum principle* The Fourier transform: Basic properties, the inversion formula and the heat equation* The Fourier transform: Tempered distributions, the wave equation and Laplace's equation* PDE and boundaries* Duhamel's principle* Separation of variables* Inner product spaces, symmetric operators, orthogonality* Convergence of the Fourier series and the Poisson formula on disks* Bessel functions* The method of stationary phase* Solvability via duality* Variational problems* Bibliography* Index.
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QA377 .V38 2015  Unknown 
 Arrigo, Daniel J. (Daniel Joseph), 1960 author.
 Hoboken, New Jersey : John Wiley & Sons, Inc., [2015]
 Description
 Book — xiii, 176 pages ; 25 cm
 Summary

 Preface i Acknowledgements iii Dedication iv
 1 An Introduction
 1 1.1 What is a symmetry?
 1 1.2 Lie Groups
 4 1.3 Invariance of Differential Equations
 6 1.4 Some Ordinary Differential Equations
 8 1.5 Exercises
 11
 2 Ordinary Differential Equations
 13 2.1 Infinitesimal Transformations
 16 2.2 Lie s Invariance Condition
 19 2.2.1 Exercises
 22 2.3 Standard Integration Techniques
 23 2.3.1 Linear Equations
 24 2.3.2 Bernoulli Equation
 25 2.3.3 Homogeneous Equations
 26 2.3.4 Exact Equations
 27 2.3.5 Riccati Equations
 30 2.3.6 Exercises
 31 2.4 Infinitesimal Operator and Higher Order Equations
 32 2.4.1 The Infinitesimal Operator
 32 2.4.2 The Extended Operator
 32 2.4.3 Extension to Higher Orders
 33 2.4.4 First Order Infinitesimals (revisited)
 33 2.4.5 Second Order Infinitesimals
 34 2.4.6 The Invariance of Second Order Equations
 35 2.4.7 Equations of arbitrary order
 36 2.5 Second Order Equations
 36 2.5.1 Exercises
 46 2.6 Higher Order Equations
 47 2.6.1 Exercises
 51 2.7 ODE Systems
 52 2.7.1 First Order Systems
 52 2.7.2 Higher Order Systems
 56 2.7.3 Exercises
 60
 3 Partial Differential Equations
 62 3.1 First Order Equations
 62 3.1.1 What do we do with the symmetries of PDEs?
 65 3.1.2 Direct Reductions
 68 3.1.3 The Invariant Surface Condition
 70 3.1.4 Exercises
 71 3.2 Second Order PDEs
 71 3.2.1 Heat Equation
 71 3.2.2 Laplace s Equation
 76 3.2.3 Burgers Equation and a Relative
 80 3.2.4 Heat equation with a source
 85 3.2.5 Exercises
 91 3.3 Higher Order PDEs
 93 3.3.1 Exercises
 98 3.4 Systems of PDEs
 99 3.4.1 First order systems
 99 3.4.2 Second order systems
 103 3.4.3 Exercises
 106 3.5 Higher Dimensional PDEs
 107 3.5.1 Exercises
 113
 4 Nonclassical Symmetries and Compatibility
 114 4.1 Nonclassical Symmetries
 114 4.1.1 Invariance of the Invariant Surface Condition
 116 4.1.2 The nonclassical method
 117 4.2 Nonclassical Symmetry Analysis and Compatibility
 125 4.3 Beyond Symmetries Analysis General compatibility
 126 4.3.1 Compatibility with First Order PDEs  Charpit s Method
 127 4.3.2 Compatibility of systems
 134 4.3.3 Compatibility of the nonlinear heat equation
 136 4.4 Exercises
 137 4.5 Concluding Remarks
 138 Solutions
 139 References 145.
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QA387 .A77 2015  Unknown 
 Drábek, Pavel, 1953 author.
 2nd, revised and extended edition.  Berlin ; Boston : De Gruyter, [2014]
 Description
 Book — xiii, 277 pages : illustrations ; 25 cm.
 Summary

