기록

27. Differentiation of Scalar Function Scalar Function $ \phi =\phi (s) $ in the $ x_{i},x_{i}' $ coordinates, $ \phi =\phi ', s=s' \Rightarrow d\phi =d\phi ', ds=ds' $ $ \frac{d\phi }{ds}=\frac{d\phi '}{ds'}=(\frac{d\phi }{ds})' $ 28. Differentiationn of Vector Function Vector Function $ \vec{A} $ w.r.t. a scalar S $ A_{i}'=\sum_{j}^{}\lambda _{ij}A_{j} $ $ \frac{dA_{i}'}{ds'}=\frac{d}{ds'}\sum..

19. Scalar Product(Dot Product) $ \vec{A}\cdot \vec{B}=\sum_{i}^{}A_{i}B_{i}=AB\cos (\vec{A},\vec{B}) $ $ |\vec{A}|=\sqrt{A_{1}^{2}+A_{2}^{2}+A_{3}^{2}}\equiv A $: Magnitude(Length) of $ \vec{A} $ $ \frac{A_{i}}{A}=\Lambda_{i}^{A}, \frac{B_{i}}{B}=\Lambda_{i}^{B} $: Direction Cosines of $ \vec{A} $ and $ \vec{B} $ $ \cos \Theta =\cos (\vec{A},\vec{B})=\cos \alpha \cos \alpha'+\cos \beta+\cos \be..

17. Definitions of a Scalar and a Vector in Terms of Transformation Properties $ x_{i}'=\sum_{j}^{}\lambda _{ij}x_{j} $의 좌표변환($ \sum_{j}^{}\lambda _{ij}\lambda _{kj}=\delta _{ik} $) $ \phi $ is unaffected → scalar $ A_{i}'=\sum_{j}^{}\lambda _{ij}A_{j} $ is transformed from the $ x_{i} $ system to the $ x_{i}' $ system → vector 18. Properties of Scalar and Vector $ \vec{A}, \vec{B} $: Vector, $ ..

vector calculus 카테고리는 5th (Marion)의 chapter 1 순서를 따라갑니다 순서 1. Scalar 2. Vector 3. Coordinate Transformation 4. Direction Cosine, Transformation Matrix(Rotation Matrix) 5. Inverse Transformation 6. Properties of Rotation Matrices 7. Kronecker Delta 8. Kind of Matrix 9. Multiply Tow Matrices 10. Further Definitions of Matrix 11. Orthogonal Matrix 12. Rules of Matrix Algebra 13. Rotating Coordinate..