# 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

Basic Algebra I：Second Edition
Nathan Jacobson 著
One, Two, Three...Infinity：Facts and Speculations of Science
George Gamow 著
Basic Algebra II：Second Edition
Nathan Jacobson 著
The Thirteen Books of Euclid's Elements, Books 1 and 2
Euclid 著；Sir Thomas Heath 编
Introduction to Topology：Third Edition
Bert Mendelson 著
Calculus：An Intuitive and Physical Approach
Morris Kline 著
A Book of Abstract Algebra（second edition）：Second Edition
Charles C. Pinter 著
General Topology
Stephen Willard 著
Mathematics for the Nonmathematician
Morris Kline 著
Differential Geometry of Curves and Surfaces Se
Manfredo P. do Carmo 著
Elements of the Theory of Functions and Functional Analysis
A.N.Kolmogorov、S.V.Fomin 著
The Theory of Groups and Quantum Mechanics
Hermann Weyl 著

Ordinary Differential Equations and Their Solutions
George Moseley Murphy
Ordinary Language Criticism
Dauber；Kenneth（EDT）；Jost；Walter（EDT）
Ordinary Love & Good Will
Smiley；Jane
OrdinaryGenius:AGuideforthePoetWithin
Ordinary Men：Reserve Police Battalion 101 and the Final Solution in Poland
Christopher R. Browning
OrdinaryDifferentialEquations:ABriefEclecticTour(ClassroomResourceMaterials)
David A. S.nchez 著
Ordinary Greatness It's Where You Least Expect It ... Everywhere
Bilbrey, Pamela；Jones, Brian；Lencioni, Patrick M
Ordinary meaning：A Theory of the Most Fundamental Principle of Legal Interpretation
Brian G. Slocum
OrdinaryandExtraordinaryMeans:FiftiethAnniversaryIssue
Daniel A. Cronin 著
Ordinary Beauty
Wiess, Laura
Ordinary Differential Equations and Dynamical Systems
Gerald Teschl
Ordinary Life Stories
Elizabeth Berg 著

Morton 著；[澳]凯特·莫顿、Kate、杜松 译

Morris 著；[英]马克·莫里斯、Marc、晓秋 译

YearBookofOrthopedics,1e(YearBooks)
Morrey、Bernard 著
Heaven's Command：An Imperial Progress
Morris；Jan
Drama and Desire：Japanese paintings from the floating world, 1690 - 1850
Morse；Anne Nishimura
Mutant Message Down Under
Morgan, Marlo
DevelopingGlobalExecutives
Morgan W. McCall 著
Warren Court & the Pursuit of Justice
Morton Horwitz
The Thinker's Toolkit
Morgan D. Jones（摩根·D·琼斯） 著
Greek Fiction
Morgan, ). R.,Stoneman, Richard
Essays in the Unknown Wittgenstein
Morris Lazerowitz 著