一次問幾題得唔得
R係1
4:直接chain rule
5:用first principle個quotient limit,left limt!=right limit
6.d一次, argue f'>0 in domain,所以係strightly monotone
5同6都係唔明
好悶 有無人問數
一舊膠買起你
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5同6都係唔明
樓主的post 大部份都係applied maths 層面...
如果同你講analysis 會唔會已經露餡？
早就露左係廢柴啦
A real function is borel measurable iff it is continuous?
cts implies borel measurable.
converse not true.
f(x)=1 iff x is rational
一次問幾題得唔得
4)
(f(h(x)))'
=(f' at h(x)) * h'(x)
=g(h(x)) * h'(x)
5)
cts唔知有乜好寫...
R|x+1| is cts at -1 by composition.
f is cts at -1 since it is product of function cts at -1
痴線佬答法, in case 你係MATH STUDENT:
Let e=epsilon>0, take d=delta=0.5min{1,e/(2|R|)}<all things in the bracket
then d>0 and, -d-1<x<d-1<0, |x|<|d+1|<d+1<2
thus, |f(x)-f(-1)|=|R||x||x+1|<|R|*2 * d<epsilon
thus f is continuous
differentiable:
(f(x)-f(-1)) / (x-(-1))=Rx -> -R as x->-1
and differentiable 痴線佬答法唔好問我
6)
f(x):=LHS
then f'(x)=<0 iff x>=-5/3 and x=<5
thus, f(x) is decreasing iff x in [-5/3,5]
and f(5)>0
so, only one root in (-inf,-5/3]
想問下functional analysis有咩applications? 同埋佢同variational calculus個functional有咩關係?
好似無乜關係
calculus of variation要minimize嘅通常都係nonlinear functional (linear嘅都無乜好做optimization啦)
都係係某個functional space 揀element?
個functional space應該係linear?
其實都係名一個 意義不大
樓主的post 大部份都係applied maths 層面...
如果同你講analysis 會唔會已經露餡？
早就露左係廢柴啦
其實只要有數讀我就開心
不過本身個人廢，日日刨都FIRST HON唔到
如果搵到份工同數學有關就好
樓主的post 大部份都係applied maths 層面...
如果同你講analysis 會唔會已經露餡？
早就露左係廢柴啦
其實只要有數讀我就開心
不過本身個人廢，日日刨都FIRST HON唔到
如果搵到份工同數學有關就好
我都無first hon，照讀無誤。
我識有人third hon讀PhD就快畢業。
樓主的post 大部份都係applied maths 層面...
如果同你講analysis 會唔會已經露餡？
早就露左係廢柴啦
其實只要有數讀我就開心
不過本身個人廢，日日刨都FIRST HON唔到
如果搵到份工同數學有關就好
我都無first hon，照讀無誤。
我識有人third hon讀PhD就快畢業。
first hon都可以好廢
如何搵non symmetrical matrix 的 eigenvalue ?
最原始方法永遠都係Solve det(A+tI)=0 for t
寫錯左
係
det(A-tI)=0
想問下functional analysis有咩applications? 同埋佢同variational calculus個functional有咩關係?
好似無乜關係
calculus of variation要minimize嘅通常都係nonlinear functional (linear嘅都無乜好做optimization啦)
都係係某個functional space 揀element?
個functional space應該係linear?
其實都係名一個 意義不大
一般min I[f], where I is some integral operator integrating over domain Ω, given f|∂Ω = g.
咁你做個variation I[f+tη] 個η要係zero on ∂Ω
所以η 係某個subspace入面揀嘅
有冇人講下topology
咩係topology既世界圓形同正方形一樣,講緊乜
簡單黎講你係唔整爛個圓形泥膠的情況之下, 可以慢慢拉到變左個正方形 (反之亦然)
有冇人講下topology
咩係topology既世界圓形同正方形一樣,講緊乜
簡單黎講你係唔整爛個圓形泥膠的情況之下, 可以慢慢拉到變左個正方形 (反之亦然)
正方形同骰仔都一樣？㩒扁或整脹返就得
唔同, 佢地係唔同dimension的野
有冇人講下topology
咩係topology既世界圓形同正方形一樣,講緊乜
簡單黎講你係唔整爛個圓形泥膠的情況之下, 可以慢慢拉到變左個正方形 (反之亦然)
咁樣既話咩都一樣嫁喎
正式definition係有一個bijection f, 而且f, f^-1 都係continuous
有冇人講下topology
咩係topology既世界圓形同正方形一樣,講緊乜
簡單黎講你係唔整爛個圓形泥膠的情況之下, 可以慢慢拉到變左個正方形 (反之亦然)
正方形同骰仔都一樣？㩒扁或整脹返就得
唔同, 佢地係唔同dimension的野
又話唔整爛泥膠就得，好亂
咁你可唔可以將粒骰仔壓到無厚度?
有冇人講下topology
咩係topology既世界圓形同正方形一樣,講緊乜
簡單黎講你係唔整爛個圓形泥膠的情況之下, 可以慢慢拉到變左個正方形 (反之亦然)
正方形同骰仔都一樣？㩒扁或整脹返就得
唔同, 佢地係唔同dimension的野
又話唔整爛泥膠就得，好亂
但係正方形既話 塊泥膠無限薄
同埋係“簡單黎講”
有冇人講下topology
咩係topology既世界圓形同正方形一樣,講緊乜
簡單黎講你係唔整爛個圓形泥膠的情況之下, 可以慢慢拉到變左個正方形 (反之亦然)
正方形同骰仔都一樣？㩒扁或整脹返就得
唔同, 佢地係唔同dimension的野
又話唔整爛泥膠就得，好亂
咁你可唔可以將粒骰仔壓到無厚度?
咁你都唔會整到個完美嘅圓形啦，講呢啲冇意思
咁呢D係比喻幫你visualize姐
有冇人講下topology
咩係topology既世界圓形同正方形一樣,講緊乜
簡單黎講你係唔整爛個圓形泥膠的情況之下, 可以慢慢拉到變左個正方形 (反之亦然)
正方形同骰仔都一樣？㩒扁或整脹返就得
唔同, 佢地係唔同dimension的野
又話唔整爛泥膠就得，好亂
咁你可唔可以將粒骰仔壓到無厚度?
咁你都唔會整到個完美嘅圓形啦，講呢啲冇意思
咁呢D係比喻幫你visualize姐
topology唔係話可以將2D既野match落3D到咩
