Real Analysis (Google eBook)

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American Mathematical Soc., 2005 - Mathematics - 151 pages
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Real Analysis builds the theory behind calculus directly from the basic concepts of real numbers, limits, and open and closed sets in $\mathbb{R}^n$. It gives the three characterizations of continuity: via epsilon-delta, sequences, and open sets. It gives the three characterizations of compactness: as ``closed and bounded,'' via sequences, and via open covers. Topics include Fourier series, the Gamma function, metric spaces, and Ascoli's Theorem. The text not only provides efficient proofs, but also shows the student how to come up with them. The excellent exercises come with select solutions in the back. Here is a real analysis text that is short enough for the student to read and understand and complete enough to be the primary text for a serious undergraduate course. Frank Morgan is the author of five books and over one hundred articles on mathematics. He is an inaugural recipient of the Mathematical Association of America's national Haimo award for excellence in teaching. With this book, Morgan has finally brought his famous direct style to an undergraduate real analysis text.
  

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Capítulo 17: Sequencias de funções

Contents

III
3
IV
9
V
13
VI
21
VII
25
VIII
27
IX
33
X
35
XXIII
81
XXIV
85
XXV
89
XXVII
93
XXVIII
99
XXIX
105
XXX
109
XXXI
111

XI
37
XII
41
XIII
45
XIV
47
XV
49
XVI
53
XVII
59
XVIII
61
XIX
65
XX
71
XXII
75
XXXII
115
XXXIII
119
XXXIV
121
XXXV
125
XXXVI
129
XXXVII
133
XXXVIII
137
XXXIX
147
XL
149
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About the author (2005)

Frank Morgan, M.D., is the author of Ruth and Esther: Shadows of our Future, and the soon coming book, The Watchmen's Cry. He is a family physician with a busy practice in Northern Colorado, and is married with five children. After heartbreaking personal failures left him broken emotionally and spiritually, Frank had a life-changing encounter with the God of Israel. Realizing that blindly following traditional church doctrines had not protected him from his own fallen nature, the author began to earnestly search out the ways of God. For the past several years, Frank has carefully examined matters of law and grace and has developed a keen interest in eschatology. It was through his study of the end times that Frank came to the startling realization of our identity as Believers in Messiah Yeshua. This realization has led to a deeper love for the God of Israel and for His instruction, the Torah. Morgan's desire to better understand the end-times is unique in that he writes with an understanding of both the houses of Israel, Ephraim and Judah (Isa 8:14). His works issue a a clarion call for those of Ephraim to arise, to love their brother, Judah, and to respond to their high call in the Messiah. One also hears a heart cry for the restoration of the whole house of Israel.

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