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Titlebook: Mathematical Analysis; Approximation and Di Mariano Giaquinta,Giuseppe Modica Textbook 2004 Springer Science+Business Media New York 2004 C

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發(fā)表于 2025-3-21 19:57:07 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Mathematical Analysis
副標題Approximation and Di
編輯Mariano Giaquinta,Giuseppe Modica
視頻videohttp://file.papertrans.cn/626/625963/625963.mp4
概述This fairly self-contained work embraces a broad range of topics in analysis at the graduate level, requiring only a sound knowledge of calculus and the functions of one variable.Replete with beautifu
圖書封面Titlebook: Mathematical Analysis; Approximation and Di Mariano Giaquinta,Giuseppe Modica Textbook 2004 Springer Science+Business Media New York 2004 C
描述This volume! aims at introducing some basic ideas for studying approxima- tion processes and, more generally, discrete processes. The study of discrete processes, which has grown together with the study of infinitesimal calcu- lus, has become more and more relevant with the use of computers. The volume is suitably divided in two parts. In the first part we illustrate the numerical systems of reals, of integers as a subset of the reals, and of complex numbers. In this context we intro- duce, in Chapter 2, the notion of sequence which invites also a rethinking of the notions of limit and continuity2 in terms of discrete processes; then, in Chapter 3, we discuss some elements of combinatorial calculus and the mathematical notion of infinity. In Chapter 4 we introduce complex num- bers and illustrate some of their applications to elementary geometry; in Chapter 5 we prove the fundamental theorem of algebra and present some of the elementary properties of polynomials and rational functions, and of finite sums of harmonic motions. In the second part we deal with discrete processes, first with the process of infinite summation, in the numerical case, i.e., in the case of numerical series
出版日期Textbook 2004
關(guān)鍵詞Complex analysis: one variable; Probability theory; Taylor series; approximation/probability; calculus; d
版次1
doihttps://doi.org/10.1007/978-0-8176-4414-7
isbn_softcover978-0-8176-4337-9
isbn_ebook978-0-8176-4414-7
copyrightSpringer Science+Business Media New York 2004
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沙發(fā)
發(fā)表于 2025-3-21 23:49:04 | 只看該作者
Power Series,The manipulation of series reaches such levels of subtlety that is hard to imagine even nowadays in the works of Jacob Bernoulli (1654–1705), Johann Bernoulli (1667–1748) and Leonhard Euler (1707–1783), and particularly in the . by Jacob Bernoulli in . and in . by Euler.
板凳
發(fā)表于 2025-3-22 01:38:13 | 只看該作者
Discrete Processes,The laws of classical physics are .: if we know . the state of a system at a given instant, we know its state for all times. Such a principle, which mathematically corresponds to the ., has been (and is) a key idea in scientific thought. Pierre-Simon Laplace (1749–1827) wrote in his ..
地板
發(fā)表于 2025-3-22 08:24:11 | 只看該作者
Real Numbers and Natural Numbers,ll identify the natural numbers as the . ?. Further information about natural numbers will be discussed in Chapter 3, while the notions of . and of ., which are specially relevant in mathematics, are discussed in Chapter 2; in Section 2.2 we present, in particular, several equivalent formulations of the ..
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Sequences of Real Numbers, Greek mathematicians the process which generates the approximations ., ., ... never ends; for us, instead, such a process is the realization of . as the . {.}. In this chapter we shall discuss the notions of sequence and of limit of a sequence.
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https://doi.org/10.1007/978-0-8176-4414-7Complex analysis: one variable; Probability theory; Taylor series; approximation/probability; calculus; d
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