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An Introduction to Differential Equations and Their Applications
| An Introduction to Differential Equations and Their Applications |
| Autore | Farlow Stanley J |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Newburyport, : Dover Publications, 2012 |
| Descrizione fisica | 1 online resource (1408 p.) |
| Disciplina | 515/.35 |
| Collana | Dover Books on Mathematics |
| Soggetto topico |
Differential equations
Mathematics Physical Sciences & Mathematics Calculus |
| ISBN |
9780486135137
0486135136 9781621985747 1621985741 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title Page; Copyright Page; Dedication; Contents; Preface; Chapter 1: Introduction to Differential Equations; Prologue; 1.1 Basic Definitions and Concepts; 1.2 Some Basic Theory; Chapter 2: First-Order Differential Equations; 2.1 First-Order Linear Equations; 2.2 Separable Equations; 2.3 Growth and Decay Phenomena; 2.4 Mixing Phenomena; 2.5 Cooling and Heating Phenomena; 2.6 More Applications; 2.7 The Direction Field and Euler's Method; 2.8 Higher-Order Numerical Methods; Chapter 3: Second-Order Linear Equations; 3.1 Introduction to Second-Order Linear Equations
3.2 Fundamental Solutions of the Homogeneous Equation3.3 Reduction of Order; 3.4 Homogeneous Equations with Constant Coefficients: Real Roots; 3.5 Homogeneous Equations with Constant Coefficients: Complex Roots; 3.6 Nonhomogeneous Equations; 3.7 Solving Nonhomogeneous Equations: Method of Undetermined Coefficients; 3.8 Solving Nonhomogeneous Equations: Method of Variation of Parameters; 3.9 Mechanical Systems and Simple Harmonic Motion; 3.10 Unforced Damped Vibrations; 3.11 Forced Vibrations; 3.12 Introduction to Higher-Order Equations (Optional); Chapter 4: Series Solutions 4.1 Introduction: A Review of Power Series4.2 Power Series Expansions about Ordinary Points: Part I; 4.3 Power Series Expansions about Ordinary Points: Part II; 4.4 Series Solutions about Singular Points: The Method of Frobenius; 4.5 Bessel Functions; Chapter 5: The Laplace Transform; 5.1 Definition of the Laplace Transform; 5.2 Properties of the Laplace Transform; 5.3 The Inverse Laplace Transform; 5.4 Initial-Value Problems; 5.5 Step Functions and Delayed Functions; 5.6 Differential Equations with Discontinuous Forcing Functions; 5.7 Impulse Forcing Functions; 5.8 The Convolution Integral Chapter 6: Systems of Differential Equations6.1 Introduction to Linear Systems: The Method of Elimination; 6.2 Review of Matrices; 6.3 Basic Theory of First-Order Linear Systems; 6.4 Homogeneous Linear Systems with Real Eigenvalues; 6.5 Homogeneous Linear Systems with Complex Eigenvalues; 6.6 Nonhomogeneous Linear Systems; 6.7 Nonhomogeneous Linear Systems: Laplace Transform (Optional); 6.8 Applications of Linear Systems; 6.9 Numerical Solution of Systems of Differential Equations; Chapter 7: Difference Equations; 7.1 Introduction to Difference Equations; 7.2 Homogeneous Equations 7.3 Nonhomogeneous Equations7.4 Applications of Difference Equations; 7.5 The Logistic Equation and the Path to Chaos; 7.6 Iterative Systems: Julia Sets and the Mandelbrot Set (Optional); Chapter 8: Nonlinear Differential Equations and Chaos; 8.1 Phase Plane Analysis of Autonomous Systems; 8.2 Equilibrium Points and Stability for Linear Systems; 8.3 Stability: Almost Linear Systems; 8.4 Chaos, Poincare Sections and Strange Attractors; Chapter 9: Partial Differential Equations; 9.1 Fourier Series; 9.2 Fourier Sine and Cosine Series; 9.3 Introduction to Partial Differential Equations 9.4 The Vibrating String: Separation of Variables |
| Record Nr. | UNINA-9911007194403321 |
Farlow Stanley J
|
||
