Principles of Mathematical Analysis |
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Page 20
... notation α ( 1 ) S = U Ea . αε Α If A consists of the integers 1,2 , • n , one usually writes n S = Ü Em ( 2 ) or ( 3 ) m = 1 S = E1UE2U • • • U En . If A is the set of all positive integers , the usual notation is ( 4 ) S Ů Em . = m ...
... notation α ( 1 ) S = U Ea . αε Α If A consists of the integers 1,2 , • n , one usually writes n S = Ü Em ( 2 ) or ( 3 ) m = 1 S = E1UE2U • • • U En . If A is the set of all positive integers , the usual notation is ( 4 ) S Ů Em . = m ...
Page 44
... notation ап ( p ≤ q ) n = p + ag . With an } we associate a to denote the sum ap + ap + 1 + sequence { 8 } , where Sn = ak . k = 1 For { s } we also use the symbolic expression or , more concisely ( 4 ) a1 + a2 + aз + • Σ ап . n = 1 ...
... notation ап ( p ≤ q ) n = p + ag . With an } we associate a to denote the sum ap + ap + 1 + sequence { 8 } , where Sn = ak . k = 1 For { s } we also use the symbolic expression or , more concisely ( 4 ) a1 + a2 + aз + • Σ ап . n = 1 ...
Page 172
... notation ( 17 ) af axi for Dif . When using ( 17 ) , it is always troublesome to indicate the point at which the derivative is evaluated . One could of course write ( 18 ) af მე : ( a ) , but very often one finds the notation ( 19 ) ...
... notation ( 17 ) af axi for Dif . When using ( 17 ) , it is always troublesome to indicate the point at which the derivative is evaluated . One could of course write ( 18 ) af მე : ( a ) , but very often one finds the notation ( 19 ) ...
Contents
Preface V | 1 |
Elements of Set Theory | 18 |
Numerical Sequences and Series | 36 |
Copyright | |
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B₂ bounded variation c₂ called Cauchy sequence Chap choose compact set complex numbers consider contains continuous function continuous on a,b converges uniformly Corollary countable set Definition denote derivative differentiable discontinuous diverges equations Example exists f be defined f is continuous f(x+ fn(x Fourier series function defined function f ƒ and g ƒ ɛ given Heine-Borel theorem Hence implies inequality integral interval Let f lim inf lim sup limit point mean value theorem metric space monotonic functions monotonically increasing neighborhood nonnegative notation obtain open set partial sums partition polynomials positive integer power series Proof prove rational number Riemann Riemann integrable say that ƒ series converges set of points set of real Suppose f uniform convergence vacuous variation on a,b write Zan converges zero