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(In-)stability of differential inclusions : notions, equivalences, and Lyapunov-like characterizations / / Philipp Braun, Lars Grüne, Christopher M. Kellett
(In-)stability of differential inclusions : notions, equivalences, and Lyapunov-like characterizations / / Philipp Braun, Lars Grüne, Christopher M. Kellett
Autore Braun Philipp
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (123 pages)
Disciplina 003.71
Collana SpringerBriefs in Mathematics
Soggetto topico Estabilitat
Equacions diferencials
Lyapunov stability
Differential equations
Soggetto genere / forma Llibres electrònics
ISBN 3-030-76317-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910492152103321
Braun Philipp  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
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(In-)stability of differential inclusions : notions, equivalences, and Lyapunov-like characterizations / / Philipp Braun, Lars Grüne, Christopher M. Kellett
(In-)stability of differential inclusions : notions, equivalences, and Lyapunov-like characterizations / / Philipp Braun, Lars Grüne, Christopher M. Kellett
Autore Braun Philipp
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (123 pages)
Disciplina 003.71
Collana SpringerBriefs in Mathematics
Soggetto topico Estabilitat
Equacions diferencials
Lyapunov stability
Differential equations
Soggetto genere / forma Llibres electrònics
ISBN 3-030-76317-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISA-996466391503316
Braun Philipp  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
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500 Examples and Problems of Applied Differential Equations [[electronic resource] /] / by Ravi P. Agarwal, Simona Hodis, Donal O’Regan
500 Examples and Problems of Applied Differential Equations [[electronic resource] /] / by Ravi P. Agarwal, Simona Hodis, Donal O’Regan
Autore Agarwal Ravi P
Edizione [1st ed. 2019.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019
Descrizione fisica 1 online resource (IX, 388 p. 84 illus., 3 illus. in color.)
Disciplina 515.35
Collana Problem Books in Mathematics
Soggetto topico Differential equations
Difference equations
Functional equations
Partial differential equations
Sequences (Mathematics)
Numerical analysis
Ordinary Differential Equations
Difference and Functional Equations
Partial Differential Equations
Sequences, Series, Summability
Numerical Analysis
ISBN 3-030-26384-3
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1. First Order Linear Differential Equations -- 2. Some First Order Nonlinear Differential Equations -- 3. Second and Higher Order Differential Equations -- 4. Power Series Solutions -- 5. Systems of First Order Linear Differential Equations -- 6. Runge–Kutta Method -- 7. Stability Theory -- 8. Linear Boundary Value Problems -- 9. Nonlinear Boundary Value Problems -- Index.
Record Nr. UNINA-9910349335203321
Agarwal Ravi P  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
6th International Congress on Industrial and Applied Mathematics Zürich, Switzerland, 16-20 July 2007 [[electronic resource] ] : Invited Lectures / / Rolf Jeltsch, Gerhard Wanner
6th International Congress on Industrial and Applied Mathematics Zürich, Switzerland, 16-20 July 2007 [[electronic resource] ] : Invited Lectures / / Rolf Jeltsch, Gerhard Wanner
Pubbl/distr/stampa Zuerich, Switzerland, : European Mathematical Society Publishing House, 2009
Descrizione fisica 1 online resource (530 pages)
Soggetto topico Numerical analysis
Differential equations
Mathematics for scientists & engineers
Theoretical methods
Partial differential equations
Computer science