| Newburyport, : Dover Publications, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Partial Differential Equations for Scientists and Engineers
| Partial Differential Equations for Scientists and Engineers |
| Autore | Farlow Stanley J |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Newburyport, : Dover Publications, 2012 |
| Descrizione fisica | 1 online resource (663 p.) |
| Disciplina |
515.3/53
515.353 |
| Collana | Dover Books on Mathematics |
| Soggetto topico |
Differential equations, Partial
Mathematics Physical Sciences & Mathematics Calculus |
| ISBN |
9780486134734
0486134733 9781621985846 1621985849 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Title Page; Copyright Page; Preface; Table of Contents; PART 1 - Introduction; LESSON 1 - Introduction to Partial Differential Equations; What Are PDEs?; Why Are PDEs Useful?; How Do You Solve a Partial Differential Equation?; Kinds of PDEs; PART 2 - Diffusion-Type Problems; LESSON 2 - Diffusion-Type Problems (Parabolic Equations); A Simple Heat-Flow Experiment; The Mathematical Model of the Heat-Flow Experiment; More Diffusion-Type Equations; LESSON 3 - Boundary Conditions for Diffusion-Type Problems; Type 1 BC (Temperature specified on the boundary)
Type 2 BC (Temperature of the surrounding medium specified)Type 3 BC (Flux specified-including the special case of insulated boundaries); Typical BCs for One-Dimensional Heat Flow; LESSON 4 - Derivation of the Heat Equation; Derivation of the Heat Equation; LESSON 5 - Separation of Variables; Overview of Separation of Variables; Separation of Variables; LESSON 6 - Transforming Nonhomogeneous BCs into Homogeneous Ones; Transforming Nonhomogeneous BCs to Homogeneous Ones; Transforming Time Varying BCs to Zero BCs; LESSON 7 - Solving More Complicated Problems by Separation of Variables Heat-Flow Problem with Derivative BCLESSON 8 - Transforming Hard Equations into Easier Ones; Transforming a Heat-Flow Problem with Lateral Heat Loss into an Insulated Problem; LESSON 9 - Solving Nonhomogeneous PDEs (Eigenfunction Expansions); Solution by the Eigenfunction Expansion Method; Solution of a Problem by the Eigenfunction-Expansion Method; LESSON 10 - Integral Transforms (Sine and Cosine Transforms); The Spectrum of a Function; Solution of an Infinite-Diffusion Problem via the Sine Transform; Interpretation of the Solution; LESSON 11 - The Fourier Series and Transform Discrete Frequency Spectrum of a Periodic FunctionThe Fourier Transform; LESSON 12 - The Fourier Transform and Its Application to PDEs; Useful Properties of the Fourier Transform; Example of a Convolution of Two Functions; Solution of an Initial-Value Problem; LESSON 13 - The Laplace Transform; Properties of the Laplace Transform; Sufficient Conditions to Insure the Existence of a Laplace Transform; Definition of the Finite Convolution; Heat Conduction in a Semi Infinite Medium; LESSON 14 - Duhamel's Principle; Heat Flow within a Rod with Temperature Fixed on the Boundaries The Importance of Duhamel's PrincipleLESSON 15 - The Convection Term ux in the Diffusion Problems; Laplace Transform Solution to the Convection Problem; PART 3 - Hyperbolic-Type Problems; LESSON 16 - The One-Dimensional Wave Equation (Hyperbolic Equations); Vibrating-String Problem; Intuitive Interpretation of the Wave Equation; LESSON 17 - The D'Alembert Solution of the Wave Equation; D'Alembert's Solution to the One-Dimensional Wave Equation; Examples of the D'Alembert Solution; LESSON 18 - More on the D'Alembert Solution; The Space-Time Interpretation of D'Alembert's Solution Solution of the Semi-infinite String via the D'Alembert Formula |
| Record Nr. | UNINA-9911006803503321 |
|
Farlow Stanley J
|
||
| Newburyport, : Dover Publications, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||