Calculus

Notes

1. Functions & Limits & Continuous: 9/19
   Include: eplison and delta

2. Derivatives: 10/3
   Include: little o & Leibniz’s product rule

3. Integrals: 10/24
   Include: concrete example for L’Hopital rule

4. Applications of Definite Integrals: 11/14
   Include: Brachistochrone (curve of fastest descent) problem & soap film

5. Infinite Sequences and Series: 11/20
   Include: Riemann rearrangement theorem

6. Taylor Series: 11/28
   Include: concrete example for Taylor theorem & Lagrange interpolation

7. Partial Derivatives: 12/19
   Include: concrete example for change order of partial derivatives & concept of gradients

8. Extreme Value Problem & Multiple Integrals 12/26
   Include: multi-variable Taylor series (second derivative test) & concrete example for change order of integrals (Fubini theorem)

• Review of Midterm Exam 10/31
  These problems are taken from NTU.

• Review of Final Exam 1/2
  These problems are taken from NTU.

Extension

NTU Calculus website