求解y' = −2xy 且y(0) = 2 解: y\neq 0 \frac{dy}{dx}=-2xy\Rightarrow\frac{1}{y}dy=-2xdx ,两边同时积分得到 \int\frac{1}{y}dy=\int(-2x)dx+C\Rightarrow \ln|y| = −x^2 +C 最终有 |y|=e^C e^{-x^2} \Rightarrow y= \pm e^C e^{-x^2}=C_1 e^{-...
8.1b: Examples of Fourier Series Even functions use only cosines (F(–x) = F(x)) and odd functions use only sines. The coefficientsanandbncome from integrals ofF(x)cos(nx) andF(x)sin(nx). 14:03Video length is 14:03 8.1c: Fourier Series Solution of Laplace's Equation ...
4.1.1 A first change of variables It is possible to make the change of variable xi = log(Si), i = 1, …, d; calling x the vector (x1,…, xd) and P˜ the function, P˜(x,t) = P(S, t), the final value problem (4.5) (4.6) becomes (4.8)(∂P˜∂t+L˜P...
The line x =12h is such a line of symmetry for our tube flow. In order to exploit this symmetry, we introduce the new analytic function (2)w(ζ)=g13i[z(ζ+i)−12h], which is real for all real values of the complex potential ζ. In terms of w, the free boundary condition (...
线性无关,若方程 c1y1(x)+c2y2(x)+···+cnyn(x)=0 仅在c1=c2=···=cn=0 时成立 若不是线性无关那么就是线性相关 Wronskian of n functions n个函数的Wronskian 若p_1, p_2, ··· , p_n ∈ C(I) ,那么n个函数的Wronskian为 W\left(f_1, f_2, \cdots, f_n\right)(x)=\...
具体方法是d(expressions(x,y))dx=d(expressions(x,y))dx=some functions ofxxalone 将微分方程整理成这种方式后,再对两边积分∫∫ 积分因子法 Integration Factor 积分因子法适合解决 First order linear ODE dydx+p(x)y=q(x)dydx+p(x)y=q(x) ...
of the form (4+1)/(x-1)(Bx+c)/(x^2+3) with values for A, B, C , with no extra fractions Integrates 1/(x^2+3) to obtain ktan^(-1)α/(√3)Obtains a completely correct expression for the general solution:xy=ln(x-1)+√3tan^(-1)x/(√3)+C Condone omission of c ....
Department of ScienceCNKIChinese Physics B李永庆,李健,赵丽娜,倪艳清,马凤才.The differential interference angle of ~2Π [Case(a)] diatom on rotational energy transfer in NO (X~2Π ) collision with He,Ne and Ar system[J]. Chinese Physics B.2008(10)The differential interference angle of ~2Π...
Continuity Properties : Laws of Continuity 注意第四个:只有当f(x)f(x)连续时,极限符号才能从括号外面移到里面 Continuous Extension to a Point 观察这个函数: 函数sinxxsinxx在x=0x=0上不连续:原因是,虽然limx→0−sinxx=limx→0+sinxx=1limx→0−sinxx=limx→0+sinxx=1,但是sin...
例: (eax)′=a⋅eax ; (lnx2)′=1x2⋅2x 高阶导数的运算 (x^{a})^{(n)}=x^{a-n} \prod_{k=0}^{n-1} (a-k) (\frac{1}{x})^{(n)}=(-1)^n\frac{n!}{x^{n+1}} \quad\quad (n=1,2,...)(\ln x)^{(n)}=(-1)^{(n-1)}\frac{(n-1)!}{x^{n}...