| Weeks |
Dates |
Topics |
Sections and Lecture Notes |
| week 0 & 1 |
Sept. 9 - 18 |
Starting out, prerequisites, goals of course, intuitive limits and instantaneous velocity |
Sections 1.1, 1.2, 1.3 and appendix D |
| week 2 |
Sept. 19 - 25 |
Precise definition of limit,
Game version of limit,
Rules for calculating limits,
Limit for sin(x)/x,
Pinching theorem
|
Sections 1.5, 1.6 and 1.7 |
| week 3 |
Sept. 26 - Oct. 2 |
Continuity,
Sums, products and reciprocals of continuous functions,
Composition of continuous functions,
Intermediate Value Theorem
|
Sections 1.7 and 1.8 |
| week 4 |
Oct. 3 - 9 |
Tangents and instantaneous velocity again,
Derivative of sin(x),
Rate of change,
Derivative as a function
|
Sections 1.8, 2.1 and 2.2 |
| Reading week |
Oct. 10 - 16 |
No lectures |
Read all previous sections |
| week 5 |
Oct. 17 - 23 |
Simple rules for derivatives,
Leibnitz rule,
Chain rule,
Quotient rule
|
Sections 2.3, 2.4 and 2.5 |
| week 6 |
Oct. 24 - 30 |
Derivative of sin(x),
Related rates,
Implicit differentiation,
Extreme Value Theorem
|
Sections 2.6, 2.7, 2.8 and 3.1 |
| week 7 |
Oct. 31 - Nov. 6 |
Rolle's Theorem,
The Mean Value Theorem,
The first derivative test,
The second derivative test
|
Sections 3.2, 3.3 and 3.4 |
| week 8 |
Nov. 7 - 13 |
Optimization problems 1,
Optimization problems 2
|
Sections 3.4, 3.5 and 3.7 |
| week 9 |
Nov. 14 - 20 |
Suprema and infima,
Completeness of the real numbers,
Proof of the Intermediate Value Theorem,
Proof of the Extreme Value Theorem
|
Notes on completeness |
| week 10 |
Nov. 21 - 27 |
The area problem,
Distance travelled,
Area under x2 by Riemann sums,
Definition of Riemann sums in general
|
Sections 4.1, Additional notes |
| week 11 & 12 |
Nov. 28 - Dec. 8 |
Monotonicty of Riemann sums,
Definition of Riemann integral,
Monotone functions are Riemann integrable,
Fundamental Theorem of Calculus Part 1,
Fundamental Theorem of Calculus Part 2
|
Sections 4.2 and 4.3 |