C A L C U L U S    I I ,    S P R I N G   2 0 2 5

Course Information

• NTU COOL
• Lectures: Tuesday and Thursday, 13:20 ~ 15:10 at Freshman Classroom Building 304
• Office hours: Wednesday 14:00 ~ 15:00, at Astro-Math 458
• Grading scheme:
  • Midterm 30%   (on April 10)
  • Final 35%   (on June 5)
  • Quiz 10%   (on March 13 and May 15)
  • Homework 25%
         You have two jokers: the lowest two grades will be discarded.
• Textbook: Tom Apostol, Calculus vol.2 - Multi-Variable Calculus and Linear Algebra with Application to Differential Equations and Probability.
• Problem session: Thursday 17:30 ~ 18:20
• Teaching Assistants:
  • 連焌凱: problem session at Freshman Classroom Building 103.        Office hour: Wednesday 13:20 ~ 14:20 at Astro-Math 446.
  • 郭立生: problem session at Freshman Classroom Building 304.        Office hour: Wednesday 15:30 ~ 16:30 at Astro-Math 405.
  • 黃篆: problem session at Freshman Classroom Building 203.        Office hour: Friday 17:30 ~ 18:30 at Astro-Math 449.

Lecture summaries and references

• (week 1)
  • basic point-set topology of Euclidean space.    reference: 8.2
  • limits and continuity.    reference: 8.4
  • partial derivative and directional derivative.    reference: 8.6 ~ 8.8
  • derivative and continuity.    reference: 8.10, and Courant&John V.II p.34 ~ 35
  • commuting second order derivatives.    reference: 8.23
• (week 2)
  • differentiability in multi-variables.    reference: 8.11 ~ 8.13, 8.19
  • chain rule.    reference: 8.20, 8.21
  • tangent plane of a graph.    reference: 8.16
  • Taylor theorem in multi-variables.    reference: 9.10
  • local extremal and 2nd derivative test.    reference: 9.9, 9.11, 9.12
• (week 3)
  • eigenvalues and eigenvectors of 2x2 symmetric matrices.
  • implicit differentiation.    reference: 9.6, 9.7
  • implicit function theorem.    reference: note on NTU COOL
  • Lagrange multiplier.    reference: 9.14
• (week 4)
  • Lagrange multiplier (continued).    reference: 9.14
  • uniform continuity and consequences in multi-variables.    reference: 9.16, 9.17
  • arc-length of a curve.    reference: (Vol. 1) 14.10, 14,11
  • vector line integral.    reference: 10.2 ~ 10.4
  • fundamental theorem of vector line integral.    reference: 10.14
• (week 5)
  • necessary and sufficient condition for a gradient vector field.    reference: 10.5 ~ 10.7
  • construction of the potential function.    reference: 10.21
  • double integral. repeated integral.    reference: 11.2 ~ 11.8
  • Jordan measure.    reference: note on NTU COOL

Homework

• Homework 01 (due 2/27) [8.3] 2 (m), 5 (c), (d), (e); [8.5] 1 (j), 3, 4; [8.8] 8, 14.
• Homework 02 (due 3/06) [8.14] 2 (b), 8 (a) to (d); [8.17] 4 (a), (b); [8.22] 5, 14; [8.24] 7 (a), (b).
• Homework 03 (due 3/13) [9.8] 4; [9.13] 14; [9.15] 6.
• Homework 04 (due 3/20) [9.15] 8, 11; [10.5] 11, 12 (a), (b); [Vol.1 14.13] 13 (a), (b).
• Homework 05 (due 3/27) [10.9] 3; [10.13] 5 (b), 7 (a), (b); [10.18] 3, 11, 15.

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