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

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OUP-43 30-1.71 5,000 OSMANIA UNIVERSITY LIBRARY Call No. g>^^ Accession No. Author This book should be returned on or before the date last marked below
Page 2 and 3: TEXT FLY WITHIN THE BOOK ONLY
Page 7 and 8: M I R PUBLISH P. KS
Page 9 and 10: G. Baranenkov* B. Drmidovich V. Efi
Page 11 and 12: CONTENTS Preface 9 Chapter I. INTRO
Page 13 and 14: Contents Sec. 18. The Vector Functi
Page 15: PREFACE This collection of problems
Page 18 and 19: 12 Introduction to Analysis \Ch. I
Page 20 and 21: 14 In t roduction to Analysis [Ch.
Page 22 and 23: 16 Introduction to Analysts [Ch. 1
Page 24 and 25: 18_Introduction to Analysis_[Ch. 1
Page 26 and 27: 20 Introduction to Analysis [C/i. /
Page 28 and 29: 22 Introdnction to Analysis (C/t. /
Page 30 and 31: 24_Introduction to Analysis_[CH. 1
Page 32 and 33: 26 Introduction to Analysis_\Ch. I
Page 34 and 35: "28_Introduction to Analysis_[Ch. 1
Page 36 and 37: 30_Introduction to Analysis_[Ch. !
Page 38 and 39: Introduction to Analysis [Ch. I (as
Page 44 and 45: 38 In t reduction to Analysis [Ch.
Page 46 and 47: 40 Introduction to Analysis [Ch. 1
Page 48 and 49: Chapter II DIFFERENTIATION OF FUNCT
Page 50 and 51: 44 ' Differentiation of Functions [
Page 52 and 53: 46_Differentiation of Functions_[C/
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48_Differentiation of Functions_[Ch
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50 Differentiation of Functions_[Ch
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52 Differentiation of Functions [C/
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54 Differentiation of Functions_[C/
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58 Differentiation of Functions [Ch
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60 Differentiation of Functions (Ch
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64_ ___Differentiation of Functions
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72 Differentiation of Functions [C/
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76_Differentiation of Functions_ [C
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82 Differentiation of Functions (Ch
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84 Extrema and the Geometric Applic
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88_Extrema and the Geometric Applic
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94 and Extrema and the Geometric Ap
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Extrema and the Geometric Applicati
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100 Extrema and the Geometric Appli
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108__Indefinite Integrals_[Ch. 4 VI
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112 Indefinite Integrals [C/i. 4 11
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114_Indefinite Integrals_[Ch. 4 If
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U6__Indefinite Integrals \Ch. 4 120
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118 Indefinite Integrals [C/i. 4 12
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J20 Indefinite Integrals [Ch. 4 3.
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122 Indefinite Integrals [C/t. 4 Wh
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124 Indefinite Integrals [Ch. 4 Sol
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12J Indefinite Integrals [Ch. 4 Int
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128 Indefinite Integrals (Ch. 4 Exa
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130 Indefinite Integrals [Ch. 4 4)
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132 Indefinite Integrals [Ch. 4 2)
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134 Indefinite Integrals_[CH. 4 Tra
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136 Indefinite Integrals [Ch. 4 142
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Chapter V DEFINITE INTEGRALS Sec. 1
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140 Definite Integrals [Ch. 5 we fi
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142 Definite Integrals [Ch. 5 Evalu
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144_Definite Integrals_[C/i. 5 Exam
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146_ Definite Integrals_(Ch. 5 00 1
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148_Definite Integrals_[Ch. 5 indic
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150_Definite Integrals_[Ch. 5 1606*
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152 Definite Integrals [Ch. b 1611.
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154 Definite Integrals (Ch. 5 Examp
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156__Definite Integrals_[Ch. 5 Solu
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158 Definite Integrals (Ch. 5 1653.
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160 Definite Integrals [Ch. 5 Examp
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162 Definite Integrals [Cft. 5 expr
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164_Definite Integrals_\Ch. 5 2. Co
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166 Definite Integrals [Ch. 5 1708.
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168 Definite Integrals \Ch. 5 1718.
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170_Definite Integrals_[Ch. 5 where
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172_Definite Integrals_[Ch. 6 1728.
