by J. Hunter, B. Nachtergaele
Publisher: World Scientific Publishing Company 2005
Number of pages: 439
Introduces applied analysis at the graduate level, particularly those parts of analysis useful in graduate applications. Only a background in basic calculus, linear algebra and ordinary differential equations, and functions and sets is required in order to fully understand the material presented.
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by Larry Clifton - arXiv
This is a detailed introduction to the real number system from a categorical perspective. We begin with the categorical definition of the natural numbers, review the Eudoxus theory of ratios, and then define the positive real numbers categorically.
by Shanti Narayan - S.Chand And Company
Contents: Dedekind's theory of Real Numbers; Bounds and Limiting Points; Sequences; Real Valued Functions of a Real Variable; The derivative; Riemann Theory of Integration; Uniform Convergence; Improper Integrals; Fourier Series; and more.
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A comprehensive treatment with a global view of the subject, emphasizing connections between real analysis and other branches of mathematics. Included throughout are many examples and hundreds of problems, with hints or complete solutions for most.
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The ideas of Du Bois-Reymond's 'Infinitarcalcul' are of great and growing importance in all branches of the theory of functions. The author brings the Infinitarcalcul up to date, stating explicitly and proving carefully a number of general theorems.