Mathematical Analysis - Giuseppe Modica

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Résumé :
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Biographie:
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Sommaire:
Preface.-Differential Calculus.-The differential calculus for scalar functions.-The differential calculus for vector-valued functions.-The theorems of the differential calculus.-Invertibility of map Rn to Rn.-Differential calculus in Banach spaces.-Exercises.-The Integral Calculus.-Lebesque's integral.-Convergence theorems.-Mollifiers and approximation.-Integral calculus.-Measure and area.-The Gauss-Green formula.-Exercises.-Curves and Differential Forms.-Differential forms, fields, and work.-Conservative fields, exact forms, and potentials.-closed forms and irrotational fields.-Stokes formula in the plane.-Exercises.-Holomorphic functions.-Functions from C to C.-The fundamental theorem of calculus in C.-The fundamental theorems about holomorphic functions.-Examples of holomorphic functions.-Pointwise singularities of holomorphic functions.-Residues.-Further consequences of Cauchy formulas.-Maximum principle.-Schwarz lemma-Local properties.-Biholomorphisms.-Riemann's theorem on conformal representations.-Harmonic functions and Riemann's theorem.-Exercises.-Surfaces and level sets.-Surfaces and immersions.-Implicit functions.-Some applications.-The curvature of curves and surfaces.-Exercises.-Systems of Ordinary Differential Equations.-Linear equations.-Stability.-The theorem of Poincar?-Bendixson.-Exercises.-Appendix A: Mathematicians and other scientists.-References.-Index

From the reviews:"This is a comprehensive introduction to the study of functions of several variables that includes several areas not commonly included in comparable textbooks. ... The Current book has a generally broader scope ... . There is a huge amount of mathematics here, presented carefully and with style. ... The treatment of holomorphic functions here is nicely done ... . In the end, I find that this text would be an agreeable source for most of its individual topics ... ." (William J. Satzer, The Mathematical Association of America, August, 2009)Aus den Rezensionen:?"... Geschrieben von weltweit anerkannten Experten der modernen Theorie partieller Differentialgleichungen ... Die Expertise der Autoren zeigt sich auch in der Aufnahme von Themen, die sonst nicht zu finden sind ... Im Gegensatz zu manchen der oben genannten Bücher sind die Autoren einem leserfreundlichen Stil verpflichtet ..." (N. Ortner, in: IMN Internationale Mathematische Nachrichten, August/2010, S. 71)