Problems in Mathematical Analysis.pdf - pwp.net.ipl.pt

More documents

Recommendations

Info

390_Approximate Calculations_[Ch. 10\ The Adams method consists in continuing the diagonal ces with the aid of the Adams formula table of differen- Thus, utilizing the numbers
Page 2 and 3:
TEXT FLY WITHIN THE BOOK ONLY
Page 5:
OUP-43 30-1.71 5,000 OSMANIA UNIVER
Page 8 and 9:
T. C. BapaneHKoe. C. M. Koean, r Jl
Page 10 and 11:
TO THE READER MIR Publishers would
Page 12 and 13:
Contents Sec. 6. Integrating Certai
Page 14 and 15:
8 Chapter Contents Sec. 13. Linear
Page 17 and 18:
Sec. 1. Functions Chapter I INTRODU
Page 19 and 20:
Sec 1] Functions 13 8. Find the rat
Page 21 and 22:
Sec. 1]_Functions_15 34. Prove that
Page 23 and 24:
Sec. 2] Graphs of Elementary functi
Page 25 and 26:
Sec. 2] Graphs of Elementary functi
Page 27 and 28:
Sec. 2] Graphs of Elementary Functi
Page 29 and 30:
Sec. 3] Limits 23 For the existence
Page 31 and 32:
Sec. 3] 179. Hm (Vn + 1 \f~n). n -+
Page 33 and 34:
Sec. #] Limits 27 209. lim 210. lim
Page 35 and 36:
^Sec 3] Limits Therefore, Example 9
Page 37 and 38:
Sec. 31 Limits 31 269. a) 270. lim-
Page 39 and 40:
Sec. 4] Infinitely Small and Large
Page 41 and 42:
Sec. 4] Infinitely Small and Large
Page 43 and 44:
Sec. 5] Continuity of Functions 37
Page 45 and 46:
Sec. 5]_Continuity of Functions_39
Page 47 and 48:
Sec. 5] Continuity of Functions 334
Page 49 and 50:
Sec. 1] Calculating Derivatives Dir
Page 51 and 52:
Sec. 1] Calculating Derivatives Dir
Page 53 and 54:
Sec. 2]__Tabular Differentiation_47
Page 55 and 56:
Sec. 2]_Tabular Differentiation_49
Page 57 and 58:
Sec. 2] Tabular Differentiation_ 51
Page 59 and 60:
Sec. 2] Tabular Differentiation 504
Page 61 and 62:
Sec. 2] Tabular Differentiation 55
Page 63 and 64:
Sec. 3] The Derivatives of Function
Page 65 and 66:
Sec. 3] The Derivatives of Function
Page 67 and 68:
Sec 4] Geometrical and Mechanical A
Page 69 and 70:
Sec. 4\ Geometrical and Mechanical
Page 71 and 72:
Sec. 4] Geometrical and Mechanical
Page 73 and 74:
Sec. 5]_Derivatives of Higher Order
Page 75 and 76:
Sec. 5]_Derivatives of Higher Order
Page 77 and 78:
Sec. 6] Differentials of First and
Page 79 and 80:
Sec. 6}_Differentials of First and
Page 81 and 82:
Sec. 7]_Mean-Value Theorems_75 745.
Page 83 and 84:
Sec. 8] Taylor's Formula 77 765. a)
Page 85 and 86:
Sec. 9]_ V Hospital-Bernoulli Rule
Page 87 and 88:
Sec. 9] L' Hospital-Bernoulli Rule
Page 89 and 90:
Chapter III THE EXTREMA OF A FUNCTI
Page 91 and 92:
Sec. 1] The Extrema of a Function o
Page 93 and 94:
Page 95 and 96:
Page 97 and 98:
Sec. 2]_The Direction of Concavity.
Page 99 and 100:
Sec. 3]_Asymptotes_93 Example 2. Fi
Page 101 and 102:
Sec. 3]_Asymptotes_95 Solution. Sin
Page 103 and 104:
Sec 4] Graphing Functions by Charac
Page 105 and 106:
CM CM -h CO O non ' > C " -~ a - >
Page 107 and 108:
Sec. />] Differential of an Arc. Cu
Page 109 and 110:
Sec 5] Differential of an Arc. Curv
Page 111 and 112:
Sec. 5]_Differential of an Arc. Cur
Page 113 and 114:
Sec. 1. Direct Integration 1. Basic
Page 115:
Sec 1] Direct Integration_109 1048*
Page 119 and 120:
Sec. 2] Integration by Substitution
Page 121 and 122:
Sec. 2] Integration by Substitution
Page 123 and 124:
Sec. 3\_Integration by Parts_H7 Exa
Page 125 and 126:
Sec 4] Standard Integrals Containin
Page 127 and 128:
Sec. 5] Integration of Rational Fun
Page 129 and 130:
Sec. 5] In t egration of Rational F
Page 131 and 132:
Sec. 6] Integrating Certain Irratio
Page 133 and 134:
Sec. 6] Integrating Certain Irratio
Page 135 and 136:
Sec. 7]_Integrating Trigonometric F
Page 137 and 138:
Sec. 7]_Integrating Trigonometric F
Page 139 and 140:
Sec. 8] Integration of Hyperbolic F
Page 141 and 142:
Sec. 11] Using Reduction Formulas 1
Page 143 and 144:
Sec. 12] Miscellaneous Examples on
Page 145 and 146:
Sec. 1] The Definite Integral as th
Page 147 and 148:
Sec. 2]_Evaluating Definite Integra
Page 149 and 150:
Sec. 3]_Improper Integrals_143 Sec.
Page 151 and 152:
Sec. 3] Improper Integrals 145 Solu
Page 153 and 154:
Sec. 4] Change of Variable in a Def
Page 155 and 156:
Sec. 5] Integration by Parts 149 Bu
Page 157 and 158:
Sec. 6] Mean-Value Theorem 151 In p
Page 159 and 160:
Sec. 7] The Areas of Plane Figures
Page 161 and 162:
Sec. 7] The Areas of Plane Figures
Page 163 and 164:
Sec. 7\_The Areas of Plane Figures_
Page 165 and 166:
Sec. 8] The Arc Length of a Curve 1
Page 167 and 168:
Sec, 9] Volumes of Solids 161 1673.
Page 169 and 170:
Sec. 9] Volumes of Solids 163' Solu
Page 171 and 172:
Sec. 9]_Volumes of Solids_165 1693.
Page 173 and 174:
Sec. 10] The Area of a Surface of R
Page 175 and 176:
Sec. II] Moments. Centres of Gravit
Page 177 and 178:
Sec 11] Moments. Centres of Gravity
Page 179 and 180:
&?c. 12] Applying Definite Integral
Page 181 and 182:
Sec. 12] Applying Definite Integral
Page 183 and 184:
Page 185 and 186:
Page 187 and 188:
Sec. 1) Basic Notions [SI Putting *
Page 189 and 190:
Sec. 1]_Basic Notions_183 1790*. Le
Page 191 and 192:
Sec. 3] Partial Derivatives 185 180
Page 193 and 194:
Sec. 4]_Total Differential of a Fun
Page 195 and 196:
Sec. 4}_Total Differential of a Fun
Page 197 and 198:
Sec. 5]_Differentiation of Composit
Page 199 and 200:
Sec. 6]_Derivative in a Given Direc
Page 201 and 202:
Sec. 6] Derivative in a Given Direc
Page 203 and 204:
Sec. 7]_Higher-Order Derivatives an
Page 205 and 206:
Sec. 7] Higher-Order Derivatives an
Page 207 and 208:
Sec. 7]_Higher-Order Derivatives an
Page 209 and 210:
Sec. ti\_Integration of Total Diffe
Page 211 and 212:
Sec. 9]_Differentiation of Implicit
Page 213 and 214:
Sec. 9] Differentiation of Implicit
Page 215 and 216:
Sec. 9]_Differentiation of Implicit
Page 217 and 218:
Sec. 10]_Change of Variables_2H 196
Page 219 and 220:
Sec. 10]_Change of Variables_213 or
Page 221 and 222:
Sec. 10] Change of Variables 215 an
Page 223 and 224:
Sec. 11]_The Tangent Plane and the
Page 225 and 226:
Sec. 11]_The Tangent Plane and the
Page 227 and 228:
Sec. 12] Taylor's Formula for a Fun
Page 229 and 230:
Sec. 13]_The Extremum of a Function
Page 231 and 232:
Sec. 13] The Extremutn of a Functio
Page 233 and 234:
Sec. 14] Finding the Greatest and S
Page 235 and 236:
Sec. 14] Finding the Greatest and S
Page 237 and 238:
Sec. 15] Singular Points of Plane C
Page 239 and 240:
Sec. 16] Envelope 233 Solution. The
Page 241 and 242:
Sec. 18] The Vector Function of a S
Page 243 and 244:
Sec. 18]_The Vector Function of a S
Page 245 and 246:
Sec. 19] The Natural Trihedron of a
Page 247 and 248:
Sec. 19] The Natural Trihedron of a
Page 249 and 250:
