1  20
Next
 First edition  New Jersey : World Scientific Publishing Co. Pte. Ltd. : Higher Education Press, [2023]
 Description
 Book — 1 online resource
 Partielle Differenzialgleichungen. English
 Arendt, Wolfgang, 1950 author.
 Cham, Switzerland : Springer, [2023]
 Description
 Book — xxiv, 452 pages : illustrations ; 25 cm
 Summary

"This textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two complementary approaches, the authors create an ideal foundation for further study. Motivating examples from the physical sciences, engineering, and economics complete this integrated approach. A showcase of models begins the book, demonstrating how PDEs arise in practical problems that involve heat, vibration, fluid flow, and financial markets. Several important characterizing properties are used to classify mathematical similarities, then elementary methods are used to solve examples of hyperbolic, elliptic, and parabolic equations. From here, an accessible introduction to Hilbert spaces and the spectral theorem lay the foundation for advanced methods. Sobolev spaces are presented first in dimension one, before being extended to arbitrary dimension for the study of elliptic equations. An extensive chapter on numerical methods focuses on finite difference and finite element methods. Computeraided calculation with Maple™ completes the book. Throughout, three fundamental examples are studied with different tools: Poisson's equation, the heat equation, and the wave equation on Euclidean domains. The BlackScholes equation from mathematical finance is one of several opportunities for extension. Partial Differential Equations offers an innovative introduction for students new to the area. Analytical and numerical tools combine with modeling to form a versatile toolbox for further study in pure or applied mathematics. Illuminating illustrations and engaging exercises accompany the text throughout. Courses in real analysis and linear algebra at the upperundergraduate level are assumed."Provided by publisher
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA374 .A78413 2023  Unknown 
 Cham, Switzerland : Springer, 2023.
 Description
 Book — 1 online resource
 Summary

 Existence and uniqueness of solution for semi linear conservation laws with velocity field in L
 Structural stability of p(x)Laplace problems with Robin type boundary condition
 Weak solutions of antiperiodic discrete nonlinear problems
 Boundary feedback controller over a bluff body for prescribed drag and lift coefficients
 Discrete potential boundary value problems of Kirchhoff type
 From Calculus of Variation to Exterior Differential Calculus: A Presentation and Some New Results
 Existence of local and maximal mild solutions for some nonautonomous functional differential equation with finite delay
 Existence, regularity and stability in the norm for some neutral partial functional differential equations in fading memory spaces
 Pseudo almost periodic solutions of class in the norm under the light of measure theory
 Global stability for a delay SIR epidemic model with general incidence function, observers design
 Threshold parameters of stochastic SIR and SIRS epidemic models with delay and nonlinear incidence
 Weak solutions for nonlinear BoltzmannPoisson system modeling electron electron interactions.
5. Analytic partial differential equations [2022]
 Treves, Francois, 1930 author.
 Cham : Springer, [2022]
 Description
 Book — xiii, 1228 pages ; 24 cm
 Summary

