We know that$$\tan t=\frac{e^{it}-e^{-it}}{i(e^{it}+e^{-it})}=\frac{e^{2i t}+1-2}{i(e^{2it}+1)}=-i(1-\frac{2}{e^{2it}+1}).$$Now we try to find the anti-derivative of $$f(t)=\frac{1}{e^{2it}+1}.$$We observe that $$\frac{1}{e^{2it}+1}=\frac{1}{(e^{i…
I Proofs1 What is a Proof?2 The Well Ordering Principle3 Logical Formulas4 Mathematical Data Types5 Induction6 State Machines7 Recursive Data Types8 Infinite SetsII Structures9 Number Theory10 Directed graphs & Partial Orders11 Communication Networks…
Background\text{Background}Background Last night, lots of students from primary school came to our class to study OI.\text{Last night, lots of students from primary school came to our class to study OI.}Last night, lots of students from primary schoo…
[Game Engine Architecture 13] 1.describe an arbitrary signal x[n] as a linear combination of unit impulse. 每个信号都可以用 unit impulse 来表示,即原始的每一个数值 x[] 与 q[n-k] 的卷积和. 2.convolution(卷积) 下面公式被称为 convolution sum(卷积和): 3.Convolution in Continuous Time everyth…