Biology and other natural sciences
ISBN 3-03719-556-8
Classificazione 65-xx35-xx68-xx92-xx
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto A level set method for the numerical simulation of damage evolution / Grégoire Allaire, François Jouve, Nicolas Van Goethem -- Dissipation inequalities in systems theory: An introduction and recent results / Christian Ebenbauer, Tobias Raff, Frank Allgöwer -- Some nonlinear problems involving non-local diffusions / Luis A. Caffarelli -- High-order methods for PDEs: Recent advances and new perspectives / Claudio Canuto -- Radar imaging / Margaret Cheney -- Adaptive approximations by greedy algorithms / Albert Cohen -- Multiscale analysis of density functional theory / Weinan E -- Frictional contact in solid mechanics / Michel Fortin, Carl Robitaille, André Fortin, Ali Rezgui -- Numerical methods for fully nonlinear elliptic equations / Roland Glowinski -- Asymptotic solutions of Hamilton-Jacobi equations for large time and related topics / Kenji Nishihara -- Hyperbolic conservation laws. Past and future / Barbara Lee Keyfitz -- Second-order PDE's and deterministic games / Robert V. Kohn, Sylvia Serfaty -- Controllability and observability: From ODEs to quasilinear hyperbolic systems / Tatsien Li -- Order-value optimization and new applications / José Mario Martínez -- Conformation dynamics / Christof Schütte, Frank Noe, Eike Meerbach, Philipp Metzner, Carsten Hartmann -- MCMC methods for sampling function space / Alexandros Beskos, Andrew M. Stuart -- Chaotic itinerancy reality in the dynamic brain - episodic memory formation / Ichiro Tsuda -- Visibility and invisibility / Gunther Uhlmann -- Optimal algorithms for discretized partial differential equations / Jinchao Xu -- Leonhard Euler: His life, the man, and his works / Walter Gautschi.
Altri titoli varianti 6th International Congress on Industrial and Applied Mathematics Zürich, Switzerland, 16-20 July 2007
Record Nr. UNINA-9910151933403321
Zuerich, Switzerland, : European Mathematical Society Publishing House, 2009
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Abstract differential equations / S. D. Zaidman
Abstract differential equations / S. D. Zaidman
Autore Zaidman, Samuel
Pubbl/distr/stampa San Francisco : Pitman Advanced Publ. Program, 1979
Descrizione fisica 130 p. ; 25 cm.
Disciplina 515.35
Collana Pitman research notes in mathematics series, ISSN 02693674 ; 36
Soggetto topico Cauchy problem
Differential equations
ISBN 0822484277
Classificazione AMS 34G
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISALENTO-991000643189707536
Zaidman, Samuel  
San Francisco : Pitman Advanced Publ. Program, 1979
Materiale a stampa
Lo trovi qui: Univ. del Salento
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Admissibility and Hyperbolicity [[electronic resource] /] / by Luís Barreira, Davor Dragičević, Claudia Valls
Admissibility and Hyperbolicity [[electronic resource] /] / by Luís Barreira, Davor Dragičević, Claudia Valls
Autore Barreira Luís
Edizione [1st ed. 2018.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018
Descrizione fisica 1 online resource (IX, 145 p.)
Disciplina 515.39
515.48
Collana SpringerBriefs in Mathematics
Soggetto topico Dynamics
Ergodic theory
Differential equations
Difference equations
Functional equations
Dynamical Systems and Ergodic Theory
Ordinary Differential Equations
Difference and Functional Equations
ISBN 3-319-90110-9
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1. Introduction -- 2. Exponential Contractions -- 3. Exponential Dichotomies: Discrete Time -- 4. Exponential Dichotomies: Continuous Time -- 5. Admissibility: Further Developments -- 6. Applications of Admissibility -- References -- Index.