 Distributions and Analyticity in Euclidean Space
 Functions and Differential Operators in Euclidean Space
 Basic Notation and Terminology
 Smooth, Realanalytic, Holomorphic Functions
 Differential Operators with Smooth Coefficients
 Distributions in Euclidean Space
 Basics on Distributions in Euclidean Space
 Sobolev Spaces
 Distribution Kernels
 Fundamental Solutions, Parametrix, Hypoelliptic PDOs
 Analytic Tools in Distribution Theory
 Analytic Parametrices, Analytic Hypoellipticity
 Ehrenpreisʼ Cutoffs and Analytic Regularity of Distributions
 Distribution Boundary Values of Holomorphic Functions
 The FBI Transform of Distributions : An Introduction
 The Analytic WaveFront Set of a Distribution
 Analyticity of Solutions of Linear PDEs : Basic Results
 Analyticity of Solutions of Elliptic Linear PDEs
 Degenerate Elliptic Equations : Influence of Lower Order Terms
 A Generalization of the Harmonic Oscillator
 Appendix : Hermite's Functions and the Schwartz Space
 The CauchyKovalevskaya Theorem
 A Nonlinear Ovsyannikov Theorem
 Application : the Nonlinear CauchyKovalevskaya Theorem
 Applications to Linear PDE
 Application to Integrodifferential Cauchy Problems
 Hyperfunctions in Euclidean Space
 Analytic Functionals in Euclidean Space
 Analytic Functionals in Complex Domains
 Analytic Functionals in Cn
 Analytic Functionals in Rn as Cohomology Classes
 Hyperfunctions in Euclidean Space
 The Sheaf of Hyperfunctions in Euclidean Space
 Boundary values of holomorphic functions in wedges
 The FBI Transform of Analytic Functionals
 Analytic Wavefront Set of a Hyperfunction
 Edge of the Wedge
 Microfunctions in Euclidean space
 Hyperdifferential Operators
 Action on Holomorphic Functions and on Hyperfunctions
 Local Representation of Hyperfunctions
 Elliptic Hyperdifferential Operators
 Solvability of Constant Coefficients Hyperdifferential Equations
 Geometric Background
 Elements of Differential Geometry
 Regular Manifolds
 Fibre Bundles, Vector Bundles
 Tangent and Cotangent Bundles of a Manifold
 Differential Complexes and Grassman Algebras
 A Primer on Sheaf Cohomology
 Basics on Sheaf Cohomology
 Fine Sheaves and Fine Resolutions
 Relative Sheaf Cohomology
 Edge of the Wedge in (Co)homological Terms
 Distributions and Hyperfunctions on a Manifold
 Distributions and Currents on a Manifold
 Plurisubharmonic functions and pseudoconvex domains
 Hyperfunctions and Microfunctions in an Analytic Manifold
 Lie Algebras of Vector Fields
 The Lie Algebra of Smooth Vector Fields
 Integral Manifolds : Frobeniusʼ Theorem
 Local Flow of a Regular Vector Field
 Foliations Defined By Analytic Vector Fields
 Systems of Vector Fields Generating Special Lie Algebras
 Elements of Symplectic Geometry
 Elements of Symplectic Algebra
 The Metaplectic Group
 Symplectic Manifolds
 Involutive Systems of Functions of Principal Type
 Real and Imaginary Symplectic Structures in C2n
 Real and Imaginary Symplectic Structures on Complex Manifolds
 Stratification of Analytic Varieties and Division of Distributions by Analytic Functions
 Analytic Stratifications
 Analytic Stratifications and Stratifiable Sets
 Analytic Subvarieties
 The Weierstrass Theorems
 Local Partitions of a Complex Hypersurface
 Local Stratifications of a RealAnalytic Variety
 Semianalytic Sets
 Division of Distributions by Analytic Functions
 The Lojasiewicz Inequality
 Division of Distributions by Analytic Functions
 Desingularization and Applications
 Appendix
 Analytic Pseudodifferential Operators and Fourier Integral Operators
 Elementary Pseudodifferential Calculus in the ... Class
 Standard Pseudodifferential Operators
 Symbolic Calculus
 Classical symbols and classical pseudodifferential operators
 The Weyl Calculus in Euclidean Space
 Analytic Pseudodifferential Calculus
 Analytic Pseudodifferential Operators
 Symbolic Calculus
 Analytic Microlocalization In Distribution Theory
 Action on Singularity Hyperfunctions
 Microdifferential Operators
 Fourier Integral Operators
 Fourier Distribution Kernels in Euclidean Space
 The Lagrangian Manifold Associated to a Phasefunction
 Fourier Integral Operators : Basics
 Reduction of the Fiber Variables
 Composition and Continuity of Fourier Integral Operators
 Globally Defined Fourier Integral Operators
 Principles of Analytic Fourier Integral Operators
 Appendix : Stationary Phase Formal Expansion
 Complex Microlocal Analysis
 Classical Analytic Formalism
 Formal Analytic Series
 Classical Analytic Differential Operators of Infinite Order
 The Complex Stationary Phase Formula
 Symbolic Calculus and the KdV Hierarchy
 Germ Fourier Integral Operators in Complex Space
 Analytic Symbols
 Contours and Function Spaces
 Sjöstrand Pairs
 Germ Fourierlike Transforms
 Sjöstrand Triads and Germ Fourier Integral Operators
 Germ Pseudodifferential Operators in Complex Space
 Germ Pseudodifferential Operators
 Classical Germ Pseudodifferential Operators
 Action on distributions
 Action on Hyperfunctions and Microfunctions
 Germ FBI Transforms
 Germ FBI Transforms
 Germ FBI Transforms of Distributions
 The Equivalence Theorem for Distributions
 Analytic Pseudodifferential Operators of Principal Type
 Analytic PDEs of Principal Type : Local Solvability
 Pseudodifferential Operators of Principal Type
 Local Solvability of Analytic PDEs of Principal Type
 Analytic PDEs of Principal Type : Regularity of the Solutions
 A New Concept : Subellipticity
 Statement of the Main Theorem
 Hypoellipticity Implies (Q)
 Property (Q) Implies Subellipticity
 Analytic Hypoellipticity Implies (Q)
 Property (Q) Implies Analytic Hypoellipticity
 The ... Situation
 Propagation of Analytic Singularities
 Appendix : Properties of Real Polynomials in a Single Variable
 Appendix : Analytic Estimates of Exponential Amplitudes
 Solvability of Constant Vector Fields of Type (1,0)
 CConvexity and Global Solvability
 Local Solvability at the Boundary : First Steps
 Local Solvability at the Boundary : Final Characterization
 The Differential Complex : Generalities
 Appendix : Minima of Families of Plurisubharmonic Functions
 Pseudodifferential Solvability and Property (...)
 Solvability : the Difference between Differential and Pseudodifferential
 Property (...)
 Microlocal Solvability in Distributions
 Pseudodifferential Complexes in Tube Structures
 Pseudodifferential Complexes of Principal Type
 Tube Pseudodifferential Complexes
 Phasefunction and Amplitude
 Approximate Homotopy Formulas
 Homotopy Formulas
 Poincaré Lemmas
 References
 Notation Index
 Index
(source: Nielsen Book Data)
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA374 .T684 2022  Unknown 
 Partielle Differenzialgleichungen. English
 Arendt, Wolfgang, 1950 author.
 Cham : Springer, 2022.
 Description
 Book — 1 online resource (1 volume) : illustrations (black and white)
 Summary

