# 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. 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. Past-year students found the online forum a useful resource. MAT137 Office Hours