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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
|
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Advanced Mathematics for Engineers and Physicists / / by Sever Angel Popescu, Marilena Jianu
| Advanced Mathematics for Engineers and Physicists / / 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 | ||
| ||