Sec. 20] Curvature and Torsion of a
Page 251 and 252:
Sec. 20]_Curvature and Torsion of a
Page 253 and 254:
Sec. 1] The Double Integral in Rect
Page 255 and 256:
Page 257 and 258:
Page 259 and 260:
Sec. 2]_Change of Variables in a Do
Page 261 and 262:
Sec. 2]_Change of Variables in a Do
Page 263 and 264:
Sec 3]_Computing Areas_257 2177. Co
Page 265 and 266:
Sec. 5]_Computing th Area* of Surfa
Page 267 and 268:
Sec. 6]_Applications of the Double
Page 269 and 270:
Sec. 7] Triple Integrals 2o3 Evalua
Page 271 and 272:
Sec 7\ Triple Integrals 265 We ther
Page 273 and 274:
gee. 7]_Triple Integrals_267 2251.
Page 275 and 276:
Sec. 8] Improper Integrals Dependen
Page 277 and 278:
Sec. 8]_Improper Integrals Dependen
Page 279 and 280:
See. 9] Line Integrals 273 Test for
Page 281 and 282:
Sec. 9]____Line Inlegtah____275 whe
Page 283 and 284:
Sec. 9]_Line Integrals__277 express
Page 285 and 286:
Sec. 9] Lim Integrals 279 (/-axis;
Page 287 and 288:
Sec 9] Line Integrals 281 Evaluate
Page 289 and 290:
Sec. 9] Line Integrals 2S& D. Appli
Page 291 and 292:
Sec. 10] Surface Integrals 285 When
Page 293 and 294:
ec. 11]_The Ostrogradsky-Gauss Form
Page 295 and 296:
Sec. 12] Fundamentals of Field Theo
Page 297 and 298:
Sec. 12] Fundamentals of Field Theo
Page 299 and 300:
Sec. 1. Number Series Chapter VIII
Page 301 and 302:
Sec. 1]_Number Series_295 c) D'Alem
Page 303 and 304:
Sec /\_Number Series_297 Note. For
Page 305 and 306:
2418. + + 0419 J___1_ . 4- 4- 4- '
Page 307 and 308:
Sec. 1] Number Series 2464. cos-2-)
Page 309 and 310:
Sec. 1]_Number Series_303 - V r(2-Q
Page 311 and 312:
Sec. 2]_Functional Series_305 In th
Page 313 and 314:
Sec. 2]_Functional Series_307 [the
Page 315 and 316:
Sec. 2] Functional Series 309 Deter
Page 317 and 318:
Sec. 3]_Taylor's Series_311 v8 s r
Page 319 and 320:
Sec. 3] Taylor's Series 313 Since a
Page 321 and 322:
Sec 3} Taylor's Series 315 2615. ln
Page 323 and 324:
Sec. 3] Taylor's Series 317 2651. F
Page 325 and 326:
Sec. 4] Fourier Series 319 If a fun
Page 327 and 328:
Sec. 4\__Fourier Series _321 2690.
Page 329 and 330:
Sec 1 1 Verifying Solutions 323 It
Page 331 and 332:
Sec. 21 First-Order Differential Eq
Page 333 and 334:
Sec. 3] Differential Equations with
Page 335 and 336:
Sec. 3\ Differential Equations with
Page 337 and 338:
Sec. 4]_First-Order Homogeneous Dif
Page 339 and 340:
Sec. 5] Bernoulli's Equation 333 Co
Page 341 and 342:
Sec. 6] Exact Differential Equation
Page 343 and 344:
Sec. 7] First-Order Differential Eq
Page 345 and 346: Sec 8]_The Lagrange and Clairaut Eq
Page 347 and 348: Sec. 9] Miscellaneous Exercises on
Page 349 and 350: Sec. 9] Miscellaneous Exercises on
Page 351 and 352: Sec. 10] Higher-Order Differential
Page 353 and 354: Sec. 10]__Higher-Order Differential
Page 355 and 356: Sec. 11]_Linear Differential Equati
Page 357 and 358: Sec. 12] Linear Differential Equati
Page 363 and 364: Sec. 14]_Euler's Equations__357 Fin
Page 365 and 366: Sec. 15]_Systems of Differential Eq
Page 367 and 368: .Sec. 16} Integration of Differenti
Page 369 and 370: Sec. 17] Problems on Fourier's Meth
Page 371 and 372: Sec. 17]_Problems on Fourier's Meth
Page 373 and 374: Chapter X APPROXIMATE CALCULATIONS
Page 375 and 376: Sec. 1] Operations on Approximate N
Page 377 and 378: Sec. /]_Operations on Approximate N
