森田茂之さんの本なので期待はしていませんが。 0494１３２人目の素数さん2018/08/25(土) 20:14:56.58ID:RnpU6cYx スチュワート微分積分学II(原著第8版): 微積分の応用 J. Stewart 固定リンク: http://amzn.asia/d/5rz3d66
↑IIが発売されますね。 0495１３２人目の素数さん2018/08/25(土) 20:17:19.89ID:RnpU6cYx Mathematical Analysis I (Universitext) by V. A. Zorich et al. Link: http://a.co/d/bOq8XgH
Mathematical Analysis II (Universitext) by V. A. Zorich et al. Link: http://a.co/d/aAaRfnn
↑Zorich さんの本ってどうですか？ 0496１３２人目の素数さん2018/08/25(土) 20:21:13.97ID:RnpU6cYx This second edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems, and fresh applications to areas seldom touched on in textbooks on real analysis.
The main difference between the second and first editions is the addition of a series of appendices to each volume. There are six of them in the first volume and five in the second. The subjects of these appendices are diverse. They are meant to be useful to both students (in mathematics and physics) and teachers, who may be motivated by different goals. Some of the appendices are surveys, both prospective and retrospective. The final survey establishes important conceptual connections between analysis and other parts of mathematics.
The first volume constitutes a complete course in one-variable calculus along with the multivariable differential calculus elucidated in an up-to-date, clear manner, with a pleasant geometric and natural sciences flavor.
This second volume presents classical analysis in its current form as part of a unified mathematics. It shows how analysis interacts with other modern fields of mathematics such as algebra, differential geometry, differential equations, complex analysis, and functional analysis. This book provides a firm foundation for advanced work in any of these directions. 0497１３２人目の素数さん2018/08/25(土) 20:37:22.75ID:RnpU6cYx “The textbook of Zorich seems to me the most successful of the available comprehensive textbooks of analysis for mathematicians and physicists. It differs from the traditional exposition in two major ways: on the one hand in its closer relation to natural-science applications (primarily to physics and mechanics) and on the other hand in a greater-than-usual use of the ideas and methods of modern mathematics, that is, algebra, geometry, and topology. The course is unusually rich in ideas and shows clearly the power of the ideas and methods of modern mathematics in the study of particular problems. Especially unusual is the second volume, which includes vector analysis, the theory of differential forms on manifolds, an introduction to the theory of generalized functions and potential theory, Fourier series and the Fourier transform, and the elements of the theory of asymptotic expansions. At present such a way of structuring the course must be considered innovative. It was normal in the time of Goursat, but the tendency toward specialized courses, noticeable over the past half century, has emasculated the course of analysis, almost reducing it to mere logical justifications. The need to return to more substantive courses of analysis now seems obvious, especially in connection with the applied character of the future activity of the majority of students.
...In my opinion, this course is the best of the existing modern courses of analysis.”
From a review by V.I.Arnold 0498１３２人目の素数さん2018/08/25(土) 20:39:10.60ID:RnpU6cYx the course of analysis, almost reducing it to mere logical justifications.
↑日本語の微分積分の本ってそういう本ばかりですよね。 0499１３２人目の素数さん2018/08/25(土) 20:41:16.07ID:RnpU6cYx It was normal in the time of Goursat, but the tendency toward specialized courses, noticeable over the past half century, has emasculated the course of analysis, almost reducing it to mere logical justifications.
a が closure(A) の集積点であるとすれば、 a の任意の近傍 (a - ε, a + ε) は、 a と異なる closure(A) の点を含む。それを b とする。 a - ε < b < a + ε であるから、いま、
ε' = min{ b - (a - ε), (a + ε) - b } とすれば ε' > 0 で、 b の近傍 (b - ε', b + ε') は無限 に多くの A の点を含む。 」 0515１３２人目の素数さん2018/08/26(日) 12:52:56.74ID:+e+/Bm3M ↑では、位相空間 R を考えています。 0516１３２人目の素数さん2018/08/26(日) 12:59:54.76ID:+e+/Bm3M A := (0, 1) ∪ {2}