 1 Modeling, or where do differential equations come from. 2 Classification and characteristics. 3 Elementary methods. 4 Hilbert spaces. 5 Sobolev spaces and boundary value problems in dimension one. 6 Hilbert space methods for elliptic equations. 7 Neumann and Robin boundary conditions. 8 Spectral decomposition and evolution equations. 9 Numerical methods. 10 Maple (R), or why computers can sometimes help. Appendix.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Salsa, S., author.
 Fourth edition.  Cham : Springer, [2022]
 Description
 Book — 1 online resource (xviii, 677 pages) : illustrations.
 Summary

 1 Introduction. 2 Diffusion. 3 The Laplace Equation. 4 Scalar Conservation Laws and First Order Equations. 5 Waves and Vibration. 6 Elements of Functional Analysis. 7 Distributions and Sobolev Spaces. 8 Variational Formulation of Elliptic Problems. 9 Weak Formulation of Evolution Problems. 10 More Advanced Topics. 11 Systems of Conservation Laws. Appendix A: Measures and Integrals. Appendix B: Identities and Formulas.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Singapore : Springer, 2022.
 Description
 Book — 1 online resource : illustrations (black and white, and color).
 Summary

 Part I: Longtime behavior of NLStype equations. 1 Scipio Cuccagna, Note on small data soliton selection for nonlinear Schroedinger equations with potential. 2 Jacopo Bellazzini and Luigi Forcella, Dynamics of solutions to the GrossPitaevskii equation describing dipolar BoseEinstein condensates. Part II: Probabilistic and nonstandard methods in the study of NLS equations. 3 Renato Luca, Almost sure pointwise convergence of the cubic nonlinear Schroedinger equation on T^2. 4 Nevena Dugandzija and Ivana Vojnovic, Nonlinear Schroedinger equation with singularities. Part III: Dispersive properties. 5 Vladimir Georgiev, Alessandro Michelangeli, Raffaele Scandone, Schroedinger flow's dispersive estimates in a regime of rescaled potentials. 6 Federico Cacciafesta, Eric Sere, Junyong Zhang, Dispersive estimates for the DiracCoulomb equation. 7 Matteo Gallone, Alessandro Michelangeli, Eugenio Pozzoli, Heat equation with inversesquare potential of bridging type across two halflines. Part IV: Wave and Kdvtype equations. 8 Felice Iandoli, On the Cauchy problem for quasilinear Hamiltonian KdVtype equations. 9 Vladimir Georgiev and Sandra Lucente, Linear and nonlinear interaction for wave equations with time variable coefficients. 10 Matteo Gallone and Antonio Ponno, Hamiltonian field theory close to the wave equation: from FermiPastaUlam to water waves.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
9. Partial differential equations in anisotropic MusielakOrlicz spaces [electronic resource] [2021]
 Chlebicka, Iwona, author.
 Cham, Switzerland : Springer, 2021.
 Description
 Book — 1 online resource Digital: text file.PDF.
 Summary

