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Lecture
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Date |
Read Sections |
Topics |
Handouts & Lecture Notes |
0
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Wednesday, January 3
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NO CLASS
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NO CLASS
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1
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Friday, January 5
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Review
Appendices
A & B
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Course Introduction
Notation and Mathematical Logic
Real, Rational and Irrational Numbers
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M35 General Notation.pdf
Download M35 General Notation.pdf
Real Analysis Appendix A-B.pdf
Download Real Analysis Appendix A-B.pdf
M35 Lecture 1 Notes.pdf
Download M35 Lecture 1 Notes.pdf
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2
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Monday, January 8
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1.1
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What is a Real Number?
Fields and Ordered Sets
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Real_Analysis_pp_1-29.pdf
Download Real_Analysis_pp_1-29.pdf
M35 Lecture 2 Notes.pdf
Download M35 Lecture 2 Notes.pdf
Rational Number Problem.pdf
Download Rational Number Problem.pdf
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3
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Wednesday, January 10
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1.2
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Absolute Value, Intervals and Inequalities
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M35 Lecture 3 Notes.pdf
Download M35 Lecture 3 Notes.pdf |
4
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Friday, January 12
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1.3
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Supremum and Infimum of Sets
Completeness Axiom
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M35 Lecture 4 Notes.pdf
Download M35 Lecture 4 Notes.pdf |
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Monday, January 15
|
|
Martin Luther King Day
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NO CLASS
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5
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Tuesday, January 16
x-hour
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1.3 |
Completeness Axiom (cont'd)
Archimedean Property of ℝ
Existence of Square Roots in ℝ
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Ordered Fields and LUB Property.pdf
Download Ordered Fields and LUB Property.pdf
Existence of Square Roots.pdf
Download Existence of Square Roots.pdf
LUB Consequences.pdf
Download LUB Consequences.pdf
M35 Lecture 5 Notes.pdf
Download M35 Lecture 5 Notes.pdf |
6
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Wednesday, January 17
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1.4
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Countable and Uncountable Sets
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Hopcroft-Ullman Pairing Function.pdf
Download Hopcroft-Ullman Pairing Function.pdf
M35 Lecture 6 Notes.pdf
Download M35 Lecture 6 Notes.pdf
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7
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Friday, January 19
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1.4 |
Countable and Uncountable Sets (cont'd)
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To Infinity and Beyond.pdf
Download To Infinity and Beyond.pdf
M35 Lecture 7 Notes.pdf
Download M35 Lecture 7 Notes.pdf
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8
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Monday, January 22
|
2.1 |
Sequences and Convergence |
M35 Lecture 8 Notes.pdf
Download M35 Lecture 8 Notes.pdf
NB: Very different from class!
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9
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Wednesday, January 24
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2.1 |
Sequences and Convergence (cont'd) |
M35 Lecture 9 Notes.pdf
Download M35 Lecture 9 Notes.pdf |
10
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Friday, January 26
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2.2 |
Unbounded, Monotone and Cauchy Sequences
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M35 Lecture 10 Notes.pdf
Download M35 Lecture 10 Notes.pdf |
11
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Monday, January 29
|
2.2 |
Cauchy Sequences (Cont'd)
Cauchy Completeness of ℝ
Nested Intervals Theorem
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M35 Lecture 11 Notes.pdf
Download M35 Lecture 11 Notes.pdf
Cauchy Sequence Proof.pdf
Download Cauchy Sequence Proof.pdf
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12
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Wednesday, January 31
|
2.3 |
Subsequences
|
M35 lecture 12 Notes.pdf