Record Nr. UNINA-9910300098603321
Barreira Luís  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018
Materiale a stampa
Lo trovi qui: Univ. Federico II
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AdS/CFT Correspondence: Einstein Metrics and Their Conformal Boundaries [[electronic resource] /] / Olivier Biquard
AdS/CFT Correspondence: Einstein Metrics and Their Conformal Boundaries [[electronic resource] /] / Olivier Biquard
Pubbl/distr/stampa Zuerich, Switzerland, : European Mathematical Society Publishing House, 2005
Descrizione fisica 1 online resource (259 pages)
Collana IRMA Lectures in Mathematics and Theoretical Physics (IRMA)
Soggetto topico Differential & Riemannian geometry
Differential equations
Relativistic quantum mechanics & quantum field theory
Differential geometry
Partial differential equations
Quantum theory
Relativity and gravitational theory
ISBN 3-03719-513-4
Classificazione 53-xx35-xx81-xx83-xx
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Geometric aspects of the AdS/CFT correspondence / Michael T. Anderson -- Some aspects of the AdS/CFT correspondence / Jan de Boer, Liat Maoz, Asad Naqvi -- The ambient obstruction tensor and Q-curvature / C. Robin Graham, Kengo Hirachi -- AdS/CFT correspondence and geometry / Ioannis Papadimitriou, Kostas Skenderis -- Mass formulae for asymptotically hyperbolic manifolds / Marc Herzlich -- Reconstructing Minkowski space-time / Sergey N. Solodukhin -- Non-trivial, static, geodesically complete space-times with a negative cosmological constant II. n ≥ 5 / Michael T. Anderson, Piotr T. Chruściel, Erwann Delay -- The conformal boundary of anti-de Sitter space-times / Charles Frances -- Supersymmetric AdS backgrounds in string and M-theory / Jerome P. Gauntlett, Dario Martelli, James Sparks, Daniel Waldram.
Altri titoli varianti AdS/CFT Correspondence
Record Nr. UNINA-9910151938403321
Zuerich, Switzerland, : European Mathematical Society Publishing House, 2005
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Advanced functional evolution equations and inclusions [[electronic resource] /] / by Saïd Abbas, Mouffak Benchohra
Advanced functional evolution equations and inclusions [[electronic resource] /] / by Saïd Abbas, Mouffak Benchohra
Autore Abbas Saïd
Edizione [1st ed. 2015.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015
Descrizione fisica 1 online resource (423 p.)
Disciplina 515.352
Collana Developments in Mathematics
Soggetto topico Differential equations
Dynamics
Ergodic theory
System theory
Ordinary Differential Equations
Dynamical Systems and Ergodic Theory
Systems Theory, Control
ISBN 3-319-17768-0
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1. Preliminary Background -- 2. Partial Functional Evolution Equations with Finite Delay -- 3. Partial Functional Evolution Equations with Infinite Delay -- 4. Perturbed Partial Functional Evolution Equations -- 5. Partial Functional Evolution Inclusions with Finite Delay -- 6. Partial Functional Evolution Inclusions with Infinite Delay -- 7. Densely Defined Functional Differential Inclusions with Finite Delay -- 8. Non-Densely Defined Functional Differential Inclusions with Finite Delay -- 9. Impulsive Semi-linear Functional Differential Equations -- 10. Impulsive Functional Differential Inclusions with Unbounded Delay -- 11. Functional Differential Inclusions with Multi-valued Jumps -- 12. Global Existence Results for Functional Differential Equations and Inclusions with Delay -- 13. Global Existence Results of Second Order Functional Differential Equations with Delay -- References -- Index.
