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71 2 <strong>Advanced</strong> <strong>Calculus</strong>, Fifth EditionSouthwell, R. V., Relaxation Methods in Engineering Science. Oxford: Oxford UniversityPress, 1946.Southwell, R. V., Relaxation Methods in Theoretical Physics. Oxford: Oxford UniversityPress, 1946.Tarnarkin, J. D., and W. Feller, Partial Differential Equations. Mimeographed notes of lecturesat Brown University, 194 1.Titchmarsh, E. C., Eigenfunction Expansions Associated with Second-Order DifferentialEquations, 2nd ed. Oxford: Oxford University Press, 1962.Titchmarsh, E. C., Fourier Integrals. Oxford: Oxford University Press, 1948.Wiener, N., The Fourier Integral. New York: Dover, 195 1.
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L'' . ' '(SZilt6i) (SX156i).'Advanc
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ContentsVectors and Matrices1.1 Int
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3.6 Combined Operations 183*3.7 Cur
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*6.24 Principal Value of Improper I
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Case of Two Particles 662Case of N
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Advanced Calculus. Fifth Editionhas
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Advanced Calculus, Fifth Edition8.
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Advanced Calculus, Fifth EditionBy
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Differential Calculusof Functionsof
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Chapter 2 Differential Calculus of
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PROBLEMSChapter 2 Differential Calc
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Chapter 2 Differential ~alculus of
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defined analogously:Chapter 2 Diffe
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magnitudeand the force is inversely
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*I. 421 8 Advanced Calculus, Fifth
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Advanced Calculus, Fifth EditionFig
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Vector Integral CalculusPART I.TWO-
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Chapter 5 Vector Integral Calculus
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3. Evaluate the following line inte
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5. Evaluate by Green's theorem:a) $
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Chapter 5 Vector Integral' Calculus
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Green's theorem now givesChapter 5
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*5.15 PHYSICAL APPLICATIONSChapter
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Infinite Series6.1 INTRODUCTIONAn i
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Chapter 6 Infinite Series 377These
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Chapter 6 Infinite Series 379If a s
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Chapter 6 Infinite Series 381Every
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Chapter 6 Infinite Series 383PROBLE
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Chapter 6 Infinite Series 385EXAMPL
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Chapter 6 Infinite Series 387If ELP
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Chapter 6 Infinite Seriesi ,Figure
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n Chapter 6 Infinite Series 391If L
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Chapter 6 Infinite Series 393of con
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EXAMPLE 8zz, 5. Again the ratio tes
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12. Determine convergence or diverg
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The theorem has a counterpart in te
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Chapter 6 Infinite Series 401Proof.
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Chapter 6 Infinite Series 403as alg
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Chapter 6 Infinite Series 405b) Sho
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at. Chapter 6 Infinite Series 407Fi
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Chapter 6 Infinite Series 409Furthe
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F; Chapter 6 .Infinite Series 41 1C
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Chapter 6 Infinite Series 41 3Figur
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for when x = $, the numerator Ixn 1
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EXAMPLE 1Ezl 5. Here the ratio test
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Chapter 6 Infinite Series 41 9Figur
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Chapter 6 Infinite Series 421This h
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. ,. Chapter 6 Infinite Series 423D
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, Chapter 6 Infinite Series 425by T
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Chapter 6 Infinite Series 427THEORE
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nL: Chapter 6 Infinite Series 429ha
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[Hint: Use induction. For n = 0 the
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Chapter 6 Infinite Series 439%Let z
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Chapter 6 Infinite Series 441is not
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Chapter 6 Infinite Series 443Figure
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Chapter 6 Infinite Series 445The th
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Chapter 6 Infinite Series 447d 2 =
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6Chapter 6 Infinite Series 453diver
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Chapter 6 Infinite Series 459Figure
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Chapter 6 Infinite Series 461b) Let
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Chapter 6 Infinite Series 463By ana
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Therefore R3 lies in some annulus h
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Fourier Series andOrthogonal Functi
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Chapter 7 Fourier Series and Orthog
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Chapter 7Fourier Series and Orthogo
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y the Schwarz inequality (7.46). By
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IiChapter 7 Fourier Series and Orth
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Functions of aComplex VariableWe as
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Chapter 8 Functions of a Complex Va
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TChapter 8 Functions of a Complex V
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PROBLEMSChapter 8 Functions of a Co
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2f 'c) J, zeZ dz on the line segmen
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Rule IV could also be used, with A
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RULE V If f (z) has a zero of first
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+aJ 12. Evaluate the following inte
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The function U is Airy's stress fun
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'Chapter 8 Functions of a Complex V
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PassibleChapter 8 Functions of a Co
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C) the first quadrant of the w plan
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Ordinary DifferentialEquations9.1 D
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Chapter 9 Ordinary Differential Equ
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Here we make a change of variable,
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Partial DifferentialEquationsA part
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Page 735 and 736: dii Answers to ProblemsCHAPTER 6Sec
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Page 745 and 746: IndexAbel's formula, 461 (Rob. 10)A
Page 747 and 748: Index 735Curvilinear coordinates, 1
Page 749 and 750: Index 737Hypergeometric equation, 6
Page 751 and 752: IndexOdd function, 480One-to-one tr
Page 753: Index 741Ion a surface, 208-209orde
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