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
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.  (3.13.3) 
Lecture 12  17 Oct.  Differentiation Rule.  (3.43.7) 
Lecture 13  19 Oct.  Derivative of Trigonometric Functions. The Chain Rule. Implicit Differentiation.  (3.83.12) 
Lecture 14  24 Oct.  Derivative of Exponential and Logatithm.  (3.133.18) 
Lecture 15  26 Oct.  Inverse Functions I.  (4.14.5) 
Lecture 16  31 Oct.  Inverse Functions II. Inverse Trigonometric Functions.  (4.64.8) 
Lecture 17  02 Nov.  Related Rates. Local Extrema.  (5.15.4) 
Lecture 18  14 Nov.  Rolle's Theorem  (5.55.6) 
Lecture 19  16 Nov.  Applications of the Mean Value Theorem.  (5.75.12) 
Lecture 20  21 Nov.  Optimization  No Videos 
Lecture 21  23 Nov.  Indeterminate forms. L'Hopital's Rule.  No video. Read pages 554556 and 560562 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.  9.59.9. 
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. See Page 11 for Cylindrical Shells.  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 
Lecture 39  01 March  Improper Integrals and Series.  12.8  12.10 + 13.1  13.4 
Lecture 40  06 Feb  More Series.  13.5  13.8 
Lecture 41  08 March  Convergence Tests  13.9  13.14 
Lecture 42  13 March  Absolute Convergence  13.15  13.17 
Lecture 43  15 March  Ratio Test. Power Series.  13.18  13.19 and 14.1  14.2 
Lecture 44  20 March  Taylor Polynomials.  14.3  14.5 
Lecture 45  22 March  Taylor Series.  14.6  14.8 
Lecture 46  27 March  Taylor Series II.  14.9  14.10 
Lecture 47  29 March  Taylor Series  Applications.  14.11  14.14 
Lecture 48  03 April  Taylor Series  More Applications.  14.11  14.14 
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
Piazza
There is an online forum for this course on Piazza. This group is a resource for students to meet other MAT137 students, ask questions, discuss problems, make study groups, and in general help each other. Pastyear students found the online forum a useful resource. 

MAT137 Office Hours 