Real Analysis

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American Mathematical Soc., 2005 - Mathematics - 151 pages
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This book is written by award-winning author, Frank Morgan. It offers a simple and sophisticated point of view, reflecting Morgan's insightful teaching, lecturing, and writing style. Intended for undergraduates studying real analysis, this book 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. This concise text not only provides efficient proofs, but also shows students how to derive them. The excellent exercises are accompanied by select solutions. Ideally suited as an undergraduate textbook, this complete book on real analysis will fit comfortably into one semester. Frank Morgan received the first Haimo Award for distinguished college teaching from the Mathematical Association of America. He has also garnered top teaching awards from Rice University (Houston, TX) and MIT (Cambridge, MA).

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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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