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