An Introduction to AnalysisOffering readability, practicality and flexibility, Wade presents Fundamental Theorems from a practical viewpoint. Introduces central ideas of analysis in a one-dimensional setting, then covers multidimensional theory. Offers separate coverage of topology and analysis. Numbers theorems, definitions and remarks consecutively. Uniform writing style and notation. Practical focus on analysis. For those interested in learning more about analysis. |
Contents
ONEDIMENSIONAL THEORY | 1 |
Sequences in R | 35 |
Continuity on R | 58 |
Copyright | |
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bounded variation Cauchy choose closed interval compact contains continuously differentiable converges absolutely converges uniformly convex countable curve defined definition Example Exercise exists extended real number f(xo Figure finite first-order partial derivatives following result shows formula function f ƒ is continuous ƒ is differentiable ƒ is integrable graph Hence hypothesis implies improperly integrable inequality infimum Jordan region l'Hôpital's Rule Lemma Let f lim f(x limit matrix Mean Value Theorem metric space n-dimensional nonempty nonnegative nonzero Notice open interval open set oriented parametrization partial derivatives partial sums partition pointwise power series PROOF Property Prove that ƒ rectangle relatively open Remark Riemann integral satisfies sequence smooth Squeeze Theorem subset Suppose that ƒ supremum surface tangent Test uniformly continuous variables vector zero ду