Webpage of the section LEC0501 of MAT137: "Calculus!" at UofT

Information

Instructor Jean-Baptiste (JB) Campesato
E-Mail campesat [@t) math.toronto.edu
Schedule (Fall term) Monday, 4pm to 5pm
Wednesday, 4pm to 6pm
Room MP102
(The room changed for this term)
MAT137 Website http://uoft.me/MAT137

1. Introduction to mathematical logic, quantifiers, definitions and proofs

Video playlist for this part

Date Topics Required videos Textbook sections Lecture slides
Mon, Sep 10 Introduction --- --- slides - notes about slide 8
Wed, Sep 12 Sets and quantifiers 1.1, 1.2, 1.3, 1.4, 1.5, 1.6 1.1, 1.2, 1.3 slides - printable
Mon, Sep 17 Conditional statements 1.7, 1.8, 1.9 1.3 slides - printable
Wed, Sep 19 Definitions, proofs and induction 1.10, 1.11, 1.12, 1.13, 1.14, 1.15 1.4 slides - printable

2. Limits and continuity

Video playlist for this part

Date Topics Required videos Textbook sections Lecture slides
Mon, Sep 24 Absolute value, distance and inequalities 2.4 1.2, 1.8 slides - printable
Wed, Sep 26 Limits 2.1, 2.2, 2.3, 2.5, 2.6 2.1, 2.2 slides - printable
Mon, Oct 1 Proofs using the definition of limits 2.7, 2.8, 2.9 2.2 slides - printable - notes about slide 6
Wed, Oct 3 Limit laws 2.10, 2.11, 2.12, 2.13 2.3 slides - printable - notes about slide 8
Wed, Oct 10 Continuity 2.14, 2.15, 2.16, 2.17, 2.18 2.4 slides - printable
Mon, Oct 15 Some limit computations 2.19, 2.20 2.1, 2.3, 2.4 slides - printable
Wed, Oct 17 (1st part) IVT and EVT 2.21, 2.22 2.5 slides - printable

3. Derivatives

Video playlist for this part

Date Topics Required videos Textbook sections Lecture slides
Wed, Oct 17 (2nd part) Definition of a derivative 3.1, 3.2, 3.3 3.1 slides - printable
Mon, Oct 22 Differentiation rules 3.4, 3.5, 3.6, 3.7, 3.8, 3.9 3.1, 3.2, 3.3 slides - printable
Wed, Oct 24 The chain rule + more on differentiation rules 3.10 3.5 + 3.1, 3.2, 3.3 slides - printable
Mon, Oct 29 Trig derivatives, implicit differentiation 3.11, 3.12 3.4, 3.7 slides - printable
Wed, Oct 31 Related rates + derivatives of exponentials and logarithms 3.13, 3.14, 3.15, 3.16, 3.17, 3.18, 3.19, 3.20 3.4, 3.6, 3.7, 4.7 slides - printable

You have to watch a lot of videos for Wednesday, Oct 31. Even if they are short, you shouldn't wait for the last time to watch them.

4. Inverse functions and inverse trigonometric functions

Video playlist for this part

Date Topics Required videos Textbook sections Lecture slides
Mon, Nov 12 Inverse functions 4.1, 4.2 1.5, 1.7 slides - printable
Wed, Nov 14 One-to-one functions and inverse trig functions 4.3, 4.4, 4.5, 4.6, 4.7, 4.8 1.7, 3.5, 3.6 slides - printable

5. The Mean Value Theorem and applications

Video playlist for this part

Date Topics Required videos Textbook sections Lecture slides
Mon, Nov 19 Local extrema 5.1, 5.2, 5.3, 5.4 4.1 slides - printable - notes about slide 4
Wed, Nov 21 Rolle's Theorem and the MVT 5.5, 5.6, 5.7, 5.8, 5.9 4.2 slides - printable - notes about slide 7
Mon, Nov 26 Monotonicity 5.10, 5.11, 5.12 4.3 slides - printable

6. Applications of the derivative

Video playlist for this part

Warning: I modified the order of the two first lectures.

Date Topics Required videos Textbook sections Lecture slides
Wed, Nov 28 Indeterminate forms and L'Hôpital's Rule (6.3), 6.4, 6.5, (6.6), 6.7, 6.8, (6.9), 6.10 4.4, 4.5, 4.6 slides - printable
Mon, Dec 3 Applied optimization 6.1, 6.2 4.8 slides - printable
Wed, Dec 5 Concavity and asymptotes 6.11, 6.12, 6.13, 6.14, 6.15, 6.16 2.1, 4.9 slides
Thu, Dec 6
Thanksgiving make up
Curve sketching 4.9 slides - printable

7. Integral: a definition and first properties

Video playlist for this part

Date Topics Required videos Lecture slides
Mon, Jan 7 Summation and the Σ notation 7.1, 7.2 slides - printable
Wed, Jan 9 Integrable functions 7.3, 7.4, 7.5, 7.6, 7.7 slides - printable - notes about slide 6
Mon, Jan 14 Integrable functions (continuation) 7.8, 7.9 slides - printable - notes about slides 4 and 5
Wed, Jan 16 (1st part) Properties of the integral 7.10, 7.11, 7.12 slides - printable - Recap of the notations

8. The fundamental theorem of calculus

Video playlist for this part

Date Topics Required videos Textbook sections Lecture slides
Wed, Jan 16 (2nd part) Antiderivatives and indefinite integrals 8.1, 8.2 5.5, 5.6 slides - printable
Mon, Jan 21 FTC - 1 8.3, 8.4 5.6 slides - printable
Wed, Jan 23 (1st part) FTC - 2 8.5, 8.6, 8.7 5.6 slides - printable

9. Integration methods

Video playlist for this part

Date Topics Required videos Textbook sections Lecture slides
Wed, Jan 23 (2nd part) Integration by substitution 9.1, (9.2), (9.3), (9.4) 6.1 slides - printable
Mon, Jan 28 Integration by parts (9.5), 9.6, (9.7), (9.8), (9.9) 6.2 slides - printable
Wed, Jan 30 Trigonometric and rational functions 9.10, (9.11), (9.12), 9.15, (9.16), (9.17) 6.3, 6.5 slides - printable

10. Volumes

Video playlist for this part

Date Topics Required videos Textbook sections Lecture slides
Mon, Feb 4 Volumes: slicing method 10.1 TBA slides - printable
Wed, Feb 6 (1st part)
Fri, Feb 8, 3-4pm
Room: MP203
Volumes: shell method 10.2 TBA slides

11. Sequences

Video playlist for this part

Date Topics Required videos Textbook sections Lecture slides
Wed, Feb 6 (2nd part)
Mon, Feb 11, 4-6pm
Room: MP102
Sequences:
definition and first properties
11.1, 11.2, 11.3, 11.4 8.1, 8.2 slides - printable
Wed, Feb 13 Theorems about sequences 11.5, 11.6, 11.7, 11.8 8.2 slides - printable

12. Improper integrals

Video playlist for this part

Date Topics Required videos Textbook sections Lecture slides
Mon, Feb 25 Improper integrals 12.1, (12.2), (12.3), 12.4, (12.5), (12.6) 7.8, 7.9 Posted after lecture
Wed, Feb 27 BCT and LCT for integrals 12.7, 12.8, 12.9, 12.10 7.8, 7.9 Posted after lecture



Niagara Falls