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. |
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Page 473
... surface with a smooth parametrization must have a tangent plane at each of its points ( see Exercise 7 ) . On the other hand , a surface with tangent planes at each point can have nonsmooth parametrizations ... surface 13.3 473 Surfaces.
... surface with a smooth parametrization must have a tangent plane at each of its points ( see Exercise 7 ) . On the other hand , a surface with tangent planes at each point can have nonsmooth parametrizations ... surface 13.3 473 Surfaces.
Page 476
... surface S is said to be closed if and only if ƏS = Ø . For example , if a > 0 , then the sphere x2 + y2 + z2 = a2 is ... surface if and only if S where each S , ( øj , Ej ) is a smooth surface and for each j k either S , Sk is empty , or ...
... surface S is said to be closed if and only if ƏS = Ø . For example , if a > 0 , then the sphere x2 + y2 + z2 = a2 is ... surface if and only if S where each S , ( øj , Ej ) is a smooth surface and for each j k either S , Sk is empty , or ...
Page 480
... surface S is said to be orientable if and only if it has a smooth parametrization ( ø , E ) that induces an unambiguous unit normal n on S that varies continuously over S ; i.e. , if ( uo , vo ) = $ ( U1 , V1 ) , then No ( uo , vo ) ...
... surface S is said to be orientable if and only if it has a smooth parametrization ( ø , E ) that induces an unambiguous unit normal n on S that varies continuously over S ; i.e. , if ( uo , vo ) = $ ( U1 , V1 ) , then No ( uo , vo ) ...
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