KuFun人工智能的专栏

二阶导检验：边界与无穷Question: How to do we find global min/max?→\rightarrow→最值可能在函数的临界点或边界或无穷远取得(occur the critical point or on the boundary or at infinity)使用:二阶导数(second derivate test)Example: w=x2+2xy+...

极大极小值问题,最小二乘法Partial derivativesz=f(x, y),then Δz≈fxΔx+fyΔy\Delta z \approx f_x\Delta x+f_y\Delta yΔz≈fx​Δx+fy​Δy在考虑最优化问题时，我们就要用到偏导数(application of partial derivatives optimization problems)To fi...

等值面,偏导数,切平面逼近Function of 1 variable .f(x)=sin(x)Function of 2 variables:given(x, y)→\rightarrow→get a number f(x, y)Example f(x,y)=x2+y2f(x,y)=x^2+y^2f(x,y)=x2+y2f(x, y)=temperature at point (x,...

速度，加速度和开普勒第二定律F(t)=<t-sint,1-cost)v→=dr→dt=<dxdt,dydt,dzdt>\overrightarrow{v}=\frac{d\overrightarrow{r}}{dt}=<\frac{dx}{dt},\frac{dy}{dt},\frac{dz}{dt}>v=dtdr​=<dtdx​,dtdy​,dtdz​&g...

曲线和直线的参数方程直线方程(Equations of line)we have seen: line=intersection of 2 planesAnother way:运动点的轨迹(trajectory of a moving point)也称参数方程。(also called parametric equation )More generally, parametric eq...

矩阵方程，平面方程Equation of plane:recall an equation of the form: ax+by+cz=d.defines a plane1)Plane through origin with normal vector N→=<1,5,10>\overrightarrow{N}=<1,5,10>N=<1,5,10>...

矩阵，逆矩阵A→\overrightarrow{A}AXB→\overrightarrow{B}B=−B→-\overrightarrow{B}−BXA→\overrightarrow{A}Ain particular A→\overrightarrow{A}AXA→=0\overrightarrow{A}=0A=0Application:Equation of plane P1P2...

行列式和叉积点积应用3)向量A沿着某单位向量u的分量(components of A→\overrightarrow{A}Aalong a direction u^\widehat{u}u)component of A along u^\widehat{u}u = ∣A→∣|\overrightarrow{A}|∣A∣cos(Θ\ThetaΘ)=∣A→∣∣u^∣.cosΘ|\over...

向量和点积1.1Vectors(向量)属性：direction(方向)magnitude length(大小)A→=a1i→+a2j→+a3k→=<a1,a2,a3>\overrightarrow{A}=a_1\overrightarrow{i}+a_2\overrightarrow{j}+a_3\overrightarrow{k}=< a_1,a_2,a_3>...