Chapter 11 on infinite series and sequences is very different from the earlier material. It is much more theoretical. It is almost like we are starting a new course. It involves a very differnt way of thinking. You may need to double or triple your study time belofe you "get it."

The text does not have many applications. This can make it hard for some students to stay motivated. I'll try to do some applications in class, but, be forewarned, the applications can be messy in themselves.

• Section 11.1
  • [1] Definition: know & understand.
  • [2] Theorem: Know this easy fact.
  • [3] Know this.
  • [4] Definition: Know & understand.
  • Limit Laws for Sequences: Know these; be able to prove the frist and third.
  • Sqeeze Theorem for Sequences: Know & understand.
  • [5] Theorem: Know & be able to prove.
  • [7] (Theorem): Know and be able to prove.
  • [8] Definition: Know & understand.
  • [9] Definition: Know & understand.
  • [10] Monomtone Sequence Theorem: Know and understand pictorially.
• Section 11.2
  • [2] Definition: Know & understand.
  • [4] (Theorem): Know and be able to prove!
  • [5] A useful special case of [4].
  • [6] Theorem: Know and understand intuitively.
  • [7] The Test for Divergence: Know & understand.
  • [8] Theorem: Know and be able to prove (i) & (ii).
• Section 11.3
  • The Integral Test: Know & understand pictorially.
  • [1] (p-series theorem): Know and be able to prove using Integral Test.
  • [2] remainder Estimate for the Inegral Test: Know & be able to use.
• Section 11.4
  • The Comparison Test: Know and be able to prove.
  • The Limit Comparison Test: Know & try to understand pictorially.
• Section 11.5
  • The Alternating Series Test: Know & try to understand pictorially.
  • Alternating Series Estimation Theorem: Know.
• Section 11.6
  • [1] Definition: Know & understand.
  • [2] Definition: KNow & understand.
  • [3] Theorem: Know and be able to prove.
  • The Ratio Test: Know & be able use.
  • The Root Test: Know & be able to use.
• Section 11.7
  • Nothing new here.
• Section 11.8
  • [1] & [2]: Know these definitions.
  • [3] Theorem: Know this.
• Section 11.9
  • [2] Theorem: Know this simple theorem. (It looks messy, but is not.)
• Section 11.10
  • [5] & [6] are the same: They are of fundamental importance!
  • [7]: a useful special case of [6].
  • [8] Theorem: a minor factiod.
  • [9] Taylor's Inequality (usually called Taylor's Remainder Theorem): Know this and be able to use it.
  • [11] Know the this!! ([12] is the same thing.)
  • [15] Know this!
  • [16] Know this!
  • Ask me why e^it = cos(t)+i*sin(t).
  • Know the table on page 758.
• Section 11.11
  • [2] The Binomial Series: Know & be able to use.
• Section 11.12
  • No more theorems!