 Part I Overture:
 1. Introduction.
 2. NFunctions.
 3. MusielakOrlicz Spaces. Part II PDEs:
 4. Weak Solutions.
 5. Renormalized Solutions.
 6. Homogenization of Elliptic Boundary Value Problems.
 7. NonNewtonian Fluids. Part III Auxiliaries:
 8. Basics.
 9. Functional Inequalities. References. List of Symbols. Index. .
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Beijing, China : Higher Education Press Limited Company ; Singapore ; Hackensack, NJ : World Scientific Publishing Co. Pte. Ltd., [2019]
 Description
 Book — 1 online resource.
 Summary

 Intro; Contents; Preface; Control of Partial Differential Equations: Theoretical Aspects;
 1. Introduction;
 2. Introduction to Controllability; 2
 .1. Approximate Controllability; 2
 .2. Null Controllability; 2
 .3. Exact Controllability; 2
 .4. Exact Controllability to Trajectories;
 3. Simple Examples; 3
 .1. Transport Equation in 1D; 3
 .2. Wave Equation in 1D;
 4. Exact Controllability for the Wave Equation; 4
 .1. Exact Controllability for Boundary Control; 4
 .2. Case of Distributed Control;
 5. Controllability of Schrödinger Equation; 5
 .1. Schrödinger Equation; 5
 .2. Controllability Results
 6. Controllability of Linear Diffusion Convection Equations6
 .1. Statement of the Problem and Result; 6
 .2. An Auxiliary Optimal Control Problem; 6
 .3. Null Controllability Modulo Observability Inequality; 6
 .4. Global Carleman Inequality; 6.4
 .1. Weight Functions; 6.4
 .2. Proof of a Global Carleman Inequality; 6.4
 .3. Case of a General DiffusionConvection Operator; 6
 .5. Observability Inequality; 6
 .6. Another Strategy; Bibliography; Control of Partial Differential Equations: Numerical Aspects;
 1. Introduction;
 2. Controllability of FiniteDimensional Linear Systems; 2
 .1. Introduction
 2
 .2. FiniteDimensional Case, First Comments2
 .3. Examples; 2
 .4. Duality Techniques; 2
 .5. Observability Property; 2
 .6. Comments on the Control Map; 2
 .7. Kalman Rank Condition; 2
 .8. A Data Assimilation Problem;
 3. The Wave Equation; 3
 .1. The Continuous Setting; 3.1
 .1. Functional Setting; 3.1
 .2. Control and Observability Results; 3
 .2. The Discrete Wave Equation: The Naive Approach; 3.2
 .1. Setting; 3.2
 .2. Existence of the Discrete NullControls; 3.2
 .3. Numerical Experiments; 3.2
 .4. Lack of Uniform Observability; 3.2
 .5. Blow up of Discrete Controls; 3
 .3. Remedies
 3.3
 .1. A Fourier Filtering Technique3.3
 .2. Designing a Mesh Guaranteeing Uniform Observability Properties; 3
 .4. Further Comments; 3.4
 .1. Higher Dimensions; 3.4
 .2. The Effect of TimeDiscretization; 3.4
 .3. Rate of Convergence of the Discrete Controls;
 4. The Heat Equation; 4
 .1. The Continuous Case; 4
 .2. Difficulties of Computing Numerical Controls for the Heat Equation; 4
 .3. A Remedy; 4
 .4. Further Comments; Bibliography; Complex Geometrical Optics and Calderón's Problem;
 0. Introduction;
 1. The DirichlettoNeumann Map;
 2. Boundary Determination and Layer Stripping
 3. Complex Geometrical Optics Solutions4. Applications of Complex Geometrical Optics Solutions; 4.1. Uniqueness for Calderón's Problem; 4.2. Determining Cavities; 5. Complex Geometrical Optics Solutions for First Order Perturbations of the Laplacian; 5.1. Intertwining Property (Part 1); 5.2. Intertwining Property (Part 2); 5.3. Intertwining Property (Part 3)
 Some Reductions; 5.4. Construction of Pseudoanalytic Matrices; Bibliography; A MiniCourse on Stochastic Control; 1. Introduction; 2. Some Preliminary Results from Probability Theory and Stochastic Analysis
(source: Nielsen Book Data)
11. Partial differential equations arising from physics and geometry : a volume in memory of Abbas Bahri [2019]
 Cambridge : Cambridge University Press, 2019.
 Description
 Book — xvi, 453 pages : illustrations ; 23 cm.
 Summary

