Youtube Channels: Wrath of Math: Large Real Analysis Playlist that goes over many definitions and proof explanations. 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:

1. Real Numbers
2. Sequences
3. Topology
4. Series
5. Limits and Continuity

Link to Dr. Peyam's Youtube playlists

Other Misc. Links :

Ross Chapter 1

1. §1 The set N of Natural Numbers
2. §2 The set Q of Rational Numbers
3. §3 The Set R of Real Numbers
4. §4 The completeness Axiom

Link to Textbook Notes: midterm_1_ch_1.pdf

Ross Chapter 2

1. §7 Limits of Sequences
2. §9 Limit Therorems for Sequences
3. §10 Monotone Sequences and Cauchy Sequences
4. §11 Subsequences
5. §12 lim sup's and lim inf's
6. Exrta: Intro to Proofs

Link to Textbook Notes: midterm_1_ch_2.pdf

Rudin Ch.2, Ross §13

Rudin Ch.2 Basic Topology

1. Finite, Countable, and Uncountable Sets
2. Metric Spaces
3. Compact Sets
4. Perfect Sets
5. Connected Sets

Ross Ch 2. Sequences §13 *Some Topological Concepts in Metric Spaces

Link to Textbook Notes: rudin_ch_2_ross_13.pdf

Ross Ch 2. Sequences

1. §14 Series
2. §15 Alternating Series and Integral Tests

Link to Textbook Notes: ross_14_15.pdf

Rudin Ch. 4 Continuity

1. Limits of Functions
2. Continuous Functions
3. Continuity and Compactness
4. Continuity and Connectedness
5. Discontinuities
6. Montotonic Functions
7. Infinite Limits and Limits at Infinity

Link to Textbook Notes: rudin_ch_4.pdf

Ross Ch. 4 §24, §25, §26; Rudin Ch. 7 (sections 1-2)

Ross Ch. 4 - Sequences and Series of Functions

1. §24 Uniform Convergence
2. §25 More on Uniform Convergence
3. §26 Differentiation and Integration of Power Series

Rudin Ch. 7 - Sequences and Series of Functions

1. Uniform Convergence
2. Uniform Convergence and Continuity

Link to Textbook Notes: ross_24_25_26_rudin_7.pdf

Rudin Ch. 5 - Differentiation

1. The Derivative of Real Functions
2. Mean Value Theorems
3. The Continuity of Derivatives
4. L'Hospital's Rule
5. Derivatives of Higher Order
6. Taylor's Theorem

rudin_chapter_5.pdf

Rudin Ch. 6 - The Riemann-Stieltjes Integral

1. Definition and Existence of the Integral
2. Properties of the Integral
3. Integration and Differentiation

rudin_chapter_6.pdf

Rudin Ch. 7 - Sequences and Series of Functions 7.16-7.18

1. Uniform Convergence and Continuity
2. Uniform Convergence and Integration

rudin_chapter_7.pdf