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.

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