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MAT 3751 Analysis II

MAT 3751 Analysis II. 8.2+8.4 Sequences. http://myhome.spu.edu/lauw. References. Bloch 8.2, 8.4 Read 8.3 for Friday. HW. No HW. Two Approaches for Real Analysis. Two Approaches for Real Analysis.

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MAT 3751 Analysis II

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  1. MAT 3751Analysis II 8.2+8.4 Sequences http://myhome.spu.edu/lauw

  2. References • Bloch 8.2, 8.4 • Read 8.3 for Friday

  3. HW • No HW

  4. Two Approaches for Real Analysis

  5. Two Approaches for Real Analysis • We will walk through some of the important aspects of sequences without going into all the details.

  6. Sequence

  7. Limit (Duct Tape?)

  8. Logic Symbols

  9. Example 1

  10. Lemma 8.2.3

  11. Bounded Sequences

  12. Two Equivalent Conditions

  13. Lemma 8.2.6

  14. Converse

  15. Lemma 8.2.7

  16. Theorem 8.2.9

  17. Theorem 8.2.11

  18. Theorem 8.2.12 (Squeeze Theorem for Sequences) .

  19. Diverges to Infinities

  20. Theorem 8.4.1 (Sequential Characterization of Limits)

  21. Theorem 8.4.1 (Sequential Characterization of Limits)

  22. Corollary 8.4.2 (Sequential Characterization of Continuity)

  23. Theorem 8.4.4

  24. Final Exam –Take Home • Design to see to access your comprehension of the materials we covered in this class. • All questions are labeled with the section it is related. Do not use any results from the lecture or textbook after the given section. • Make sure you do not have irrelevant materials in your proofs. Points will be taken off for irrelevant materials.

  25. Final Exam –Take Home • 80 points • 6 problems • As usual, type all your solutions • Due 5pm on Friday 3/21 • Note that this is the absolute deadline. I am expecting most of you will finish and turn in your paper before that.

  26. Final Exam – In Class • 40 points • Focus on materials after the first exam (>=section 5.4). • You still need to know some of the background materials from the first exam.

  27. In Class: Optional Substitution • You may opt for a substitution of additional take home problems for the in class exam. • 3 problems (40 points) • Due 5pm on Friday 3/21 • Once you opt for this option, you cannot go back and take the in class exam. • Your request need to be made by 5pm tomorrow. (By default, you will do the in class exam.)

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