# Ordinary Differential Equations

1985-10

ISBN: 9780486649405

• 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
• ##### 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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