기록

23. Vector Product(Cross Product) $ \vec{C}=\vec{A}\times \vec{B} $ $ C_{i}=\sum_{j,k}^{}\epsilon_{ijk}A_{j}B_{k} $ Levi-Civita Density(Permutation Symbol): $ \epsilon_{ijk}=\left\{\begin{matrix} 0 \\ +1 \\ -1 \end{matrix}\right. $ 0: two or three indexes are same ($ \epsilon_{112},\epsilon_{113},\epsilon_{121},\epsilon_{131},\epsilon_{211},\epsilon_{311} $) ($ \epsilon_{221},\epsilon_{223},\eps..

21. Position Vector $ \vec{A}=(x_{1},x_{2},x_{3}) $ $ \vec{B}=(\bar{x_{1}},\bar{x_{2}},\bar{x_{3}}) $ $ |\vec{A}|=\sqrt{\vec{A}\cdot \vec{A}}=\sqrt{x_{1}^{2}+x_{2}^{2}+x_{3}^{2}}=\sqrt{\sum_{i}^{}x_{i}^{2}} $: Distance from the Origin to the Point $ (x_{1},x_{2},x_{3}) $ $ \sqrt{\sum_{i}^{}(x_{i}-\bar{x_{i}})^{2}}=\sqrt{(\vec{A}-\vec{B})\cdot(\vec{A}-\vec{B})}=|\vec{A}-\vec{B}| $: Distance from ..

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, $ ..

13. Rotating Coordinate Axes 1) Counterclockwise about the $ x_{3} $-axis $ x_{1}'=x_{2}, x_{2}'=-x_{1}, x_{3}'=x_{3} $ $ \lambda _{11}=\lambda _{13}=\lambda _{22}=\lambda _{23}=\lambda _{31}=\lambda _{32}=0 $ $ \lambda _{12}=\cos (x_{1}',x_{2})=1 $ $ \lambda _{21}=\cos (x_{2}',x_{1})=-1 $ $ \lambda _{33}=\cos (x_{3}',x_{3})=1 $ $ \Rightarrow \vec{\lambda_{1}} =\bigl(\begin{smallmatrix} 0 & 1 & ..

(전공 수업 들으면서 계속 추가할 예정) 1. University Physics with modern physics(Young and Freedman) 2. Classical Dynamics of Particles and Systems(Thornton, Marion) 3. Concepts of Modern Physics(Arthur Beiser) 4. Semiconductor Physics and Devices(Donald A.Neamen) 5. Electronic Devices(Thomas L. Floyd)

(전공 수업 들으면서 계속 추가할 예정) 1. Essentials of Geology(Stephen Marshak) 2. Principles of Sedimentology and Stratigraphy(Sam Boggs) 3. Mineralogy and Optical Mineralogy(Dyar, Gunter, Tasa) 4. Guide to Thin Section Microscopy(Raith, Raase, Reinhardt) 5. Introduction to Optical Mineralogy(William D. Nesse)

10. Further Definitions of Matrix 1) Transposed Matrix: row와 column 바꾸기 $ \vec{\lambda} _{ij}^{t}=\vec{\lambda}_{ji} $ $ (\vec{\lambda}^{t})^{t}=\vec{\lambda} $ $ (\vec{A}\vec{B})^{t}=\vec{B}^{t}\vec{A}^{t} $ ex) Inverse Transformation $ x_{i}=\sum_{j}^{}\lambda _{ji}x_{j}' $ $ x_{i}=\sum_{j}^{}\lambda _{ij}^{t}x_{j}' $ $ \vec{X}=\vec{\lambda }^{t}\vec{X}' $ $ \bigl(\begin{smallmatrix} x_{1}\\ x..

8. Kind of Matrix Matrix: set을 만들기(필요로 하는 물리량을 하나의 괄호 안에) Square Matrix: n x n Column Matrix: $ \vec{X}=\bigl(\begin{smallmatrix} x_{1}\\ x_{2} \\ x_{3} \end{smallmatrix}\bigr) $ Row Matrix: $ \vec{X}=\bigl(\begin{smallmatrix} x_{1} & x_{2} & x_{3} \end{smallmatrix}\bigr) $ 9. Multiply Tow Matrices $ \vec{C}=\vec{A}\vec{B} $ $ C_{ij}=[\vec{A}\vec{B}]_{ij}=\sum_{k}^{}A_{ik}B_{kj} $ number of colu..

6. Properties of Rotation Matrices $ (\alpha ,\beta ,\gamma )\rightarrow (\alpha ',\beta ',\gamma ') $ $ (x_{1},x_{2},x_{3}) $ coordinate에서 $ \Theta $ 만큼 회전한 $ (x_{1}',x_{2}',x_{3}') $ coordinate 1) $ \cos ^{2}\alpha +\cos ^{2}\beta +\cos ^{2}\gamma =1 $ $ x_{1}=r\cos \alpha , x_{2}=r\cos \beta , x_{3}=r\cos \gamma $ $ r^{2}=x_{1}^{2}+x_{2}^{2}+x_{3}^{2}=r^{2}\cos ^{2}\alpha +r^{2}\cos ^{2}\beta..