analysissyllabus - 5 Functions sequences and series(uniform...

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Topics for the Ph.D. Preliminary Examination ANALYSIS Fundamentals of Analysis (MAT 601-602) The basic material is contained in Rudin's "Principles of Mathematical Analysis" 3rd Edition, Chapters 1 through 9. Important topics are: 1. Properties of real and complex numbers. 2. Elementary topology of metric spaces: compactness, completeness, etc. 3. Numerical sequences and series. 4. Functions: continuity, differentiation, Riemann-Stieltjes integration.
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Unformatted text preview: 5. Functions: sequences and series (uniform convergence and applications, equicontinuous families, Stone-Weierstrass Theorems, power series). 6. Calculus of several variables: differentiation, Inverse and Implicit Function Theorems. References 1. Rudin (listed above). 2. W. Flemming, "Functions of Several Variables"....
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