 Preface Mohamed Ben Ayed, Mohamed Ali Jendoubi, Yomna Rebai, Hassna Riahi and Hatem Zaag
 Abbas Bahri: a dedicated life Mohamed Ben Ayed
 1. Blowup rate for a semilinear wave equation with exponential nonlinearity in one space dimension Asma Azaiez, Nader Masmoudi and Hatem Zaag
 2. On the role of anisotropy in the weak stability of the NavierStokes system Hajer Bahouri, JeanYves Chemin and Isabelle Gallagher
 3. The motion law of fronts for scalar reactiondiffusion equations with multiple wells: the degenerate case Fabrice Bethuel and Didier Smets
 4. Finitetime blowup for some nonlinear complex GinzburgLandau equations Thierry Cazenave and Seifeddine Snoussi
 5. Asymptotic analysis for the LaneEmden problem in dimension two Francesca de Marchis, Isabella Ianni and Filomena Pacella
 6. A data assimilation algorithm: the paradigm of the 3D Leray model of turbulence Aseel Farhat, Evelyn Lunasin and Edriss S. Titi
 7. Critical points at infinity methods in CR geometry Najoua Gamara
 8. Some simple problems for the next generations Alain Haraux
 9. Clustering phenomena for linear perturbation of the Yamabe equation Angela Pistoia and Giusi Vaira
 10. Towards better mathematical models for physics Luc Tartar.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA377 .P378 2019  Unknown 
12. Topics in partial differential equations [2019]
 Gupta, Parmanand, author.
 First edition.  Bengaluru : Firewall Media, an imprint of Laxmi Publications Pvt. Ltd., 2019.
 Description
 Book — 1 online resource
 Kavallaris, Nikos I.
 Cham : Springer, [2018]
 Description
 Book — 1 online resource. Digital: text file; PDF.
 Summary

 Dedication. Preface. Acknowledgements. Part I Applications in Engineering. Microelectromechanicalsystems(MEMS). Ohmic Heating Phenomena. Linear Friction Welding. Resistance Spot Welding. Part II Applications in Biology. GiererMeinhardt System. A Nonlocal Model Illustrating Replicator Dynamics. A Nonlocal Model Arising in Chemotaxis. A Nonlocal ReactionDiffusion System Illustrating Cell Dynamics. Appendices. Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
14. Analytical methods for Kolmogorov equations [2017]
 Lorenzi, Luca, author.
 Second edition  Boca Raton, Florida : CRC Press, [2017]
 Description
 Book — 1 online resource
 Summary

 1. Autonomous Kolmogorov equations
 2. Nonautonomous Kolmogorov equations
 3. Appendices
 Schönlieb, CarolaBibiane, author.
 Cambridge : Cambridge University Press, 2015.
 Description
 Book — 1 online resource : digital, PDF file(s).
 Summary

 1. Introduction
 2. Overview of mathematical inpainting methods
 3. The principle of good continuation
 4. Secondorder diffusion equations for inpainting
 5. Higherorder PDE inpainting
 6. Transport inpainting
 7. The MumfordShah image for inpainting
 8. Inpainting mechanisms of transport and diffusion
 9. Applications.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Shearer, Michael, author.
 Princeton : Princeton University Press, [2015]
 Description
 Book — x, 274 pages : illustrations ; 26 cm
 Summary

