ORDINARY DIFFERENTIAL EQUATIONSPDF电子书下载

PART Ⅰ DIFFERENTIAL EQUATIONS IN THE REAL DOMAIN 3

Ⅰ.INTRODUCTORY 3

Ⅱ.ELEMENTARY METHODS OF INTEGRATION 16

Ⅲ.THE EXISTENCE AND NATURE OF SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS 62

Ⅳ.CONTINUOUS TRANSFORMATION-GROUPS 93

Ⅴ.THE GENERAL THEORY OF LINEAR DIFFERENTIAL EQUATIONS 114

Ⅵ.LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS 133

Ⅶ.THE SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS IN AN INFINITE FORM 158

Ⅷ.THE SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS BY DEFINITE INTEGRALS 186

Ⅸ.THE ALGEBRAIC THEORY OF LINEAR DIFFERENTIAL SYSTEMS 204

Ⅹ.THE STURMIAN THEORY AND ITS LATER DEVELOPMENTS 223

Ⅺ.FURTHER DEVELOPMENTS IN THE THEORY OF BOUNDARY PROBLEMS 254

PART Ⅱ DIFFERENTIAL EQUATIONS IN THE COMPLEX DOMAIN 281

Ⅻ.EXISTENCE THEOREMs IN THE COMPLEX DOMAIN 281

ⅩⅢ.EQUATIONS OF THE FIRST ORDER BUT NOT OF THE FIRST DEGREE 304

ⅩⅣ.NON-LINEAR EQUATIONS OF HIGHER ORDER 317

ⅩⅤ.LINEAR EQUATIONS IN THE COMPLEX DOMAIN 356

ⅩⅥ.THE SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS IN SERIES 396

ⅩⅦ.EQUATIONS WITH IRREGULAR SINGULAR POINTS 417

ⅩⅧ.THE SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS BY METHODS OF CONTOUR INTEGRATION 438

ⅩⅨ.SYSTEMS OF LINEAR EQUATIONS OF THE FIRST ORDER 469

ⅩⅩ.CLASSIFICATION OF LINEAR DIFFERENTIAL EQUATIONS OF THE SECOND ORDER WITH RATIONAL COEFFICIENTS 494

ⅩⅪ.OSCILLATION THEOREMS IN THE COMPLEX DOMAIN 508

APPENDICES 529

A.HISTORICAL NOTE ON FORMAL METHODS OF INTEGRATION 529

B.NUMERICAL INTEGRATION OF ORDINARY DIFFERENTIAL EQUATIONS 540

C.LIST OF JOURNALS QUOTED IN FOOTNOTES TO THE TEXT 548

D.BIBLIOGRAPHY 551

INDEX OF AUTHORS 553

GENERAL INDEX 555