Record Nr. UNINA-9910299768603321
Abbas Saïd  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Advanced Mathematics for Engineers and Physicists [[electronic resource] /] / by Sever Angel Popescu, Marilena Jianu
Advanced Mathematics for Engineers and Physicists [[electronic resource] /] / by Sever Angel Popescu, Marilena Jianu
Autore Popescu Sever Angel
Edizione [1st ed. 2022.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022
Descrizione fisica 1 online resource (833 pages)
Disciplina 620.00151
Soggetto topico Mathematical analysis
Probabilities
Mathematical optimization
Calculus of variations
Differential equations
Analysis
Probability Theory
Calculus of Variations and Optimization
Differential Equations
Matemàtica per a enginyers
Física matemàtica
Soggetto genere / forma Llibres electrònics
ISBN 3-031-21502-8
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- Basic Notations -- Sets -- Hyperbolic Functions -- Euler Integrals -- 1 First-Order Differential Equations -- 1.1 Introduction to Ordinary Differential Equations -- 1.2 Separable Equations -- 1.3 Homogeneous Equations -- 1.4 First-Order Linear Differential Equations -- 1.5 Bernoulli Equations -- 1.6 Riccati Equations -- 1.7 Exact Differential Equations -- 1.8 Lagrange Equations and Clairaut Equations -- 1.9 Existence and Uniqueness of Solution of the Cauchy Problem -- 1.10 Exercises -- 2 Higher-Order Differential Equations -- 2.1 Introduction -- 2.2 Homogeneous Linear Differential Equations of Order n -- 2.3 Non-Homogeneous Linear Differential Equations of Order n -- 2.4 Homogeneous Linear Equations with Constant Coefficients -- 2.5 Nonhomogeneous Linear Equations with Constant Coefficients -- 2.6 Euler Equations -- 2.7 Exercises -- 3 Systems of Differential Equations -- 3.1 Introduction -- 3.2 First-Order Systems and Differential Equations of Order n -- 3.3 Linear Systems of Differential Equations -- 3.4 Linear Systems with Constant Coefficients -- 3.4.1 The Homogeneous Case (the Algebraic Method) -- 3.4.2 The Non-Homogeneous Case (the Method of Undetermined Coefficients) -- 3.4.2.1 The Diagonalizable Case -- 3.4.2.2 The Non-Diagonalizable Case -- 3.4.3 Matrix Exponential and Linear Systems with Constant Coefficients -- 3.4.3.1 Fundamental Matrix -- 3.4.3.2 Matrix Exponential -- 3.4.3.3 The Exponential of a Diagonalizable Matrix -- 3.4.3.4 The Exponential of a Nondiagonalizable Matrix -- 3.4.4 Elimination Method for Linear Systems with Constant Coefficients -- 3.5 Autonomous Systems of Differential Equations -- 3.6 First-Order Partial Differential Equations -- 3.6.1 Linear Homogeneous First-Order PDE -- 3.6.2 Quasilinear First-Order Partial Differential Equations -- 3.7 Exercises -- 4 Fourier Series.
4.1 Introduction: Periodic, Piecewise Smooth Functions -- 4.1.1 Periodic Functions -- 4.1.2 Piecewise Continuous and Piecewise Smooth Functions -- 4.2 Fourier Series Expansions -- 4.2.1 Series of Functions -- 4.2.2 A Basic Trigonometric System -- 4.2.3 Fourier Coefficients -- 4.3 Orthogonal Systems of Functions -- 4.3.1 Inner Product -- 4.3.2 Best Approximation in the Mean: Bessel's Inequality -- 4.4 The Convergence of Fourier Series -- 4.5 Differentiation and Integration of the Fourier Series -- 4.6 The Convergence in the Mean: Complete Systems -- 4.7 Examples of Fourier Expansions -- 4.8 The Complex form of the Fourier Series -- 4.9 Exercises -- 5 Fourier Transform -- 5.1 Improper Integrals -- 5.2 The Fourier Integral Formula -- 5.3 The Fourier Transform -- 5.4 Solving Linear Differential Equations -- 5.5 Moments Theorems -- 5.6 Sampling Theorem -- 5.7 Discrete Fourier Transform -- 5.8 Exercises -- 6 Laplace Transform -- 6.1 Introduction -- 6.2 Properties of the Laplace Transform -- 6.3 Inverse Laplace Transform -- 6.4 Solving Linear Differential Equations -- 6.5 The Dirac Delta Function -- 6.6 Exercises -- 7 Second-Order Partial Differential Equations -- 7.1 Classification: Canonical Form -- 7.2 The Wave Equation -- 7.2.1 Infinite Vibrating String: D'Alembert Formula -- 7.2.2 Finite Vibrating String: Fourier Method -- 7.2.3 Laplace Transform Method for the Vibrating String -- 7.2.4 Vibrations of a Rectangular Membrane: Two-Dimensional Wave Equation -- 7.3 Vibrations of a Simply Supported Beam: Fourier Method -- 7.4 The Heat Equation -- 7.4.1 Modeling the Heat Flow from a Body in Space -- 7.4.2 Heat Flow in a Finite Rod: Fourier Method -- 7.4.3 Heat Flow in an Infinite Rod -- 7.4.4 Heat Flow in a Rectangular Plate -- 7.5 The Laplace's Equation -- 7.5.1 Dirichlet Problem for a Rectangle -- 7.5.2 Dirichlet Problem for a Disk -- 7.6 Exercises.
