IUM-02 Limit

Transcript

1. pineapple.cc ௕࡚େֶ৘ใσʔλՊֶ෦ େֶ਺ֶೖ໳
    Introduction to University Mathematics
2. pineapple.cc ߨٛͷਐΊํʢୈճʙୈճʣ Agenda (Day 2 to Day 8) w େֶ਺ֶ΁ͷೖ໳
   Introduction to University Mathematics ⭐⭐
   w ਺ֶΛ޷͖ʹͳΔ࿩
   Stories about math that makes you fun ⭐
   w ܭࢉػՊֶʢ৘ใՊֶʣ΁ͷڮ౉͠
   A bridge to computer science ⭐⭐⭐
3. pineapple.cc ධՁ Credits w ग़੮
   Attendance
   w ΫΠζͱϛχϨϙʔτ
   Quiz and mini report
   w Ϩϙʔτʢ೚ҙʣ
   Report (optional)
4. pineapple.cc ؔ਺
   function
11. pineapple.cc ౳߸
    equal sign
13. pineapple.cc a = b a ≡ b a ≜ b
14. pineapple.cc ۃݶ
    limit
15. pineapple.cc θϊϯͷύϥυοΫε ඈΜͰ͍Δ໼͸ࢭ·͍ͬͯΔ
21. pineapple.cc {an } ≜ {a1 , a2 , a3 , …}
22. pineapple.cc lim n→∞ an = l
23. pineapple.cc ͨͱ͑͹ʜʜ
24. pineapple.cc {an } ≜ {1, 1 2 , 1 4 , …}
25. pineapple.cc {an } ≜ { 1 2n−1 }
26. pineapple.cc lim n→∞ an = 0
27. pineapple.cc {an } ≜ {1, − 1 3 , 1 5 , − 1 7 , 1 9 , …}
28. pineapple.cc {an } ≜ { (−1)n−1 2(n − 1) + 1}
29. pineapple.cc lim n→∞ an = 0
30. pineapple.cc sn ≜ n ∑ k=1 ak , n ∈ {1,2,3,…}
31. pineapple.cc {sn } ≜ {s1 , s2 , s3 , …}
32. pineapple.cc lim n→∞ sn = S
33. pineapple.cc lim n→∞ n ∑ k=1 ak = S
34. pineapple.cc ∞ ∑ k=1 ak = S
35. pineapple.cc ͨͱ͑͹ʜʜ
36. pineapple.cc {an } ≜ {1, 1 2 , 1 4 , …}
37. pineapple.cc {an } ≜ { 1 2n−1 }
38. pineapple.cc ∞ ∑ k=1 ak = 2
39. pineapple.cc {an } ≜ {1, − 1 3 , 1 5 , − 1 7 , 1 9 , …}
40. pineapple.cc {an } ≜ { (−1)n−1 2(n − 1) + 1}
41. pineapple.cc ∞ ∑ k=1 ak = π 4
42. pineapple.cc 1 − 1 3 + 1 5 − 1 7 + 1 9 − … = π 4
43. pineapple.cc lim x→∞ f(x) = l
45. pineapple.cc lim x→a f(x) = l
47. pineapple.cc ͨͱ͑͹ʜʜ
48. pineapple.cc f(x) ≜ sin(x) x
49. pineapple.cc sinc(x) ≜ sin(x) x
50. pineapple.cc
51. pineapple.cc ਺஋ղੳͷੈք
52. pineapple.cc x2 + 2bx + c = 0
53. pineapple.cc x = − b ± b2 − c b > 0, c > 0, b ≫ c What if…
54. pineapple.cc x = − c b + b2 − c
55. pineapple.cc @kanaya