Tuesday, April 8, 2014

12.4, due April 9

1. (difficult) Following the proofs of theorems 12.23, 12.24, 12.25, 12.26, and 12.27 was pretty difficult. After last class period, I now understand the purpose of the deltas, but now I am struggling particularly with the manipulation of delta1, delta2 and delta together to prove the theorems. However, I appreciate the tools that the theorems provide.
2. (reflective) Theorems 12.28-12.31 are applications of the above listed theorems. I can't see the broad application because they seem very specializes or specific to certain problem types rather than problems in general.

Sunday, April 6, 2014

12.3, due April 7

1. (difficult) I didn't understand the selection of delta in the last section, and delta becomes a much more used term in this section and in proving the limits of functions. I am starting to see the patterns that develop in choosing delta, but no real explanation has been given here either.
2. (reflective) Deleted neighborhoods is an interesting concept, and I think the name for it is what causes it to seem difficult at first, but is entirely easy to understand upon examination. The images they use to describe it remind me of function mapping from earlier sections.

Thursday, April 3, 2014

12.2, due April 4

1. (difficult) While trying to understand the proofs for convergence of an infinite series, I am having a hard time grasping the concept of epsilon ad it's necessity in the proof. I am also very confused by the notation in the book. It is possible that it is a misprint, but on page 275 directly above the second Lemma 12.8 It has an almost bracket looking symbol around 1/epsilon. I don't have a clue what that means.
2. (reflective) I am realizing as I am trying to understand these proofs how integral an understanding of epsilon is, and I don't know what it means, nor can I glean any sort of understanding from the text. All I know about it is that it is crucial to these proofs.

Tuesday, April 1, 2014

12.1, due April 2

1. (difficult) The proofs for divergence or convergence are difficult to follow, with many cases and new assumptions.
2. (reflective) Most of the work on these proofs is done in the proof strategy -  the proofs are relatively short. It seems like if you have a good strategy, you won't need to have a long proof.