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--- math104-s22:s:jdamaj [2022/02/04 00:08]
50.115.87.182 [Homework]
+++ math104-s22:s:jdamaj [2022/05/12 19:55] (current)
jdamaj [Jad Damaj]
@@ Line 6: / Line 6: @@
-{{ :math104-s22:s:jdamaj:math_104.pdf | Course Notes}}
+{{  :math104-s22:s:jdamaj:104_notes.pdf | Course Notes}}
 ===== Course Journal =====
@@ Line 41: / Line 41: @@
   * Subseqeunces
   * Cantor's Diagonal trick to produce a convergent subsequence
+==== Feb 3 ====
+  * All sequences have a monotone subsequence
+  * All bounded sequences have a convergent (monotone) subsequence
+  * If  $S$  is the set of subsequential limits of  $s_n$ , then sup $S$  = limsup $s_n$  and inf $S$  = liminf $s_n$
+==== Feb 8 ====
+  * limsup(a_nb_n) = lim(a_n)limsup(b_n) for convergent series  $a_n$  with limit greater than 0
+  * Introduced Series
+  * "Sanity Check" and Comparison Test
+  * Root and Ratio Tests
+==== Feb 10 ====
+  * Series
+  * Summation by Parts
+  * Power Series
+==== 5 Questions ====
+  * What is a good way to approach coming up with inequalities to use in proof, as in the Rudin exercises this week.
+  * What are some good counterintuitive counterexamples to keep in mind when working on problems.
+  * What specific properties of absolute convergence should we be familiar with for the exam, eg. rearrangements etc.
+  * What properties does multiplication in limsup(a_nb_n) have in general.
+  * Is there a good way to get intuition for accumulation of infinite series, eg. the case of sum(1\n)
+==== February 22 ====
+  * Definition of Metric Space + examples
+  * Topology
+  * Open Sets
+==== February 24 ====
+  * More Metric Space examples
+  * Sequences + Cauchy Criterion
+  * Closure/ Closed Sets
+ ==== March 1 ====
+  * Continuous Maps (open cover def and sequential def)
+  * Inherited Topology
+==== March 3 ====
+  * Open cover compactness
+  * Sequential compactness
+==== March 8 ====
+  * Sequential Compactness  $\to$  Open Cover Compactness
+==== March 10 ====
+  * Connectedness
+==== March 15 ====
+  * Continuous maps preserve compactness and connectedness
+  * Uniform Continuity
+  * Discontinuity
+==== March 17 ====
+  * Sequences and Series of Functions
+  * Uniform Convergence
+==== March 29 ====
+  * Differentiation
+  * Rolle's Theorem
+==== March 31 ====
+  * Generalized Mean Value Theorem
+  * L'Hopital's rule
+==== April 7 ====
+  * Higher Derivatives
+  * Taylor's Theorem
+==== April 12 ====
+  * Taylor Series
+  * Power Series
+  * Reimann Integral
+==== April 14 ====
+  * Integration
+  * Reimann - Stieltjes Integral
+==== April 19 ====
+   *  Reimann - Stieltjes Integral
+==== April 21 ====
+  * Properties of Integrals
+==== April 26 ====
+  * Uniform Convergence with Integration
+  * Uniform Convergence with Differentiation
 ===== Homework =====
@@ Line 46: / Line 134: @@
   * {{ :math104-s22:s:jdamaj:math_104_hw2.pdf |Hw 2}}
   * {{ :math104-s22:s:jdamaj:math_104_hw3.pdf |Hw 3}}
+  * {{ :math104-s22:s:jdamaj:math_104_hw4.pdf |Hw 4}}
+  * {{ :math104-s22:s:jdamaj:math_104_hw5.pdf |Hw 5}}
+  * {{ :math104-s22:s:jdamaj:math_104_hw6.pdf |Hw 6}}
+  * {{ :math104-s22:s:jdamaj:math_104_hw7.pdf |Hw 7}}
+  * {{ :math104-s22:s:jdamaj:math_104_hw8.pdf |Hw 8}}
+  * {{ :math104-s22:s:jdamaj:math_104_hw9.pdf |Hw 9}}
+  * {{ :math104-s22:s:jdamaj:math_104_hw10.pdf |Hw 10}}
+  * {{ :math104-s22:s:jdamaj:math_104_hw11.pdf |Hw 11}}

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