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Network Abstract ISO-OSI Model Physical layer, data link layer, network layer, transport layer, session layer, presentation layer and application layer TCP-IP Architecture link layer, internet layer, transport layer, application layer Ethernet topology: bus or star. CSMA/CD listen before sending, listen while sending, stop when afflict, delay then resend. Wireless Network 802.11 AP IBSS CSMA/CA CA aka conflict avoid. RTS CTS IP Protocol IPv4 IPv6 ICMP Broadcast address: 255.255.255.255 ...

Signal Sampling: sensor→A/D Digital signal VS analog signal analog: both X Y are contiguous. digital: both are discrete. Basic Operations on Digital Signal x[n]={⋯ ,−0.2,2.2,1.1,0.2,−3.7,⋯ }x[n]=\{\cdots,-0.2,2.2,1.1,0.2,-3.7,\cdots\}x[n]={⋯,−0.2,2.2,1.1,0.2,−3.7,⋯} addition, multiplication, time shifting(delay), reversing(反折), stretching(拉伸) difference(差分): x′[n]=x[n+1]−x[n]x'[n]=x[n+1]-x[n]x′[n]=x[n+1]−x[n] accumulation(累加) ⚠️Convolution(卷积​，非常重要): F(t)=x(n)∗h(n)=∑kx[n−k]h[k]F(t)=x(n) ...

Lagrange Interpolation 拉格朗日插值 Pn(x)=∑i=1nyi(Πj≠i1≤j≤nx−xjxi−xj)P_n(x)=\sum_{i=1}^ny_i(\Pi_{j\neq i}^{1\leq j\leq n}\frac{x-x_j}{x_i-x_j})Pn​(x)=∑i=1n​yi​(Πj=i1≤j≤n​xi​−xj​x−xj​​) Using polynomials to approximate the original function. Residuals R(x)=f(x)−p(x)=f(n+1)(ξ)(n+1)!ω(x)R(x)=f(x)-p(x)=\frac{f^{(n+1)}(\xi)}{(n+1)!}\omega(x)R(x)=f(x)−p(x)=(n+1)!f(n+1)(ξ)​ω(x), ξ∈(a,b)\xi\in(a,b)ξ∈(a,b) relies on x. Newton Interpolation Difference Quotient aka 差商 f[xi,xi+1]=f(xi+1)−f(xi)xi+1−xif[x_i,x_ ...

Logic and Reasoning details in Introduction to AI. Modern Algebra Magma magma 代数系统 Binary operation assume S is a set mapping f: S×S→SS\times S\rightarrow SS×S→S is a dyadic operation on S. dyadic operation 二元运算: The result of the dyadic operation is still belong to S. Every element in S can participate in the dyadic operation and get a unique result. e.g. In the natural number set N addition and multiplication are binary operators on N, but subtraction and division are not. Quasigroup ...

Data Structure List 1234list1 = ['physics', 'chemistry', 1997, 2000]list2 = [1, 2, 3, 4, 5, 6, 7 ]print ("list1[0]: ", list1[0])print ("list2[1:5]: ", list2[1:5]) Tuple similar to List, but the element in tuple can’t be changed 1234tup1 = ('physics', 'chemistry', 1997, 2000)tup2 = (1, 2, 3, 4, 5, 6, 7 )print ("tup1[0]: ", tup1[0])print ("tup2[1:5]: ", tup2[1:5]) Dictionary { key : value } 123dict = {'Na ...

Number System Decimal, binary, octal, hexadecimal (how to transfer) Logic Operation and or not nand(与非) nor(或非) xor(异或) Boolean Function Y=AB‾+A‾B+B‾C‾+ACY=A\overline B+\overline AB+\overline B\overline C+ACY=AB+AB+BC+AC Karnaugh Map simplify the Boolean function. A\BC 00 01 11 10 0 1 1 1 1 1 1 1 Adjacent 2 ‘1’ can be merged result is not only. both A‾C‾+AB‾+BC\overline A\overline C+A\overline B+BCAC+AB+BC and A‾B+AC+B‾C‾\overline AB+AC+\overline B\overline CAB+AC+BC are correc ...

Displacement velocity, time and displacement displacement=integral of speed with respect to time. Common Force Netwon’s laws of motion Work and Energy Kinetic energy theorem law of conservation of mechanical energy law of conservation of energy Momentum Law of conservation of momentum Circumferential Motion law of conservation of angular momentum moment of momentum Simple Harmonic Motion details Electric Field Electric Field Intensity Gauss’s Law: the electric flux through a closed surfac ...

Data Type 12345678910int aint;float afloat;long long alonglong;double adouble;typedef struct{ int num; char name[20]; float fsocre;}student;student stu1, stu[31]; Pointer A pointer holds the address of the other objects, and we can directly access the physical memory address of the pointed object by using pointer. 123int var_run=10;int *p;p=&var_run; datatype of pointer p must align with var_run. Function Overloading 123456789101112131415161718#include<stdlib.h>#i ...

Determinant It’s a function whose definition domain is the n×nn\times nn×n matrix AAA. Für eine nur aus einem Koeffizienten bestehende 1×11\times11×1-Matrix AAA ist det⁡A=det⁡(a11)=a11\det A=\det(a_{11})=a_{11}detA=det(a11​)=a11​ ist AAA eine 2×22\times 22×2-Matrix, dann ist det⁡A=det⁡(a11a12a21a22)=a11∗a22−a12∗a21\det A=\det\left(\begin{array}{cc}a_{11} & a_{12} \\ a_{21} & a_{22} \end{array}\right)=a_{11}*a_{22}-a_{12}*a_{21}detA=det(a11​a21​​a12​a22​​)=a11​∗a22​−a12​∗a21​ für eine N× ...

Single Variable Derivative A function of a real variable y=f(x)y=f(x)y=f(x) is differentiable at a point aaa of its domain, if its domain contains an open interval III containing aaa, the limit: L=lim⁡h→0f(a+h)−f(a)hL=\lim_{h\rightarrow0}\frac{f(a+h)-f(a)}{h}L=limh→0​hf(a+h)−f(a)​ L’Hôpital’s Rule Used to find the limit value of an expression The limits of the numerator (分子) and denominator (分母) are both 0 or infinite. Taylor’s Formular f(x)=∑i=0∞fi(x0)i!(x−x0)if(x)=\sum_{i=0}^\infty\frac{f^ ...