C A L C U L U S
I ,
F A L L 2 0 2 4

#### Course Information

- NTU COOL
- Lectures: Tuesday and Thursday, 13:20 ~ 15:10 at Freshman Classroom Building 204
- Office hours: Monday 14:20 ~ 15:20, at Astro-Math 458
- Grading scheme:
- Midterm 30% (on Thursday, October 24)
- Final 35% (on Thursday, December 19)
- Quiz 10% (on September 26 and November 14)
- Homework 20%

You have two jokers: the lowest three grades will be discarded.
- Webwork 5%

- Textbook: Tom Apostol, Calculus vol.1 - One-variable Calculus with an Introduction to Linear Algebra
- Problem session: Thursday 17:30 ~ 18:20
- Teaching Assistants:
- 連焌凱: problem session at Freshman Classroom Building 204. Office hour: Wednesday 13:20 ~ 14:20 at Astro-Math 446.
- 郭立生: problem session at Freshman Classroom Building 203. Office hour: Wednesday 15:30 ~ 16:30 at Astro-Math 405.
- 黃篆: problem session at Freshman Classroom Building 202. Office hour: Monday 17:30 ~ 18:30 at Astro-Math 405.

#### Lecture summaries and references

- (week 1)
- completeness of real numbers: upper bound, least upper bound/supremum. reference: I 3.8, I 3.9
- partition, step function and its integral. reference: 1.9 ~ 1.13
- integral of general functions. reference: 1.16, 1.17
- monotone functions and their integrability. reference: 1.20 ~ 1.23

- (week 2)
- properties of integrals. reference: 1.24 ~ 1.27
- *(Riemann) measurable set. reference: 1.6
- integration of cosine. reference: 2.1 ~ 2.6
- polar coordinate. reference: 2.9, 2.10
- indefinite integral. reference: 2.18
- continuity. reference: 3.1 ~ 3.3

- (week 3)
- basic limit theorems. reference: 3.4, 3.5
- composition and continuity. reference: 3.7
- intermediate value theorem and strictly monotone functions. reference: 3.9 ~ 3.14

- (week 4)
- Heine-Borel theorem, uniform continuity, properties of continous functions on closed and bounded intervals. reference: 3.16 ~ 3.19
- tangent line and derivative. reference: 4.7
- basic properties of derivatives. reference: 4.3 ~ 4.5
- chain rule. reference: 4.10

#### Homework

- Homework 01 (due September 12): [1.15] #1 (d) (e), #4 (a) (b), #11, #12, #16.
- Homework 02 (due September 19): [1.26] #23, #27; [2.8] #31; [2.11] #8, #13, #14.
- Homework 03 (due September 26): [3.6] #5, #18, #22, #27; [3.8] #17, #21.
- Homework 04 (due October 3): [3.6] #31; [3.20] #2, #4, #7, #8.

Last modified: October 1, 2024.

Up to the homepage of Chung-Jun Tsai