《ORDINARY DIFFERENTIAL EQUATIONS》

作者 E.L. INCE 编者
出版 DOVER PUBLICATIONS
参考页数 558
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ORDINARY DIFFERENTIAL EQUATIONS PDF电子版封面 E.L. INCE

PART ⅠDIFFERENTIAL EQUATIONS IN THE REAL DOMAIN3

Ⅰ.INTRODUCTORY3

Ⅱ.ELEMENTARY METHODS OF INTEGRATION16

Ⅲ.THE EXISTENCE AND NATURE OF SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS62

Ⅳ.CONTINUOUS TRANSFORMATION-GROUPS93

Ⅴ.THE GENERAL THEORY OF LINEAR DIFFERENTIAL EQUATIONS114

Ⅵ.LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS133

Ⅶ.THE SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS IN AN INFINITE FORM158

Ⅷ.THE SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS BY DEFINITE INTEGRALS186

Ⅸ.THE ALGEBRAIC THEORY OF LINEAR DIFFERENTIAL SYSTEMS204

Ⅹ.THE STURMIAN THEORY AND ITS LATER DEVELOPMENTS223

Ⅺ.FURTHER DEVELOPMENTS IN THE THEORY OF BOUNDARY PROBLEMS254

PART ⅡDIFFERENTIAL EQUATIONS IN THE COMPLEX DOMAIN281

Ⅻ.EXISTENCE THEOREMs IN THE COMPLEX DOMAIN281

ⅩⅢ.EQUATIONS OF THE FIRST ORDER BUT NOT OF THE FIRST DEGREE304

ⅩⅣ.NON-LINEAR EQUATIONS OF HIGHER ORDER317

ⅩⅤ.LINEAR EQUATIONS IN THE COMPLEX DOMAIN356

ⅩⅥ.THE SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS IN SERIES396

ⅩⅦ.EQUATIONS WITH IRREGULAR SINGULAR POINTS417

ⅩⅧ.THE SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS BY METHODS OF CONTOUR INTEGRATION438

ⅩⅨ.SYSTEMS OF LINEAR EQUATIONS OF THE FIRST ORDER469

ⅩⅩ.CLASSIFICATION OF LINEAR DIFFERENTIAL EQUATIONS OF THE SECOND ORDER WITH RATIONAL COEFFICIENTS494

ⅩⅪ.OSCILLATION THEOREMS IN THE COMPLEX DOMAIN508

APPENDICES529

A.HISTORICAL NOTE ON FORMAL METHODS OF INTEGRATION529

B.NUMERICAL INTEGRATION OF ORDINARY DIFFERENTIAL EQUATIONS540

C.LIST OF JOURNALS QUOTED IN FOOTNOTES TO THE TEXT548

D.BIBLIOGRAPHY551

INDEX OF AUTHORS553

GENERAL INDEX555

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