Category Engineering

Mathematical Methods for Physics and Engineering 1. Basic definitions: (0) Definition of linear vector space: a set of $\mathbf{a}$,$\mathbf{b}$,$\mathbf{c}$,$\dots$ forms…

Mathematical Methods for Physics and Engineering 1. Some conclusions: (1) Ratio theorem: Line segment AB is divided into AP and…

Mathematical Methods for Physics and Engineering 1. Some integrals: (1) 2-D integrals: $\iint_{D} f(x,y) \, dx \, dy$; (2) 3-D…

Mathematical Methods for Physics and Engineering 1. Some properties of partial differentiation: 1.1 Clairaut’s theorem: Let $f(x,y)$ be a function.…

Mathematical Methods for Physics and Engineering 1. Basic sum of series [Page 117-118]: Basic series: $$\begin{array}{ll} Arithmetic\ series:S_N=\frac{N}{2}(first\ term+last\ term)\\…

Mathematical Methods for Physics and Engineering 1. Complex number division [Page 90-91]: $\frac{z_1}{z_2}=\frac{x_1x_2+y_1y_2}{x_2^2+y_2^2}+i\frac{x_2y_1-x_1y_2}{x_2^2+y_2^2}$ Especially for conjugate division: $\frac{z}{z^*}=\frac{x^2-y^2}{x^2+y^2}+i\frac{2xy}{x^2+y^2}$ 2. Complex…

Mathematical Methods for Physics and Engineering 1. Basic derivatives of some functions [Page 44] $$\frac{d}{dx}sec(ax)=asec(ax)tan(ax)\\ \frac{d}{dx}tan(ax)=asec^2(ax)\\ \frac{d}{dx}cosec(ax)=-acosec(ax)cot(ax)\\ \frac{d}{dx}cot(ax)=-acosec^2(ax)\\ \frac{d}{dx}sin^{-1}\frac{x}{a}=\frac{1}{\sqrt{a^2-x^2}}\\ \frac{d}{dx}cos^{-1}\frac{x}{a}=\frac{-1}{\sqrt{a^2-x^2}}\\…