دانلود کتاب A course in mathematical analysis - Applications to Geometry, Expansion in Series, Definite Integrals, Derivatives and Differentias

فهرست مطالب :

C 0 N T E N T S

CHAPTERS PAGE

I. DERIVATIVES AND DIFFERENTIALS............................ 1
I. FUNCTIONS OF A SINGLE VARIABLE.......................... 1
II. FUNCTIONS OF SEVERAL VARIABLES......................... 11
III. THE DIFFERENTIAL NOTATION............................. 19


II. IMPLICIT FUNCTIONS. FUNCTIONAL DETERMINANTS. CHANGE
OF VARIABLES............................................ 35
I. IMPLICIT FUNCTIONS...................................... 35
II. FUNCTIONAL DETERMINANTS................................. 52
III. TRANSFORMATIONS......................................... 61


III. TAYLOR SERIES.ELEMENTARY APPLICATIONS. MAXIMA
AND MINIMA.............................................. 80
I. TAYLOR\'S SERIES WITH A REMAINDER. TAYLOR’S SERIES....... 89
II. SINGULAR POINTS. MAXIMA AND MINIMA...................... 110


IV. DEFINITE INTEGRALS....................................... 134
I. SPECIAL METHODS OF QUADRATURE............................ 134
II. DEFINITE INTEGRALS. ALLIED GEOMETRICAL CONCEPTS......... 140
III. CHANGE OF VARIABLE. INTEGRATION LAY PARTS.............. 166
IV. GENERALIZATIONS OF THE IDEA OF AN INTEGRAL. IMPROPER
INTEGRALS. LINE INTEGRALS............................... 175
V. FUNCTIONS DEFINED BY INFINITE INTEGRALS................. 192
VI. APPROXIMATE EVALUATION OF DEFINITE INTEGRALS............ 196


V. INDEFINITE INTEGRALS.................................... 208
I. INTEGRATION OF RATIONAL FUNCTIONS....................... 268
II. ELLIPTIC AND HYPERELLIPTIC INTEGRALS.................... 226
III. INTEGRATION OF TRANSCENDENTAL FUNCTIONS................. 236


VI. DOUBLE INTEGRALS........................................ 250
I. DOUBLE INTEGRALS. METHODS OF EVALUATION. GREEN’S THEOREM.250
II. CHANGE OF VARIABLES. AREA OF A SURFACE.................. 264
III. GENERALIZATIONS OF DOUBLE INTEGRALS. IMPROPER INTEGRALS.
SURFACE INTEGRALS....................................... 277
IV. ANALYTICAL AND GEOMETRICAL APPLICATIONS................. 284


VII. MULTIPLE INTEGRALS. INTEGRATION OF TOTAL DIFFERENTIALS. 296
I. MULTIPLE INTEGRALS. CHANGE OF VARIABLES................ 296
II. INTEGRATION OF TOTAL DIFFERENTIALS..................... 313


VIII. INFINITE SERIES...................................... 327
I. SERIES OF REAL CONSTANT. TERMS. GENERAL PROPERTIES.
TESTS FOR CONVERGENCE ............................... 327
II. SERIES OF COMPLEX TERMS.MULTIPLE SERIES.............. 350
III. SERIES OF VARIABLE TERMS. UNIFORM CONVERGENCE........ 366


IX. POWER SERIES. TRIGONOMETRIC SERIES................. 375
I. POWER SERIES OF A SINGLE VARIABLE.................. 375
II. POWER SERIES OF A SEVERAL VARIABLE................. 394
III. IMPLICIT FUNCTIONS. ANALYTIC CURVES AND SURFACES... 399
IV. TRIGONOMETRIC SERIES. MISCELLANEOUS SERIES......... 411


X. PLANE CURVES......................................... 426
I. ENVELOPES............................................ 426
II. CURVATURE............................................ 433
III. CONTACT OF PLANE CURVES.............................. 443


XI. SPACE CURVES ........................................ 453
I. OSCULATING PLANE..................................... 453
II. ENVELOPES OF SURFACES................................ 459
III. CURVATURE AND TORSION OF SKEW CURVES................. 466
IV. CONTACT BETWEEN SKEW CURVES. CONTACT BETWEEN CURVES
AND SURFACES......................................... 486


XII. SURFACES............................................ 497
I. CURVATURE OF CURVES DRAWN ON A SURFACE...............497
II. ASYMPTOTIC LINES - CONJUGATE LINES.................. 506
III. LINES OF CURVATURE.................................. 514
IV. FAMILIES OF STRAIGHT LINES.......................... 520


INDEX..................................................... 541