Page 379 and 380: Sec, 2] Interpolation of Functions
Page 381 and 382: Sec. 2] Interpolation of Functions
Page 383 and 384: Sec. 3]_Computing the Real Roots of
Page 389 and 390: Sec. 4] Numerical Integration of Fu
Page 391 and 392: Sec. 5] Numerical Integration of Or
Page 393 and 394: Sec. 5] Numerical Integration of Or
Page 395: Sec. 5] Numerical Integration of Or
Page 399 and 400: [Sec. 6]_Approximating Fourier Coef
Page 401 and 402: Sec. 6] Approximating Fourier Coeff
Page 403 and 404: c) * = \ if ( oo f Answers 397 ( oo
Page 405 and 406: Answers 399 200. 3. 201. 1 . 202. i
Page 407 and 408: Answers 401 tinuity of the second k
Page 409 and 410: 429. . 430. X cos(x 5 3 Answers 403
Page 411 and 412: -24 574. . 575. 'n*. 576. 585. 590.
Page 413 and 414: d) 2 n jc 2 691 ^(OJ^-tn 1)1 692. a
Page 415 and 416: Answers (2, oo), increases. 824. (
Page 417 and 418: Answers 411 down; [7^, oo Y concave
Page 419 and 420: _Answers_413 Ji 5 * = ' T ^nin = 1
Page 421 and 422: d $93. ds = dx, cosa = ; y u Answe
Page 423 and 424: . 1075. - 5 31n|x + V^= Answers 417
Page 425 and 426: c) (5*'-3)'; d) 1194. In V 2x4-1 1
Page 427 and 428: Consequently, 2 \ y~a*x 2 dx = x V
Page 429 and 430: 1330. -retan =7+l). 1327. - *-li .
Page 431 and 432: Answers 425 1403. . 1404. ~ ^2 + x
Page 433 and 434: J481. ^-? . + ln sinhxl | . 1490. -
Page 435 and 436: Answer^ 429 1594. -- . 1599. -- 1 I
Page 437 and 438: Answers 43 1 1724. ~jia 2 . 1725. 2
Page 439 and 440: _Answers_433 The force of interacti
Page 441 and 442: _Answers__435 parabola y = ~- x*(x*
Page 443 and 444: Answers 437 -sin* In sin*). 1861. =
Page 445 and 446: d*z d*z dx*~ a*b*z> : dxdy *;*; i/
Page 447 and 448:
_Answers_441 e=3 1^25 (x\)* (f/-f2)
Page 449 and 450:
Answers 443 2085. x=cosacoso); y si
Page 451 and 452:
2133. j dx j "" t Vl - x* - J f (x,
Page 453 and 454:
2133 . 1 ~~ * V&~^ Answers 445 J dx
Page 455 and 456:
Answers 447 jn i 4 sin )dr. oo
Page 457 and 458:
_Answers_449 polar coordinates. 222
Page 459 and 460:
Answers 451 L-a 27i 2 h cosec \f Th
Page 461 and 462:
_Answers_45$ y=tx % where t is a pa
Page 463 and 464:
Answers__455 -'' 2504. --
Page 465 and 466:
Answers 457 ** x / , * . 2589. cos
Page 467 and 468:
Hint. Make the substitution . = Ans
Page 469 and 470:
2689 . 2691 . i_ 2694. Solution. 1)
Page 471 and 472:
_Answers_463 2780. Paraboloid of re
Page 473 and 474:
-0. 2873. y^Cx + -~, i/ = ~^/2?. 28
Page 475 and 476:
_Answers_467 x. 4- C* H Xcosh - |-C
Page 477 and 478:
and x = ccos f t . 3043. y J . 3043
Page 479 and 480:
Answers 471 0, x I/Q 0, r i; cosa,
Page 481 and 482:
J129. 3130. Answers 473 Hint. Compu
Page 483 and 484:
APPENDIX I. Greek Alphabet II. Some
Page 485 and 486:
Appendix 477 Continued
Page 487 and 488:
Appendix V. Exponential, Hyperbolic
Page 489 and 490:
8a. Neile's p arabola, x^t* 2 - y-^
Page 491 and 492:
Appendix 13. Graphs of the inverse
Page 493 and 494:
Appendix ^30. Spiral of Archimedes,
Page 495 and 496:
Concave down 91 Concave up 91 Conca
Page 497 and 498:
Force lines Form 288 Lagrange's 311
Page 499 and 500:
Pascal's 158 Limit of a function 22
Page 501 and 502:
Rose four-leafed 487 three-leafed 2
show all

Problems in Mathematical Analysis.pdf - pwp.net.ipl.pt

Create successful ePaper yourself

Delete template?

Save as template?