Lecture Notes

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====== Yanbing Jiang  ======
I am majoring in Applied Math and the classes I've taken were Math53, Math54, Math55, Math110, and Math128A.



===== Course Journal =====

=== Jan 18th ===



=== Jan 20th ===


===== Homework =====
{{ :math104-s22:s:math104_hw1_.pdf |}}

{{ :math104-s22:s:hw2.pdf |}}

{{ :math104-s22:s:hw3.pdf |}}

{{ :math104-s22:s:math104_hw4.pdf |}}

{{ :math104-s22:s:math104_hw5.pdf |}}

{{ :math104-s22:s:hw6.pdf |}}

{{ :math104-s22:s:hw7.pdf |}}

{{ :math104-s22:s:hw8.pdf |}}

{{ :math104-s22:s:hw9.pdf |}}

{{ :math104-s22:s:hw10.pdf |}}

{{ :math104-s22:s:hw11.pdf |}}



Q's:
 
1. In the proof of Cantor's diagonalization argument in midterm 1 review, why do we highlight a_n11 in the subsequence set A={n11, n12, ...}, a_n22 in the subsequence set A={n21, n22, ...},a_33 ...? What is the motivation behind this?

2. Can anyone explain the thought process of coming up with the series that is diverging by the Root test but no info for the Ratio test (as in HW4 problem 14.10)? Any trick for tackling this kind of problem? 

3. In the proof of Thm9.1 "Convergent sequences are bounded" in lec3, why do we set M1 = max{...}, M2 = max{...}? Why do we use the max? Is it a necessary step in completing the proof or there is also an alternative approach that can achieve this proof? 

4. For HW4 problem 6d), how can we show if the series a_n is convergent/divergent for the case in which |z|>1?

5. Can someone explain figure 11.1 on P70 Ross? What is figure 11.1 trying to show?

Lecture Notes

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