This textbook provides beginning graduate students and advanced undergraduates with an accessible introduction to the rich subject of partial differential equations (PDEs). It presents a rigorous and clear explanation of the more elementary theoretical aspects of PDEs, while also drawing connections to deeper analysis and applications. The book serves as a needed bridge between basic undergraduate texts and more advanced books that require a significant background in functional analysis. Topics include first order equations and the method of characteristics, second order linear equations, wave and heat equations, Laplace and Poisson equations, and separation of variables. The book also covers fundamental solutions, Green's functions and distributions, beginning functional analysis applied to elliptic PDEs, traveling wave solutions of selected parabolic PDEs, and scalar conservation laws and systems of hyperbolic PDEs. Provides an accessible yet rigorous introduction to partial differential equations Draws connections to advanced topics in analysis Covers applications to continuum mechanics An electronic solutions manual is available only to professors An online illustration package is available to professors.
(source: Nielsen Book Data)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA374 .S45 2015  Unknown 
 Rădulescu, Vicenţiu D., 1958 author.
 Boca Raton, FL : CRC Press, [2015]
 Description
 Book — xxi, 301 pages : illustrations ; 24 cm.
 Summary

 Isotropic and Anisotropic Function Spaces Lebesgue and Sobolev Spaces with Variable Exponent History of function spaces with variable exponent Lebesgue spaces with variable exponent Sobolev spaces with variable exponent Dirichlet energies and EulerLagrange equations Lavrentiev phenomenon Anisotropic function spaces Orlicz spaces
 Variational Analysis of Problems with Variable Exponents Nonlinear Degenerate Problems in NonNewtonian Fluids Physical motivation A boundary value problem with nonhomogeneous differential operator Nonlinear eigenvalue problems with two variable exponents A sublinear perturbation of the eigenvalue problem associated to the Laplace operator Variable exponents versus Morse theory and local linking The CaffarelliKohnNirenberg inequality with variable exponent
 Spectral Theory for Differential Operators with Variable Exponent Continuous spectrum for differential operators with two variable exponents A nonlinear eigenvalue problem with three variable exponents and lack of compactness Concentration phenomena: the case of several variable exponents and indefinite potential Anisotropic problems with lack of compactness and nonlinear boundary condition
 Nonlinear Problems in OrliczSobolev Spaces Existence and multiplicity of solutions A continuous spectrum for nonhomogeneous operators Nonlinear eigenvalue problems with indefinite potential Multiple solutions in OrliczSobolev spaces Neumann problems in OrliczSobolev spaces
 Anisotropic Problems: Continuous and Discrete Anisotropic Problems Eigenvalue problems for anisotropic elliptic equations Combined effects in anisotropic elliptic equations Anisotropic problems with noflux boundary condition Bifurcation for a singular problem modelling the equilibrium of anisotropic continuous media
 Difference Equations with Variable Exponent Eigenvalue problems associated to anisotropic difference operators Homoclinic solutions of difference equations with variable exponents Lowenergy solutions for discrete anisotropic equations
 Appendix A: Ekeland Variational Principle Appendix B: Mountain Pass Theorem Bibliography Index A Glossary is included at the end of each chapter.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA377 .R33 2015  Unknown 
18. Introduction to partial differential equations for scientists and engineers using Mathematica [2014]
 Adzievski, Kuzman, author.
 Boca Raton, FL : CRC Press, [2014]
 Description
 Book — xiii, 634 pages : illustrations ; 25 cm
 Summary

 Fourier Series The Fourier Series of a Periodic Function Convergence of Fourier Series Integration and Differentiation of Fourier Series Fourier Sine and Fourier Cosine Series Mathematica Projects Integral Transforms The Fourier Transform and Elementary Properties Inversion Formula of the Fourier Transform Convolution Property of the Fourier Transform The Laplace Transform and Elementary Properties Differentiation and Integration of the Laplace Transform Heaviside and Dirac Delta Functions Convolution Property of the Laplace Transform Solution of Differential Equations by the Integral Transforms The SturmLiouville Problems Regular SturmLiouville Problem Eigenvalues and Eigenfunctions Eigenfunction Expansion Singular SturmLiouville Problem: Legendre's Equation Singular SturmLiouville Problem: Bessel's Equation Partial Differential Equations Basic Concepts and Definitions Formulation of Initial and Boundary Problems Classification of Partial Differential Equations Some Important Classical Linear Partial Differential Equations The Principle of Superposition First Order Partial Differential Equations Linear Equations with Constant Coefficients Linear Equations with Variable Coefficients First Order NonLinear Equations Cauchy's Method of Characteristics Mathematica Projects Hyperbolic Partial Differential Equations The Vibrating String and Derivation of the Wave Equation Separation of Variables for the Homogeneous Wave Equation D'Alambert's Solution of the Wave Equation Inhomogeneous Wave Equations Solution of the Wave Equation by Integral Transforms Two Dimensional Wave Equation: Vibrating Membrane The Wave Equation in Polar and Spherical Coordinates Numerical Solutions of the Wave Equation Mathematica Projects Parabolic Partial Differential Equations Heat Flow and Derivation of the Heat Equation Separation of Variables for the One Dimensional Heat Equation Inhomogeneous Heat Equations Solution of the Heat Equation by Integral Transforms Two Dimensional Heat Equation The Heat Equation in Polar and Spherical Coordinates Numerical Solutions of the Heat Equation Mathematica Projects Elliptic Partial Differential Equations The Laplace and Poisson Equations Separation of Variables for the Laplace Equation The Laplace Equation in Polar and Spherical Coordinates Poisson Integral Formula Numerical Solutions of the Laplace Equation Mathematica Projects Appendix A. Special Functions Appendix B. Table of the Fourier Transform of Some Functions Appendix C. Table of the Laplace Transform of Some Functions.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA377 .A47 2014  Unknown 
19. Partial differential equations [2013]
 Jost, Jürgen, 1956
 Third edition.  New York : Springer, c2013.
 Description
 Book — xiii, 410 pages ; 24 cm.
 Summary

