MAT137 | Calculus!

L0601 (Beatriz's Slides)


Course Information

About this course

title Calculus!
code MAT137Y1Y
website http://uoft.me/MAT137

All information about the course will be posted in the official website.

Lecture Slides

I will be posting here any slides that we use in class. Notice that this only contains the slides, not a summary of the lectures. s

Lecture Slides from Beatriz's lectures (L0601)
lecture date topics videos
Logic and Proofs
Lecture 01
07 Sept. Why do we need proofs?
Sets and Notation. Intro to Quantifiers.
Sets and Notation ( 1.1, 1.2)
Quantifiers (1.3)

Lecture 02
12 Sept. Quantifiers.
Quantifiers (1.4 - 1.6)

Lecture 03
14 Sept. Conditionals. Definitions and Proofs.
Conditionals (1.7 - 1.9)
Definitions and Proofs (1.10 - 1.13)

Lecture 04
19 Sept. Proofs by Induction.
Induction. (1.14 - 1.15)
Limits and Continuity
Lecture 05
21 Sept. Inequalities and Absolute Value.
Inequalities and Abs. Value. (2.4)
Intro to Limits. (2.1 - 2.3)
Lecture 06
26 Sept. Limits. Definition of Limit.
Definition of Limit. (2.5)
Lecture 07
Handout
28 Sept. Limits. Some Limit Theorems.
Limits. (2.6 - 2.10)
Lecture 08
03 Oct. Squeeze Theorem. Some Trigonometric Limits.
Squeeze Theorem. (2.11 - 2.12, 2.17)
Lecture 09
05 Oct. Continuity.
(2.13 - 2.16)
Lecture 10
10 Oct. Trigonometric Limits. Itermediate Value Theorem (IVT) and Extreme Value Theorem (EVT).
(2.17 - 2.19)
Derivatives
Lecture 11
12 Oct. Derivatives.
(3.1-3.3)
Lecture 12
17 Oct. Differentiation Rule.
(3.4-3.7)
Lecture 13
19 Oct. Derivative of Trigonometric Functions. The Chain Rule. Implicit Differentiation.
(3.8-3.12)
Lecture 14
24 Oct. Derivative of Exponential and Logatithm.
(3.13-3.18)
Lecture 15
26 Oct. Inverse Functions I.
(4.1-4.5)
Lecture 16
31 Oct. Inverse Functions II. Inverse Trigonometric Functions.
(4.6-4.8)
Lecture 17
02 Nov. Related Rates. Local Extrema.
(5.1-5.4)
Lecture 18
14 Nov. Rolle's Theorem
(5.5-5.6)
Lecture 19
16 Nov. Applications of the Mean Value Theorem.
(5.7-5.12-)
Lecture 20
21 Nov. Optimization No Videos
Lecture 21
23 Nov. Indeterminate forms. L'Hopital's Rule. No video. Read pages 554-556 and 560-562 from the textbook.
Lecture 22
28 Nov. L'Hopital's Rule. No video.
Lecture 23
30 Nov. Concavity. Asymptotes. No video.
Lecture 24
05 Dec. Curve Sketching. No video.
Integration
Lecture 25
04 Jan. Sigma Notation. Infima and Suprema. 7.1 - 7.4
Lecture 26
09 Jan. Definition of the Integral. 7.5 - 7.7
Lecture 27
11 Jan. Definition of the Integral. Riemann Sums. 7.8 - 7.12
Lecture 28
16 Jan. Fundamental Theorem of Calculus. 8.1 - 8.4
Integration Methods
Lecture 29
18 Jan. Indefinite Integrals. Area. Sustitution Rule. 8.5 - 8.7. 9.1 - 9.4.
Lecture 30
23 Jan. Integration by Parts. 9.5-9.9.
Lecture 31
25 Jan. More Integration by parts. Intregral of Trig. Functions. Trig. Substitution. 9.10 - 9.15
Lecture 32
30 Jan. Partial Fractions. 9.16 - 9.18
Lecture 33
01 Feb. Volume. Integration Hodgepodge. No video. Section 6.2
Lecture 34
06 Feb. Volume by Shells with Assaf. No video. Section 6.3
Lecture 35
08 Feb Sequences (Part I) 11.1 - 11.3
Lecture 36
13 Feb Sequences (Part II) 11.4 - 11.6
Lecture 37
15 Feb Sequences (Part III) + Improper Integrals 11.6 - 11.8 + 12.1 - 12.5
Lecture 38
26 Feb Improper Integrals with Joel. 12.6 - 12.10

Resources

Extra Resources

Notes on Logic, Definitions, and Proofs.

Quantifiers. Conditionals. Definitions. Proofs. Mathematical Induction.

These are addtional notes that expand on the topics in the YouTube videos on logic, notation, definitions, and proofs.

Useful Links

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MAT137 Office Hours