物理数学 · 2020/05/04

■定義 　\(sec \theta =\displaystyle\frac{1}{cos \theta}\)　　\(sech \theta =\displaystyle\frac{1}{cosh \theta}\) 　\(csc \theta =\displaystyle\frac{1}{sin \theta}\)　　\(csch \theta =\displaystyle\frac{1}{sinh \theta}\) 　\(cot \theta =\displaystyle\frac{1}{tan \theta}\)　　\(coth \theta =\displaystyle\frac{1}{tanh \theta}\) ■相互関係 　\(sin^2 \theta + cos^2\theta=1\)　　\(cosh^2 \theta - sinh^2 \theta=1\) 　\(sec^2 \theta - tan^2 \theta=1\)　　\(sech^2 \theta + tanh^2...

物理数学 · 2020/05/02

■勾配(grad) 　直交座標　\(\nabla f=\displaystyle\frac{\partial f}{\partial x}\mathbf{e_x}+\frac{\partial f}{\partial y}\mathbf{e_y}+\frac{\partial f}{\partial z}\mathbf{e_z}\) 　球座標　　\(\nabla f=\displaystyle\frac{\partial f}{\partial r}\mathbf{e_r}+\frac{1}{r}\frac{\partial f}{\partial \theta}\mathbf{e_{\theta}}+\frac{1}{rsin\theta}\frac{\partial f}{\partial \phi}\mathbf{e_{\phi}}\) 　円筒座標　\(\nabla f=\displaystyle\frac{\partial f}{\partial...

物理数学 · 2020/05/02

内積(スカラー積) 　\(\mathbf{a}･\mathbf{b}=|\mathbf{a}||\mathbf{b}|cos\theta\) 外積(ベクトル積) 　\(\mathbf{a}×\mathbf{b}=|\mathbf{a}||\mathbf{b}|sin\theta \mathbf{\hat{n}}=\begin{vmatrix} \mathbf{\hat{x}} & \mathbf{\hat{y}} & \mathbf{\hat{z}} \\ a_x & a_y & a_z \\ b_x & b_y & b_z \end{vmatrix}\) 　\(\mathbf{\hat{n}}\)は\(\mathbf{a}、\mathbf{b}\)と右手系をなす単位ベクトル \(Lagrange\)の恒等式 　\(...