Ordinary Differential Equations

Ordinary Differential Equations
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作者: ,
1985-10
版次: 1
ISBN: 9780486649405
定价: 230.20
装帧: 平装
开本: 其他
纸张: 胶版纸
页数: 818页
正文语种: 英语
  • Skillfullyorganizedintroductorytextexaminesoriginofdifferentialequations,thendefinesbasictermsandoutlinesthegeneralsolutionofadifferentialequation.Subsequentsectionsdealwithintegratingfactors;dilutionandaccretionproblems;linearizationoffirstordersystems;LaplaceTransforms;Newton'sInterpolationFormulas,more. PREFACE FOR THE TEACHER

    PREFACE FOR THE STUDENT

    1 BASIC CONCEPTS

      Lisson 1 How Differential Equations Originate

      Lisson 2 The Meaning of the Terms Set and Function.Im-plicit Function.Elementary Functions.

      Lisson 3 The Differential Equation

      Lisson 4 The General Solution of a Differential Equation

      Lisson 5 Direction Field.

    2 SPECIAL TYPES OF DIFFERENTIAL EQUATIONS OF THE FIRST ORDER

      Lisson 6 Meaning of the Differential of a Function.Separable Differential Differential Equations.  

      Lisson 7 First Order Differential Equation with Homogeneous Coefficients

      Lisson 8 Differential Equations with Linear Coefficients.

      Lisson 9 Exact Differential Equations

      Lisson 10 Recognizable Exact Differential Equations.Integrating Factors.

      Lisson 11 The Linear Differential Equation of the Firat Order.Bernoulli Equation

      Lisson 12 Miscellaneous Methods of Solving a First Order Differential Equation.

    3 PROBLEMS LEADING TO DIFFERENTIAL EQUATIONS OF THE FIRST ORDER

      Lisson 13 Geometric Problems.

      Lisson 14 Trajectories

      ……

    4 LINEAR DIFFERENTIAL EQUATIONS OF ORDER GREATER THAN ONE

    5 OPERATORS AND LAPLACE TRANSFORMS

    6 PROBLEMS LEADING TO LINEAR DIFFERENTIAL EQUATIONS OF ORDER TWO

    7 SYSTEMS OF DIFFERENTIAL EQUATIONS.LINEARIZATION OF FIRST ORDER SYSTEMS

    8 PROBLEMS GIVING RISE TO SYSTEMS OF EQUATIONS.SPECIAL TYPES OF SECOND ORDER LINEAR AND NON-LINEAR EQUATIONS SOLVABLE BY REDUCING TO SYSTEMS

    9 SERIES METHODS

    10 NUMERICAL METHODS

    11 EXISTENCE AND UNIQUENESS THEOREM FOR THE FIRSST ORDER DIFFERENTIAL EQUATION y'=f(x,y).PICARD'S METHOD.ENVELOPES.CLAIRAUT EQUATION.

    12 EXISTENCE AND UNIQUENESS THEOREMS FOR A SYSTEM OF FIRST ORDER DIFFERENTIAL EQUATIONS AND FOR LINEAR AND NONLINEAR DIFFERENTIAL EQUATIONS OF ORDER GREATER THAN ONE.WRONSKIANS.

    Bibliography

    Index
  • 内容简介:
    Skillfullyorganizedintroductorytextexaminesoriginofdifferentialequations,thendefinesbasictermsandoutlinesthegeneralsolutionofadifferentialequation.Subsequentsectionsdealwithintegratingfactors;dilutionandaccretionproblems;linearizationoffirstordersystems;LaplaceTransforms;Newton'sInterpolationFormulas,more.
  • 目录:
    PREFACE FOR THE TEACHER

    PREFACE FOR THE STUDENT

    1 BASIC CONCEPTS

      Lisson 1 How Differential Equations Originate

      Lisson 2 The Meaning of the Terms Set and Function.Im-plicit Function.Elementary Functions.

      Lisson 3 The Differential Equation

      Lisson 4 The General Solution of a Differential Equation

      Lisson 5 Direction Field.

    2 SPECIAL TYPES OF DIFFERENTIAL EQUATIONS OF THE FIRST ORDER

      Lisson 6 Meaning of the Differential of a Function.Separable Differential Differential Equations.  

      Lisson 7 First Order Differential Equation with Homogeneous Coefficients

      Lisson 8 Differential Equations with Linear Coefficients.

      Lisson 9 Exact Differential Equations

      Lisson 10 Recognizable Exact Differential Equations.Integrating Factors.

      Lisson 11 The Linear Differential Equation of the Firat Order.Bernoulli Equation

      Lisson 12 Miscellaneous Methods of Solving a First Order Differential Equation.

    3 PROBLEMS LEADING TO DIFFERENTIAL EQUATIONS OF THE FIRST ORDER

      Lisson 13 Geometric Problems.

      Lisson 14 Trajectories

      ……

    4 LINEAR DIFFERENTIAL EQUATIONS OF ORDER GREATER THAN ONE

    5 OPERATORS AND LAPLACE TRANSFORMS

    6 PROBLEMS LEADING TO LINEAR DIFFERENTIAL EQUATIONS OF ORDER TWO

    7 SYSTEMS OF DIFFERENTIAL EQUATIONS.LINEARIZATION OF FIRST ORDER SYSTEMS

    8 PROBLEMS GIVING RISE TO SYSTEMS OF EQUATIONS.SPECIAL TYPES OF SECOND ORDER LINEAR AND NON-LINEAR EQUATIONS SOLVABLE BY REDUCING TO SYSTEMS

    9 SERIES METHODS

    10 NUMERICAL METHODS

    11 EXISTENCE AND UNIQUENESS THEOREM FOR THE FIRSST ORDER DIFFERENTIAL EQUATION y'=f(x,y).PICARD'S METHOD.ENVELOPES.CLAIRAUT EQUATION.

    12 EXISTENCE AND UNIQUENESS THEOREMS FOR A SYSTEM OF FIRST ORDER DIFFERENTIAL EQUATIONS AND FOR LINEAR AND NONLINEAR DIFFERENTIAL EQUATIONS OF ORDER GREATER THAN ONE.WRONSKIANS.

    Bibliography

    Index
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