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174 Definite Integrals [Ch. 5 and S
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ITS formula Definite Integrals \Cfi
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178 Definite Integrals [C/i. 5 Misc
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Sec. 1. Faiic Notions Chapter VI FU
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182 Functions of Several Variables
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184_Functions of Several Variables_
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J88 Functions of Several Variables
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198 _Functions of Several Variables
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210__Functions of Several Variables
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220_ Functions of Several Variables
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236__Functions of Several Variables
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238 Functions of Several Variables_
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Hence, on the basis of formulas (1)
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Chapter VII MULTIPLE AND LINE INTEG
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248_Multiple and Line Integrals_[Ch
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250 Multiple and Line Integrals [Ch
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252_Multiple and Line Integrals_(Ch
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254 Multiple and Line Integrals (Ch
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256_Multiple and Line Integrals__[C
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258 Multiple and Line Integrals (Ch
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266 Multifile and Lire Integrals [C
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272_Multiple and Line Integrals__\C
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280_Multiple and Line Integrals___[
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282_Multiple and Line Integrals_[C/
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286_Multiple and Line Integrals_[C/
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292_Multiple and Line Integrals_(Ch
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294 Series [Ch. 8 which converges f
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296_Series_[Ch. 8 Since the Dirichl
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298_Series_m_[Ch. 8 b) By the sum (
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300 Series [Ch. 8 2439. -+ + +... 2
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302 Series [Ch. 8 sin na 2481. (_l)
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304_Series__[Ch. 8 series 2503. Est
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306_Series_\Ch. 8 vanishes [as a pa
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308 Series [Ch. 8 CO 00 1 OCQA V f
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310_Series__[C/i. 8 points x will b
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312 Series [Ch. 8 for any*. Hence,
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314 Series (Ch. 8 The expansion (7)
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316 Series [Ch. 8 2640. Expand -* i
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318 _Series_[C/i. 8 Write the first
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320_Series_g_(Ch. 8 2680. Expand th
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Chapter IX DIFFERENTIAL EQUATIONS S
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324 _Differential Equations_[Ch. 9
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326 Differential Equations (Ch. 9 3
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328 Differential Equations (Ch. 9 U
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330_Differential Equations_[C/i. 9
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532_Differential Equations_[Ch. 9 2
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334_Differential Equations_[Cfi. 9
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336 Differential Equations [C/t. 9
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Differential Equations_(Ch. 9 It is
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340__Differential Equations_^__[C/t
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342 Differential Equations [Ch. 9 2
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344_Differential Equations_[Ch. 9 2
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346 Differential Equations [Ch 9 Fr
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348 Differential Equations (Ch. 9 z
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350_Differential Equations_[C/i. 9
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352__Differential Equations_[Ch. 9
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354_Differential Equations_[Ch. 9 c
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356_Differential Equations_(Ch. 9 3
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358_Differential Equations_[Ch. 9 F
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360 Differential Equations [Ch. 9 S
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362 Differential Equations [Ch. 9 h
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364_Differential Equations_\Ch. 9 a
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366_' Differential Equations_[C/i.
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368 Approximate Calculations [Ch. 1
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370 _Approximate Calculations_[Ch.
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372_Approximate Calculations_[Ch. 1
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374 Approximate Calculations (Ch 10
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376 Approximate Calculations (Ch. 1
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.378_Approximate Calculations__[Cft
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380_Approximate Calculations_[Ch 10
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384 Approximate Calculations \Ch. 1
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390_Approximate Calculations_[Ch. 1
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[Sec. 6]_Approximating Fourier Coef
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Sec. 6] Approximating Fourier Coeff
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c) * = \ if ( oo f Answers 397 ( oo
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Answers 399 200. 3. 201. 1 . 202. i
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Answers 401 tinuity of the second k
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429. . 430. X cos(x 5 3 Answers 403
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-24 574. . 575. 'n*. 576. 585. 590.
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d) 2 n jc 2 691 ^(OJ^-tn 1)1 692. a
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Answers (2, oo), increases. 824. (
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Answers 411 down; [7^, oo Y concave
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_Answers_413 Ji 5 * = ' T ^nin = 1
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d $93. ds = dx, cosa = ; y u Answe
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. 1075. - 5 31n|x + V^= Answers 417
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c) (5*'-3)'; d) 1194. In V 2x4-1 1
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Consequently, 2 \ y~a*x 2 dx = x V
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1330. -retan =7+l). 1327. - *-li .
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Answers 425 1403. . 1404. ~ ^2 + x
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J481. ^-? . + ln sinhxl | . 1490. -
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Answer^ 429 1594. -- . 1599. -- 1 I
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Answers 43 1 1724. ~jia 2 . 1725. 2
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_Answers_433 The force of interacti
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_Answers__435 parabola y = ~- x*(x*
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Answers 437 -sin* In sin*). 1861. =
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d*z d*z dx*~ a*b*z> : dxdy *;*; i/
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_Answers_441 e=3 1^25 (x\)* (f/-f2)
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Answers 443 2085. x=cosacoso); y si
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2133. j dx j "" t Vl - x* - J f (x,
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2133 . 1 ~~ * V&~^ Answers 445 J dx
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Answers 447 jn i 4 sin )dr. oo
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_Answers_449 polar coordinates. 222
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Answers 451 L-a 27i 2 h cosec \f Th
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_Answers_45$ y=tx % where t is a pa
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Answers__455 -'' 2504. --
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Answers 457 ** x / , * . 2589. cos
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Hint. Make the substitution . = Ans
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2689 . 2691 . i_ 2694. Solution. 1)
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_Answers_463 2780. Paraboloid of re
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-0. 2873. y^Cx + -~, i/ = ~^/2?. 28
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_Answers_467 x. 4- C* H Xcosh - |-C
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and x = ccos f t . 3043. y J . 3043
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Answers 471 0, x I/Q 0, r i; cosa,
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J129. 3130. Answers 473 Hint. Compu
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APPENDIX I. Greek Alphabet II. Some
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Appendix 477 Continued
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Appendix V. Exponential, Hyperbolic
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8a. Neile's p arabola, x^t* 2 - y-^
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Appendix 13. Graphs of the inverse
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Appendix ^30. Spiral of Archimedes,
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Concave down 91 Concave up 91 Conca
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Force lines Form 288 Lagrange's 311
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Pascal's 158 Limit of a function 22
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Rose four-leafed 487 three-leafed 2
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