 Preface. Introduction: What are Partial Differential Equations?. 1 The Laplace equation as the Prototype of an Elliptic Partial Differential Equation of Second Order. 2 The Maximum Principle. 3 Existence Techniques I: Methods Based on the Maximum Principle. 4 Existence Techniques II: Parabolic Methods. The Heat Equation. 5 ReactionDiffusion Equations and Systems. 6 Hyperbolic Equations. 7 The Heat Equation, Semigroups, and Brownian Motion. 8 Relationships between Different Partial Differential Equations. 9 The Dirichlet Principle. Variational Methods for the Solutions of PDEs (Existence Techniques III). 10 Sobolev Spaces and L^2 Regularity theory. 11 Strong solutions. 12 The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV). 13The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash. Appendix: Banach and Hilbert spaces. The L^pSpaces. References. Index of Notation. Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA377 .J66 2013  Unknown 
 Basel : Birkhäuser, c2011
 Description
 Book — vi, 367 p. : ill. ; 24 cm.
 Summary

 Toeplitz operators and asymptotic equivariant index / L. Boutet de Monvel
 Boundary value problems of analytic and harmonic functions in a domain with piecewise smooth boundary in the frame of variable exponent Lebesgue spaces / V. Kokilashvili
 Edgedegenerate operators at conical exits to infinity / B.W. Schulze
 On a method for solving boundary problems for a thirdorder equation with multiple characteristics / Y.P. Apakov
 On stability and trace regularity of solutions to ReissnerMindlinTimoshenko equations / G. Avalos and D. Toundykov
 Linearization of a coupled system of nonlinear elasticity and viscous fluid / L. Bociu and J.P. Zolésio
 Some results of the identification of memory kernels / F. Colombo and D. Guidetti
 A kuniform maximum principle when 0 is an eigenvalue / G. Fragnelli and D. Mugnai
 Steadystate solutions for a general brusselator system / M. Ghergu
 Ordinary differential equations with distributions as coefficients in the sense of the theory of new generalized functions / U.U. Hrusheuski
 A boundary condition and spectral problems for the Newton potential / T.Sh. Kalmenov and D. Suragan
 An extremum principle for a class of hyperbolic type equations and for operators connected with them / I.U. Khaydarov, M.S. Salakhitdinov and A.K. Urinov
 Numerical investigations of tangled flows in a channel of constant and variable section at presence of recirculation zone / S. Khodjiev
 The optimal interior regularity for the critical case of a clamped thermoelastic system with point control revisited / C. Lebiedzik and R. Triggiani
 Multidimensional controllability problems with memory / P. Loreti and D. Sforza
 The Schrödinger flow in a compact manifold: highfrequency dynamics and dispersion / F. Macià
 Optimality of the asymptotic behavior of the energy for wave models / M. Reissig
 On singular systems of parabolic functional equations / L. Simon
 Boundaryvalue problems for a class of thirdorder composite type equations / O.S. Zikirov
 Shapemorphic metric, geodesic stability / J.P. Zolésio.
(source: Nielsen Book Data)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA374 .M76 2011  Unknown 
Articles+
Journal articles, ebooks, & other eresources
Guides
Course and topicbased guides to collections, tools, and services.