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IUM-02 Limit
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kanaya
April 27, 2024
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IUM-02 Limit
kanaya
April 27, 2024
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Transcript
pineapple.cc ࡚େֶใσʔλՊֶ෦ େֶֶೖ Introduction to University Mathematics
pineapple.cc ߨٛͷਐΊํʢୈճʙୈճʣ Agenda (Day 2 to Day 8) w େֶֶͷೖIntroduction
to University Mathematics ⭐⭐ w ֶΛ͖ʹͳΔStories about math that makes you fun ⭐ w ܭࢉػՊֶʢใՊֶʣͷڮ͠A bridge to computer science ⭐⭐⭐
pineapple.cc ධՁ Credits w ग़੮Attendance w ΫΠζͱϛχϨϙʔτQuiz and mini report
w ϨϙʔτʢҙʣReport (optional)
pineapple.cc ؔfunction
None
None
None
None
None
None
pineapple.cc ߸equal sign
None
pineapple.cc a = b a ≡ b a ≜ b
pineapple.cc ۃݶlimit
pineapple.cc θϊϯͷύϥυοΫε ඈΜͰ͍Δࢭ·͍ͬͯΔ
None
None
None
None
None
pineapple.cc {an } ≜ {a1 , a2 , a3 ,
…}
pineapple.cc lim n→∞ an = l
pineapple.cc ͨͱ͑ʜʜ
pineapple.cc {an } ≜ {1, 1 2 , 1 4
, …}
pineapple.cc {an } ≜ { 1 2n−1 }
pineapple.cc lim n→∞ an = 0
pineapple.cc {an } ≜ {1, − 1 3 , 1
5 , − 1 7 , 1 9 , …}
pineapple.cc {an } ≜ { (−1)n−1 2(n − 1) +
1}
pineapple.cc lim n→∞ an = 0
pineapple.cc sn ≜ n ∑ k=1 ak , n ∈
{1,2,3,…}
pineapple.cc {sn } ≜ {s1 , s2 , s3 ,
…}
pineapple.cc lim n→∞ sn = S
pineapple.cc lim n→∞ n ∑ k=1 ak = S
pineapple.cc ∞ ∑ k=1 ak = S
pineapple.cc ͨͱ͑ʜʜ
pineapple.cc {an } ≜ {1, 1 2 , 1 4
, …}
pineapple.cc {an } ≜ { 1 2n−1 }
pineapple.cc ∞ ∑ k=1 ak = 2
pineapple.cc {an } ≜ {1, − 1 3 , 1
5 , − 1 7 , 1 9 , …}
pineapple.cc {an } ≜ { (−1)n−1 2(n − 1) +
1}
pineapple.cc ∞ ∑ k=1 ak = π 4
pineapple.cc 1 − 1 3 + 1 5 − 1
7 + 1 9 − … = π 4
pineapple.cc lim x→∞ f(x) = l
None
pineapple.cc lim x→a f(x) = l
None
pineapple.cc ͨͱ͑ʜʜ
pineapple.cc f(x) ≜ sin(x) x
pineapple.cc sinc(x) ≜ sin(x) x
pineapple.cc
pineapple.cc ղੳͷੈք
pineapple.cc x2 + 2bx + c = 0
pineapple.cc x = − b ± b2 − c b
> 0, c > 0, b ≫ c What if…
pineapple.cc x = − c b + b2 − c
pineapple.cc @kanaya