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--- math104-s21:s:thomasdahlke [2021/05/08 20:00]
135.180.145.79 created
+++ math104-s21:s:thomasdahlke [2026/02/21 14:41] (current)
@@ Line 3: / Line 3: @@
 Notes are organized by topic collected together with both Ross and Rudin.
+====== Thomas Dahlke ======
+===== Links to resources and rages I have found helpful:  =====
+Youtube Channels:
+Wrath of Math: Large Real Analysis Playlist that goes over many definitions and proof explanations.
+ [[https://www.youtube.com/playlist?list=PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli|Link to W.o.M. youtube playlist]]
+Dr. Peyam (Used to teach math at UC Berkeley!): Extremely large bank of Real and Complex Analysis. Videos are broken up by topic where he goes into more explanation and examples for each subject.
+Topics with sub-playlists include:
+  - Real Numbers
+  - Sequences
+  - Topology
+  - Series
+  - Limits and Continuity
+[[https://www.youtube.com/c/DrPeyam/playlists|Link to Dr. Peyam's Youtube playlists ]]
+Other Misc. Links :
 ====== Midterm #1 ======
@@ Line 12: / Line 35: @@
   - §4 The completeness Axiom
 Link to Textbook Notes:
-{{ :math104:s:midterm_1_ch_1.pdf |}}
+{{ math104-s21:s:midterm_1_ch_1.pdf |}}
 Ross Chapter 2
@@ Line 22: / Line 45: @@
   - Exrta: Intro to Proofs
 Link to Textbook Notes:
-{{ :math104:s:midterm_1_ch_2.pdf |}}
+{{ math104-s21:s:midterm_1_ch_2.pdf |}}
 ====== Midterm #2 ======
+Rudin Ch.2, Ross §13
+Rudin Ch.2 Basic Topology
+  - Finite, Countable, and Uncountable Sets
+  - Metric Spaces
+  - Compact Sets
+  - Perfect Sets
+  - Connected Sets
+Ross Ch 2. Sequences
+§13 *Some Topological Concepts in Metric Spaces
+Link to Textbook Notes: {{ math104-s21:s:rudin_ch_2_ross_13.pdf |}}
+Ross Ch 2. Sequences
+  - §14 Series
+  - §15 Alternating Series and Integral Tests
+Link to Textbook Notes: {{ math104-s21:s:ross_14_15.pdf |}}
+Rudin Ch. 4 Continuity
+  - Limits of Functions
+  - Continuous Functions
+  - Continuity and Compactness
+  - Continuity and Connectedness
+  - Discontinuities
+  - Montotonic Functions
+  - Infinite Limits and Limits at Infinity
+Link to Textbook Notes: {{ math104-s21:s:rudin_ch_4.pdf |}}
+Ross Ch. 4 §24, §25, §26; Rudin Ch. 7 (sections 1-2)
+Ross Ch. 4 - Sequences and Series of Functions
+  - §24 Uniform Convergence
+  - §25 More on Uniform Convergence
+  - §26 Differentiation and Integration of Power Series
+Rudin Ch. 7 - Sequences and Series of Functions
+  - Uniform Convergence
+  - Uniform Convergence and Continuity
+Link to Textbook Notes: {{ math104-s21:s:ross_24_25_26_rudin_7.pdf |}}
+====== Midterm 2 - Final  ======
+Rudin Ch. 5 - Differentiation
+  - The Derivative of Real Functions
+  - Mean Value Theorems
+  - The Continuity of Derivatives
+  - L'Hospital's Rule
+  - Derivatives of Higher Order
+  - Taylor's Theorem
+{{ math104-s21:s:rudin_chapter_5.pdf |}}
+Rudin Ch. 6 - The Riemann-Stieltjes Integral
+   - Definition and Existence of the Integral
+   - Properties of the Integral
+   - Integration and Differentiation
+{{ math104-s21:s:rudin_chapter_6.pdf |}}
+Rudin Ch. 7 - Sequences and Series of Functions 7.16-7.18
+  - Uniform Convergence and Continuity
+  - Uniform Convergence and Integration
+{{ math104-s21:s:rudin_chapter_7.pdf |}}

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