8 Introduction to the Calculus of Variations -- 8.1 Classical Variational Problems -- 8.2 General Frame of Calculus of Variations -- 8.3 The Case F[y]=abF(x,y,y) dx -- 8.4 The Case F[y]=ab F(x, y, y,…,y(n)) dx -- 8.5 The Case F[y1,…,yn]=abF(x,y1,…,yn,y1,…,yn) dx -- 8.6 The Case F[z]=@汥瑀瑯步渠D F (x,y,z,∂z∂x, ∂z∂y)dxdy -- 8.7 Isoperimetric Problems and Geodesic Problems -- 8.7.1 Isoperimetric Problems -- 8.7.2 Geodesic Problems -- 8.8 Exercises -- 9 Elements of Probability Theory -- 9.1 Sample Space: Event Space -- 9.2 Probability Space -- 9.3 Conditional Probability: Bayes Formula -- 9.4 Discrete Random Variables -- 9.4.1 Random Variables -- 9.4.2 Expected Value -- Moments -- 9.4.3 Variance -- 9.4.4 Discrete Uniform Distribution -- 9.4.5 Bernoulli Distribution -- 9.4.6 Binomial Distribution -- 9.4.7 Poisson Distribution -- 9.4.8 Geometric Distribution -- 9.5 Continuous Random Variables -- 9.5.1 The Probability Density Function -- The Distribution Function -- 9.5.2 Expected Value, Moments and Variance for Continuous Random Variables -- 9.5.3 Characteristic Function -- 9.5.4 The Uniform Distribution -- 9.5.5 The Exponential Distribution -- 9.5.6 The Normal Distribution -- 9.5.7 Gamma Distribution -- 9.5.8 Chi-Squared Distribution -- 9.5.9 Student t-Distribution -- 9.6 Limit Theorems -- 9.7 Exercises -- 10 Answers and Solutions to Exercises -- 10.1 Chapter 1 -- 10.2 Chapter 2 -- 10.3 Chapter 3 -- 10.4 Chapter 4 -- 10.5 Chapter 5 -- 10.6 Chapter 6 -- 10.7 Chapter 7 -- 10.8 Chapter 8 -- 10.9 Chapter 9 -- 11 Supplementary Materials -- 11.1 Normed, Metric and Hilbert Spaces -- 11.1.1 Normed Vector Spaces -- 11.1.2 Sequences and Series of Functions -- 11.1.3 Metric Spaces. Some Density Theorems -- 11.1.4 The Fields Q, R and C -- 11.1.5 Hilbert Spaces -- 11.1.6 Continuous Functions and Step Functions -- 11.1.7 Orthonormal Systems in a Hilbert Space.
11.2 Complex Function Theory -- 11.2.1 Differentiability of Complex Functions -- 11.2.2 Integration of Complex Functions -- 11.2.3 Power Series Representation -- 11.2.4 Residue Theorem and Applications -- Bibliography -- Index.
