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Produktbild: Differential Equations

Differential Equations Theory, Technique, and Practice

111,99 €

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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

30.05.2022

Abbildungen

schwarz-weiss Illustrationen, Zeichnungen, schwarz-weiss

Verlag

Taylor & Francis

Seitenzahl

488

Maße (L/B/H)

24/16,1/3,1 cm

Gewicht

816 g

Auflage

3. Auflage

Sprache

Englisch

ISBN

978-1-03-210270-2

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

30.05.2022

Abbildungen

schwarz-weiss Illustrationen, Zeichnungen, schwarz-weiss

Verlag

Taylor & Francis

Seitenzahl

488

Maße (L/B/H)

24/16,1/3,1 cm

Gewicht

816 g

Auflage

3. Auflage

Sprache

Englisch

ISBN

978-1-03-210270-2

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: gpsr@libri.de

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Die Leseprobe wird geladen.
  • Produktbild: Differential Equations

  • Preface

    1. What Is a Differential Equation?
    1.1 Introductory Remarks
    1.2 A Taste of Ordinary Differential Equations
    1.3 The Nature of Solutions

    2. Solving First-Order Equations
    2.1 Separable Equations
    2.2 First-Order Linear Equations
    2.3 Exact Equations
    2.4 Orthogonal Trajectories and Curves
    2.5 Homogeneous Equations
    2.6 Integrating Factors
    2.7 Reduction of Order
    2.7.1 Dependent Variable Missing
    2.7.2 Independent Variable Missing

    3. Some Applications of the First-Order Theory
    3.1 The Hanging Chain and Pursuit Curves
    3.1.1 The Hanging Chain
    3.1.2 Pursuit Curves
    3.2 Electrical Circuits
    Anatomy of an Application
    Problems for Review and Discovery

    4. Second-Order Linear Equations
    4.1 Second-Order Linear Equations with Constant Coefficients
    4.2 The Method of Undetermined Coefficients
    4.3 The Method of Variation of Parameters
    4.4 The Use of a Known Solution to Find Another
    4.5 Higher-Order Equations

    5. Applications of the Second-Order Theory
    5.1 Vibrations and Oscillations
    5.1.1 Undamped Simple Harmonic Motion
    5.1.2 Damped Vibrations
    5.1.3 Forced Vibrations
    5.1.4 A Few Remarks About Electricity
    5.2 Newton’s Law of Gravitation and Kepler’s Laws
    5.2.1 Kepler’s Second Law
    5.2.2 Kepler’s First Law
    5.2.3 Kepler’s Third Law
    Historical Note
    Anatomy of an Application
    Problems for Review and Discovery

    6. Power Series Solutions and Special Functions
    6.1 Introduction and Review of Power Series
    6.1.1 Review of Power Series
    6.2 Series Solutions of First-Order Equations
    6.3 Ordinary Points
    6.4 Regular Singular Points
    6.5 More on Regular Singular Points
    Historical Note
    Historical Note
    Anatomy of an Application
    Problems for Review and Discovery

    7. Fourier Series: Basic Concepts
    7.1 Fourier Coefficients
    7.2 Some Remarks about Convergence
    7.3 Even and Odd Functions: Cosine and Sine Series
    7.4 Fourier Series on Arbitrary Intervals
    7.5 Orthogonal Functions
    Historical Note
    Anatomy of an Application
    Problems for Review and Discovery

    8. Laplace Transforms
    8.0 Introduction
    8.1 Applications to Differential Equations
    8.2 Derivatives and Integrals
    8.3 Convolutions
    8.3.1 Abel’s Mechanics Problem
    8.4 The Unit Step and Impulse Functions
    Historical Note
    Anatomy of an Application
    Problems for Review and Discovery

    9. The Calculus of Variations
    9.1 Introductory Remarks
    9.2 Euler’s Equation
    9.3 Isoperimetric Problems and the Like
    9.3.1 Lagrange Multipliers
    9.3.2 Integral Side Conditions
    9.3.3 Finite Side Conditions
    Historical Note
    Anatomy of an Application
    Problems for Review and Discovery

    10. Systems of First-Order Equations
    10.1 Introductory Remarks
    10.2 Linear Systems
    10.3 Systems with Constant Coefficients
    10.4 Nonlinear Systems
    Anatomy of an Application
    Problems for Review and Discovery

    11. Partial Differential Equations and Boundary Value Problems
    11.1 Introduction and Historical Remarks
    11.2 Eigenvalues and the Vibrating String
    11.2.1 Boundary Value Problems
    11.2.2 Derivation of the Wave Equation
    11.2.3 Solution of the Wave Equation
    11.3 The Heat Equation
    11.4 The Dirichlet Problem for a Disc
    11.4.1 The Poisson Integral
    11.5 Sturm—Liouville Problems
    Historical Note
    Historical Note
    Anatomy of an Application
    Problems for Review and Discovery

    12. The Nonlinear Theory
    12.1 Some Motivating Examples
    12.2 Specializing Down
    12.3 Types of Critical Points: Stability
    12.4 Critical Points and Stability
    12.5 Stability by Liapunov’s Direct Method
    12.6 Simple Critical Points of Nonlinear Systems
    12.7 Nonlinear Mechanics: Conservative Systems
    12.8 Periodic Solutions
    Historical Note
    Anatomy of an Application
    Problems for Review and Discovery

    13. Qualitative Properties and Theoretical Aspects
    13.1 A Bit of Theory
    13.2 Picard’s Existence and Uniqueness Theorem
    13.2.1 The Form of a Differential Equation
    13.2.2 Picard’s Iteration Technique
    13.2.3 Some Illustrative Examples
    13.2.4 Estimation of the Picard Iterates
    13.3 Oscillations and the Sturm Separation Theorem
    13.4 The Sturm Comparison Theorem
    Anatomy of an Application
    Problems for Review and Discovery

    Appendix: Review of Linear Algebra
    Bibliography
    Index