This textbook is an elementary introduction to the basic principles of partial differential equations. With many illustrationsitintroduces PDEs on an elementary level, enabling the reader to understand what partial differential equations are, where they come from and how they can be solved. The intention is that the reader understands the basic principles which are valid for particular types of PDEs, and to acquire some classical methods to solve them, thus the authors restrict their considerations to fundamental types of equations and basic methods. Only basic facts from calculus and linear ordinary differential equations of first and second order are needed as a prerequisite. The book is addressed to students who intend to specialize in mathematics as well as to students of physics, engineering, and economics.
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QA374 .D66 2014  Unknown 
 Haase, Markus, 1970 author.
 Providence, Rhode Island : American Mathematical Society, [2014]
 Description
 Book — xviii, 372 pages : illustrations ; 27 cm.
 Summary

 Inner product spaces Normed spaces Distance and approximation Continuity and compactness Banach spaces The contraction principle The Lebesgue spaces Hilbert space fundamentals Approximation theory and Fourier analysis Sobolev spaces and the Poisson problem Operator theory I Operator theory II Spectral theory of compact selfadjoint operators Applications of the spectral theorem Baire's theorem and its consequences Duality and the HahnBanach theorem Historical remarks Background The completion of a metric space Bernstein's proof of Weierstrass' theorem Smooth cutoff functions Some topics from Fourier analysis General orthonormal systems Bibliography Symbol index Subject index Author index.
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QA320 .H23 2014  Unknown 
 Davis, John M.
 New York : W. H. Freeman & Co., c2013.
 Description
 Book — xii, 313 p., [4] p. of plates : ill. (some col.) ; 24 cm
 Summary

 Introduction to PDEs
 Fourier's method: separation of variables
 Fourier series theory
 General orthogonal series expansions
 PDEs in higher dimensions
 PDEs in other coordinate systems
 PDEs on unbounded domains
 Appendix.
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QA374 .D364 2013  Unknown 
 Powers, David L.
 6th ed.  Amsterdam ; Boston : Elsevier/Academic Press, c2010.
 Description
 Book — xi, 506 p. : ill. ; 24 cm.
 Summary

"Boundary Value Problems" is the leading text on boundary value problems and Fourier series for professionals and students in engineering, science, and mathematics who work with partial differential equations. In this updated edition, author David Powers provides a thorough overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Additional techniques used include Laplace transform and numerical methods. Professors and students agree that Powers is a master at creating examples and exercises that skillfully illustrate the techniques used to solve science and engineering problems. New animations and graphics of solutions, additional exercises and chapter review questions on the web. The book includes nearly 900 exercises ranging in difficulty from basic drills to advanced problemsolving exercises. It also includes many exercises that are based on current engineering applications. An Instructor's Manual and Student Solutions Manual are available separately with this book.
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QA379 .P68 2010  Unknown 
 Powers, David L.
 5th ed.  Amsterdam ; Boston : Elsevier Academic Press, c2006.
 Description
 Book — xi, 501 p. : ill. ; 24 cm. + 1 CDROM (4 3/4 in.)
 Summary

 Preface
 Chapter 0
 Differential Equations
 Chapter 1
 Fourier Series and Integrals Chapter 2 The Heat Equation
 Chapter 3
 The Wave Equation
 Chapter 4
 The Potential Equation
 Chapter 5
 Higher Dimensions & Other Coordinates
 Chapter 6
 Laplace Transform
 Chapter 7
 Numerical Methods Bibliography Appendix Answers to Odd Numbered Exercises Index.
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QA379 .P68 2006  Unknown 
 Pinchover, Yehuda, 1953
 New York : Cambridge University Press, 2005.
 Description
 Book — xii, 371 p. : ill. ; 26 cm.
 Summary

 1. Introduction
 2. Firstorder equations
 3. Secondorder linear equations
 4. The 1D wave equation
 5. Separation of variables
 6. SturmLiouville problem
 7. Elliptic equations
 8. Green's function and integral representation
 9. Equations in high dimensions
 10. Variational methods
 11. Numerical methods
 12. Solutions of oddnumbered problems.
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QA374 .P54 2005  Unknown 
QA374 .P54 2005  Unknown 