A course of analysis

a₁ absolutely convergent aggregate algebra arbitrary axis bounded variation cardinal number Cauchy's coefficients complex numbers concept condition consider constant continuous function convergent series corresponding curve curvilinear integrals D₁ deduce defined definite integral denote differential diverges domain double integral dx dy equation example exists finite number follows formula function f(x fundamental ƒ x geometrical given Green's theorem Hence independent variables inequality interval irrational number lemma mean-value theorem mode of subdivision monotonic neighbourhood partial derivatives plane positive number power series proof properties prove rational function rational numbers reader should observe real numbers rectifiable curve relation right-hand side satisfied sequence shew shewn Similarly sub-intervals Suppose surface t₁ Taylor's theorem tends to zero theory transformation u₁ uniformly convergent unique limit upper bound write ду дх მყ