Webpage of the section LEC0501 of MAT137: "Calculus!" at UofT - 2018/2019

# Information

 Instructor Jean-Baptiste (JB) Campesato E-Mail campesat [@t) math.toronto.edu Schedule Monday, 4pm to 5pm Wednesday, 4pm to 6pm Room MP202 (1st term) Room MP102 MAT137 Website http://uoft.me/MAT137

# My archives

Some documents I wrote for this course. They may differ from the version on the website of the course.

 PS1 sample solutions PS2 sample solutions PS3 sample solutions PS4 sample solutions PS5 sample solutions PS6 sample solutions PS7 sample solutions PS8 sample solutions PS9 sample solutions PS10 sample solutions Some spherical caps

# 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 Lecture slides
Mon, Feb 4 Volumes: slicing method 10.1 slides - printable
Wed, Feb 6 (1st part)
Fri, Feb 8, 3-4pm
Room: MP203
Volumes: shell method 10.2 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 slides - printable
Wed, Feb 27 BCT and LCT for integrals 12.7, 12.8, 12.9, 12.10 7.8, 7.9 slides - some notes

# 13. Series

Video playlist for this part

Date Topics Required videos Textbook sections Lecture slides
Mon, Mar 4 Definition of series (13.1), 13.2, 13.3, 13.4 8.3 slides - printable - notes about slide 7
Wed, Mar 6 Properties of series 13.5, 13.6, 13.7, 13.8, 13.9 8.3, 8.4 slides - printable
Mon, Mar 11 Integral and comparison tests 13.10, 13.11, 13.12 8.5, 8.7 slides
Wed, Mar 13 Absolute convergence and alternating series 13.13, 13.14, 13.15, (13.16), (13.17) 8.6 slides - printable
Mon, Mar 18 Ratio test 13.18, 13.19 8.7 slides - printable

# 14. Power series and Taylor series

Video playlist for this part

Date Topics Required videos Textbook sections Lecture slides
Wed, Mar 20 Power series and Taylor polynomials 14.1, 14.2, 14.3, 14.4 9.1, 9.2, 9.3 slides - printable
Mon, Mar 25 Taylor series 14.5, 14.6 9.1, 9.2, 9.3 slides - printable
Wed, Mar 27 Analytic functions 14.7, 14.8, 14.9, 14.10 9.1, 9.2, 9.3 slides - printable
Mon, Apr 1 Applications 14.12, 14.14 9.1, 9.2, 9.3, 9.4 slides (with recap)
Wed, Apr 3 Applications 14.11, 14.13, 14.15 9.1, 9.2, 9.3, 9.4 slides - printable - Slide 6 solutions