Record Nr. UNISA-996508570903316
Popescu Sever Angel  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Advanced Mathematics for Engineers and Physicists [[electronic resource] /] / by Sever Angel Popescu, Marilena Jianu
Advanced Mathematics for Engineers and Physicists [[electronic resource] /] / by Sever Angel Popescu, Marilena Jianu
Autore Popescu Sever Angel
Edizione [1st ed. 2022.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022
Descrizione fisica 1 online resource (833 pages)
Disciplina 620.00151
Soggetto topico Mathematical analysis
Probabilities
Mathematical optimization
Calculus of variations
Differential equations
Analysis
Probability Theory
Calculus of Variations and Optimization
Differential Equations
Matemàtica per a enginyers
Física matemàtica
Soggetto genere / forma Llibres electrònics
ISBN 3-031-21502-8
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- Basic Notations -- Sets -- Hyperbolic Functions -- Euler Integrals -- 1 First-Order Differential Equations -- 1.1 Introduction to Ordinary Differential Equations -- 1.2 Separable Equations -- 1.3 Homogeneous Equations -- 1.4 First-Order Linear Differential Equations -- 1.5 Bernoulli Equations -- 1.6 Riccati Equations -- 1.7 Exact Differential Equations -- 1.8 Lagrange Equations and Clairaut Equations -- 1.9 Existence and Uniqueness of Solution of the Cauchy Problem -- 1.10 Exercises -- 2 Higher-Order Differential Equations -- 2.1 Introduction -- 2.2 Homogeneous Linear Differential Equations of Order n -- 2.3 Non-Homogeneous Linear Differential Equations of Order n -- 2.4 Homogeneous Linear Equations with Constant Coefficients -- 2.5 Nonhomogeneous Linear Equations with Constant Coefficients -- 2.6 Euler Equations -- 2.7 Exercises -- 3 Systems of Differential Equations -- 3.1 Introduction -- 3.2 First-Order Systems and Differential Equations of Order n -- 3.3 Linear Systems of Differential Equations -- 3.4 Linear Systems with Constant Coefficients -- 3.4.1 The Homogeneous Case (the Algebraic Method) -- 3.4.2 The Non-Homogeneous Case (the Method of Undetermined Coefficients) -- 3.4.2.1 The Diagonalizable Case -- 3.4.2.2 The Non-Diagonalizable Case -- 3.4.3 Matrix Exponential and Linear Systems with Constant Coefficients -- 3.4.3.1 Fundamental Matrix -- 3.4.3.2 Matrix Exponential -- 3.4.3.3 The Exponential of a Diagonalizable Matrix -- 3.4.3.4 The Exponential of a Nondiagonalizable Matrix -- 3.4.4 Elimination Method for Linear Systems with Constant Coefficients -- 3.5 Autonomous Systems of Differential Equations -- 3.6 First-Order Partial Differential Equations -- 3.6.1 Linear Homogeneous First-Order PDE -- 3.6.2 Quasilinear First-Order Partial Differential Equations -- 3.7 Exercises -- 4 Fourier Series.
4.1 Introduction: Periodic, Piecewise Smooth Functions -- 4.1.1 Periodic Functions -- 4.1.2 Piecewise Continuous and Piecewise Smooth Functions -- 4.2 Fourier Series Expansions -- 4.2.1 Series of Functions -- 4.2.2 A Basic Trigonometric System -- 4.2.3 Fourier Coefficients -- 4.3 Orthogonal Systems of Functions -- 4.3.1 Inner Product -- 4.3.2 Best Approximation in the Mean: Bessel's Inequality -- 4.4 The Convergence of Fourier Series -- 4.5 Differentiation and Integration of the Fourier Series -- 4.6 The Convergence in the Mean: Complete Systems -- 4.7 Examples of Fourier Expansions -- 4.8 The Complex form of the Fourier Series -- 4.9 Exercises -- 5 Fourier Transform -- 5.1 Improper Integrals -- 5.2 The Fourier Integral Formula -- 5.3 The Fourier Transform -- 5.4 Solving Linear Differential Equations -- 5.5 Moments Theorems -- 5.6 Sampling Theorem -- 5.7 Discrete Fourier Transform -- 5.8 Exercises -- 6 Laplace Transform -- 6.1 Introduction -- 6.2 Properties of the Laplace Transform -- 6.3 Inverse Laplace Transform -- 6.4 Solving Linear Differential Equations -- 6.5 The Dirac Delta Function -- 6.6 Exercises -- 7 Second-Order Partial Differential Equations -- 7.1 Classification: Canonical Form -- 7.2 The Wave Equation -- 7.2.1 Infinite Vibrating String: D'Alembert Formula -- 7.2.2 Finite Vibrating String: Fourier Method -- 7.2.3 Laplace Transform Method for the Vibrating String -- 7.2.4 Vibrations of a Rectangular Membrane: Two-Dimensional Wave Equation -- 7.3 Vibrations of a Simply Supported Beam: Fourier Method -- 7.4 The Heat Equation -- 7.4.1 Modeling the Heat Flow from a Body in Space -- 7.4.2 Heat Flow in a Finite Rod: Fourier Method -- 7.4.3 Heat Flow in an Infinite Rod -- 7.4.4 Heat Flow in a Rectangular Plate -- 7.5 The Laplace's Equation -- 7.5.1 Dirichlet Problem for a Rectangle -- 7.5.2 Dirichlet Problem for a Disk -- 7.6 Exercises.
