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ADVANCED CALCULUS - University of Alabama at Birmingham

ADVANCED CALCULUSL ecture notes forMA 440/540 & 441/5412015/16 Rudi Weikard12345x-2-11logHxLBased on lecture notes by G. Stolz and G. WeinsteinVersion of September 3, 20161 ContentsFirst things The The The language of mathematics3 Chapter 1. The real Field Order The induction Counting and The least upper bound axiom11 Chapter 2. Sequences and Sums and the Series18 Chapter 3. A zoo of functions23 Chapter 4. Limits of Continuous The intermediate value theorem and some of its Uniform convergence and continuity29 Chapter 5. The mean value theorem and Taylor s Uniform convergence and differentiation36 Chapter 6.

the presentation while the other 6 are evenly distributed among the collaborators. (10)The successor of a presenter will be chosen as the student with the smallest number of points among the volunteers taking into account the modi cation by …

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