Download M35 lecture 12 Notes.pdf
Sequences of Real Numbers.pdf
Download Sequences of Real Numbers.pdf
Monotone Sequences in the Reals.pdf
Download Monotone Sequences in the Reals.pdf
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13
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Friday, February 2
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Handouts |
The Cantor Set
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M35 Lecture 13 Notes.pdf
Download M35 Lecture 13 Notes.pdf
Cantor Set pp 318-19.pdf
Download Cantor Set pp 318-19.pdf
Cantor Set Handout.pdf
Download Cantor Set Handout.pdf
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Monday, February 5
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Midterm Exam Review |
Come to ask questions! |
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Wednesday, February 7
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Midterm Exam (In-class Part)
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Important Analysis Theorems.pdf
Download Important Analysis Theorems.pdf |
14
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Friday, February 9
|
3.1 |
Limit of a Function |
M35 Lecture 14 Notes.pdf
Download M35 Lecture 14 Notes.pdf |
15
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Monday, February 12
|
3.1 |
Limit of a Function (cont'd) |
Limit of a Function.pdf
Download Limit of a Function.pdf
M35 Lecture 15 Notes.pdf
Download M35 Lecture 15 Notes.pdf
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16
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Wednesday, February 14
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3.1 |
One-sided Limits
Limits at Infinity
Infinite Limits
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M35 Lecture 16 Notes.pdf
Download M35 Lecture 16 Notes.pdf |
17
|
Friday, February 16
|
3.2 |
Continuity |
M35 Lecture 17 Notes.pdf
Download M35 Lecture 17 Notes.pdf |
18
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Monday, February 19
|
3.2 |
Continuity (Cont'd) |
Continuity and Discontinuity.pdf
Download Continuity and Discontinuity.pdf
Continuity of Trig Functions.pdf
Download Continuity of Trig Functions.pdf
M35 Lecture 18 Notes.pdf
Download M35 Lecture 18 Notes.pdf
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19
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Tuesday, February 20
x-hour
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3.3 |
Intermediate & Extreme Value Thms |
M35 Lecture 19 Notes.pdf
Download M35 Lecture 19 Notes.pdf |
20
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Wednesday, February 21
|
3.4 |
Uniform Continuity |
Three Pillars of Continuity.pdf
Download Three Pillars of Continuity.pdf
M35 Lecture 20 Notes.pdf
Download M35 Lecture 20 Notes.pdf
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21
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Friday, February 23
|
4.1 |
The Derivative of a Function |
M35 Lecture 21 Notes.pdf
Download M35 Lecture 21 Notes.pdf
Common Derivatives.pdf
Download Common Derivatives.pdf
Differentiation Formulas.pdf
Download Differentiation Formulas.pdf
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22
|
Monday, February 26
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4.2 |
Rolle's Theorem and the Mean Value Theorem |
Mean Value Theorem Handout.pdf
Download Mean Value Theorem Handout.pdf
M35 Lecture 22 Notes.pdf
Download M35 Lecture 22 Notes.pdf
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23
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Tuesday, February 27
x-hour
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5.1 |
The Riemann Integral |
M35 Lecture 23 Notes.pdf
Download M35 Lecture 23 Notes.pdf
The Riemann Integral (Part 1).pdf
Download The Riemann Integral (Part 1).pdf
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24
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Wednesday,February 28
|
5.1 |
The Riemann Integral (cont'd) |
Integrability_Proof.pdf
Download Integrability_Proof.pdf
The Riemann Integral (Part 2).pdf
Download The Riemann Integral (Part 2).pdf
M35 Lecture 24 Notes.pdf
Download M35 Lecture 24 Notes.pdf
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25
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Friday, March 1
|
5.2 |
Conditions for Riemann Integrability |
Theorem 5.10 Animation Handout.pdf
Download Theorem 5.10 Animation Handout.pdf
Infinitely Many Discontinuities Example.pdf
Download Infinitely Many Discontinuities Example.pdf
M35 Lecture 25 Notes.pdf
Download M35 Lecture 25 Notes.pdf
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26
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Monday, March 4
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5.3 |
The Fundamental Thm of Calculus |
The Riemann Integral (Part 3).pdf
Download The Riemann Integral (Part 3).pdf
M35 Lecture 26 Notes.pdf
Download M35 Lecture 26 Notes.pdf
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Tuesday, March 5
x-hour
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Final Exam Review Session |
Come to ask questions! |