8 Introduction to the Calculus of Variations -- 8.1 Classical Variational Problems -- 8.2 General Frame of Calculus of Variations -- 8.3 The Case F[y]=abF(x,y,y) dx -- 8.4 The Case F[y]=ab F(x, y, y,…,y(n)) dx -- 8.5 The Case F[y1,…,yn]=abF(x,y1,…,yn,y1,…,yn) dx -- 8.6 The Case F[z]=@汥瑀瑯步渠D F (x,y,z,∂z∂x, ∂z∂y)dxdy -- 8.7 Isoperimetric Problems and Geodesic Problems -- 8.7.1 Isoperimetric Problems -- 8.7.2 Geodesic Problems -- 8.8 Exercises -- 9 Elements of Probability Theory -- 9.1 Sample Space: Event Space -- 9.2 Probability Space -- 9.3 Conditional Probability: Bayes Formula -- 9.4 Discrete Random Variables -- 9.4.1 Random Variables -- 9.4.2 Expected Value -- Moments -- 9.4.3 Variance -- 9.4.4 Discrete Uniform Distribution -- 9.4.5 Bernoulli Distribution -- 9.4.6 Binomial Distribution -- 9.4.7 Poisson Distribution -- 9.4.8 Geometric Distribution -- 9.5 Continuous Random Variables -- 9.5.1 The Probability Density Function -- The Distribution Function -- 9.5.2 Expected Value, Moments and Variance for Continuous Random Variables -- 9.5.3 Characteristic Function -- 9.5.4 The Uniform Distribution -- 9.5.5 The Exponential Distribution -- 9.5.6 The Normal Distribution -- 9.5.7 Gamma Distribution -- 9.5.8 Chi-Squared Distribution -- 9.5.9 Student t-Distribution -- 9.6 Limit Theorems -- 9.7 Exercises -- 10 Answers and Solutions to Exercises -- 10.1 Chapter 1 -- 10.2 Chapter 2 -- 10.3 Chapter 3 -- 10.4 Chapter 4 -- 10.5 Chapter 5 -- 10.6 Chapter 6 -- 10.7 Chapter 7 -- 10.8 Chapter 8 -- 10.9 Chapter 9 -- 11 Supplementary Materials -- 11.1 Normed, Metric and Hilbert Spaces -- 11.1.1 Normed Vector Spaces -- 11.1.2 Sequences and Series of Functions -- 11.1.3 Metric Spaces. Some Density Theorems -- 11.1.4 The Fields Q, R and C -- 11.1.5 Hilbert Spaces -- 11.1.6 Continuous Functions and Step Functions -- 11.1.7 Orthonormal Systems in a Hilbert Space.
11.2 Complex Function Theory -- 11.2.1 Differentiability of Complex Functions -- 11.2.2 Integration of Complex Functions -- 11.2.3 Power Series Representation -- 11.2.4 Residue Theorem and Applications -- Bibliography -- Index.
Record Nr. UNINA-9910647396803321
Popescu Sever Angel  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui

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