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71 4 Advanced Calculus, Fifth Editionk) meaningless.2 1-1 -4 -3 3 33. a) D-c=[ - - 1 1: b) G ) = [rSection 1.8, page 25-2 2 .I. a) meaningless; b) [I:]; c meness; d) [: I:] and [6],e) [:and [i: 1 ; I) A; g) L; h) undefined; i) 0; j) 0;' P) 51 = 5E; q) 25E; r) 125g s) meaningless.3. a) yl = 17x1 + x2, y2 = 31xl + 7x2; b) yl = x2 - 3x3, y2 = 7x1 + 13x2 - 4x3.6. It is true precisely when AB = BA.Section 1.9, page 30I. a) 12 [-2 -:I; b) A'[-! -:I;+
Answers to Problems 7358. All matrices whose inverses appear in the answers are assumed to be nonsingular.a) x = ;(A + B), Y = ;(A - B);b) x = (B- I)-~(BA - c),Y = (B- I)-~(c - A);C) X = B - A(A - c)-'(B - D), Y = (A- c)-'(B - D);d) x = (B-'A - E-~D)-~(B-~c - E-~F);Y = (A-'B - D-'E)-~(A-~C - D-IF);e) X = (CB-I - FE-')(AB-' - DE-')-~, Y = (CA-I - FD-')(BA-' - ED-l)-'.Section 1.10, page 331. a) x=-6,y=12,~=5; b) x=3,y=l,z=-1;13 10c) x = ~ , y = ~ , T9 z = ~ .d) x=I,y=l,z=l. 2. a) 21; b) 0. 3. a) x=2,y=2,z=3;b) x=4,y=l,z=l,w=l.-1 -1 ; -1 1 -314. a)4-2 -343533 -2 -2 t5. a) x = (7 - t)/5, y = (3t - 1)/5, z = t, -m < r < m; b) no solution;C) x = -3t, y = 6t, z = t, w = 8t, -00 < t < 00;d) x=t-2u,y=5t-7~,~=3t,w=3u,-m
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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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Differential Calculusof Functionsof
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Chapter 2 Differential Calculus of
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PROBLEMSChapter 2 Differential Calc
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defined analogously:Chapter 2 Diffe
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magnitudeand the force is inversely
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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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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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n Chapter 6 Infinite Series 391If L
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EXAMPLE 8zz, 5. Again the ratio tes
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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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Fourier Series andOrthogonal Functi
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y the Schwarz inequality (7.46). By
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Functions of aComplex VariableWe as
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Ordinary DifferentialEquations9.1 D
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Partial DifferentialEquationsA part
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