## Lecture notes

The schedule of topics for all sections is available in the common page for MATH 100.

Timeline PDF Topics Textbook sections Comments
Limits and continuity
Week 1
09/05 Imagine Day: no class
09/07 Intro. Lecture Introduction. Motivation and the limit of a function. 1.1 - 1.3 Reading assignment: section 1.1
Week 2
09/12 Lecture Limits to infinity. Calculating limits with limit laws. 1.3 and 1.4
09/14 Lecture More on limit laws. Limits at infinity. 1.5 - 1.6 Read Theorem 1.5.9 carefully
Week 3
09/19 Lecture Examples of limits at infinity. Continuity. 1.6
09/21 Quiz 1 Lecture Intermediate Value Theorem. Bisection Method. 1.6 A video about "the woobly table theorem"
Week 4
The derivative
09/26 Lecture The derivative 2.1 - 2.3 Two Geogebra apps: for visualizing secant and tangent lines and the derivative as the slope of the tangent .
09/28 Lecture Arithmetic of derivatives (and some proofs). Derivatives of exponential functions. 2.3-2.7 Read the review of logarithms: Section 2.7 in CLP-I.
Week 5
10/03 Lecture/Worksheet Derivatives of exponential and trigonometric functions 2.6-2.8
10/05 Quiz 2 Lecture/Worksheet The chain rule 2.9
Week 6
10/10 Lecture/Worksheet Review of inverse function and logarithms 0.6, 2.10 More on the importance of logarithms (in two comic strips): https://xkcd.com/1162/ and https://xkcd.com/482/
10/12 Lecture/Worksheet Implicit differentiation. Derivatives of inverse functions: logarithm and trigonometric functions. 2.10, 2.11, 2.12
Applications
Week 7
10/17 Lecture/Worksheet Rates of change. Exponential growth and decay. 3.1 and 3.3. A note on acceleration and speeding up
10/19 Quiz 3 Lecture/Worksheet Exponential growth and decay. 3.3
Week 8
10/24 Lecture/Worksheet Newton's law of cooling and related rates 3.3 and 3.2
10/26 Lecture/Worksheet Linear approximation, quadratic approximation and introduction to Taylor polynomials. 3.4
Week 9
10/31 Lecture/Worksheet Taylor polynomials and remainders 3.4
11/02 Quiz 4 Lecture More on Taylor polynomials and remainders. Global maxima and minima. 3.4 and 3.5
Week 10
11/07 Lecture/Worksheet Optimisation: maxima and minima 3.5
11/09 Lecture Mean Value Theorem 2.13
Week 11
11/14 Lecture/Worksheet Problems on Mean Value Theorem. Curve sketching: derivatives and the shape of a function. 2.13 and 3.6
11/16 Quiz 5 Lecture/Worksheet Curve sketching: concavity 3.6
Week 12
11/21 Lecture/Worksheet Cuve sketching: symmetries and sketching 3.6
11/23 Lecture/Worksheet L'Hôpital's rule 3.7
Week 13
11/28 Lecture/Worksheet Optimisation problems 3.5.3
11/30 Lecture/Worksheet Antiderivatives 4.1
Exams. 12/05 - 12/20
Final exam