Principles of Mathematical Analysis |
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Page 193
... inverse of f [ which exists , by ( a ) ] , defined in V by then gε C ' ( V ) . g ( f ( x ) ) = X ( x ɛ U ) , Writing the equation y = f ( x ) in component form , we arrive at the following interpretation of the conclusion of the theorem ...
... inverse of f [ which exists , by ( a ) ] , defined in V by then gε C ' ( V ) . g ( f ( x ) ) = X ( x ɛ U ) , Writing the equation y = f ( x ) in component form , we arrive at the following interpretation of the conclusion of the theorem ...
Page 198
... inverse T - 1 maps Y1 onto X1 . Let P be the linear operator on X defined by Px = x2 , if x = x1 + X2 , X1 X1 , X2 ε X2 ( this sort of operator is called a projection ) , and define Ɛ ( 40 ) f ( x ) = T - 1F1 ( x ) + Px ( x & E ) . By ...
... inverse T - 1 maps Y1 onto X1 . Let P be the linear operator on X defined by Px = x2 , if x = x1 + X2 , X1 X1 , X2 ε X2 ( this sort of operator is called a projection ) , and define Ɛ ( 40 ) f ( x ) = T - 1F1 ( x ) + Px ( x & E ) . By ...
Page 267
... Inverse function , 78 Inverse function theorem , 193 Inverse image , 21 Inverse of linear operator , 184 Inverse mapping , 78 Invertible transformation , 184 Irrational number , 1 , 57 Isolated point , 28 Jacobian , 203 Knopp , K. , 2 ...
... Inverse function , 78 Inverse function theorem , 193 Inverse image , 21 Inverse of linear operator , 184 Inverse mapping , 78 Invertible transformation , 184 Irrational number , 1 , 57 Isolated point , 28 Jacobian , 203 Knopp , K. , 2 ...
Contents
Preface | 1 |
ELEMENTS OF SET THEORY | 21 |
NUMERICAL SEQUENCES AND SERIES | 41 |
Copyright | |
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a₁ B₂ bounded variation C'-mapping called Cauchy sequence choose closed complex numbers continuous function continuous on a,b converges uniformly Corollary countable set Definition denote diverges Example Exercise exists f is differentiable finite fn(x follows Fourier series function defined function f ƒ and g ƒ ɛ ƒ is continuous given Hence Hint holds implies inequality infinite integer integral interval k-form Lebesgue Let f lim inf lim sup limit point linear mean value theorem measurable functions metric space monotonic functions neighborhood nonnegative notation number system obtain open set partial sums partition polynomials positive integer power series properties rational numbers real function real numbers Riemann integral say that ƒ shows Suppose f Theorem uniform convergence uniformly continuous upper number variation on a,b vector space y₁ Σ Σ