1. | Graph models and Kirchhoffs laws 1 | The incidence matrix Kirchhoffs current law (KCL) Kirchhoffs voltage law (KVL) |
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2. | Graph models and Kirchhoffs laws 2 | The incidence matrix Kirchhoffs current law (KCL) Kirchhoffs voltage law (KVL) |
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3. | Graph models and Kirchhoffs law / Newtworks and transfer functions | Assembling the matrix K = A^TCA The saddle point KKT matix Loop equation fow W and impedance Z |
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4. | Newtworks and transfer functions | Time domain versus frequency domain Laplace transform |
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5. | Newtworks and transfer functions / Nonlinear problem | Underdamping and overdamping Newtons method |
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6. | Nonlinear problem / Differential equations and finite elements | Newtons method Minimizing P(u) Steepest decent Second - order equations |
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7. | Differential equations and finite elements (1) | The A^TCA framework for a hanging bar The transpose of A = d/dx Galerkins method(FEM) |
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8. | Differential equations and finite elements (2) | Construction of the Finite Element Method Linear Finite element Comparison with finite differences |
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9. | Differential equations and finite elements / Cubic splines and fourth-order equations | More accurate finite elements Fourth order equations : Beam bending |
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10. | Cubic splines and fourth-order equations | Cubic splines for interpolation Continuity conditions Cubic finite elements |
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11. | Gradient and divergence | The divergence The Divergence theorem. 29분 30초 이후부터 음성이 나오지 않습니다 |
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12. | Gradient and divergence | Definition of divergence and curl. Stokes and Greens Theorem The Gauss - Green formula Gradiant and divergence plane vertor field v, w |
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13. | Gradient and divergence | Gradients and irrotational velocity field Contituous form of Kirchhoffs voltage law Plane gradient fields |
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14. | Gradient and divergence / Laplaces equation | Plane gradient fields Solutions of Laplaces equation The Cauchy-Riemann equations |
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15. | Laplaces equation | Polar coordinates :laplaces equation in a circle | ||
16. | Laplaces equation / Finite differences and fast poisson solvers | · Solver using eigenvalues · Fast Poisson solvers · Trial and test functions : Galerkins method |
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17. | Finite differences and fast poisson solvers / The finite element method | · Solver using eigenvalues · Fast Poisson solvers · Trial and test functions : Galerkins method |
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18. | The finite element method | · Paramid functions · Element matrices and element vectors |
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19. | The finite element method | · Element matrices and element vectors · Boundary conditions come last |
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20. | The finite element method | · Element matrices in two dimentions · Quadrilateral elements |
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21. | Introduction of this course / Four special matrices | Introduction of this course Properties of four special of matrices : K, C, T, B |
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22. | Four special matrices / Differences, dirivatives, boundary conditions | Properties of four special of matrices : K, C, T, B | ||
23. | Differences, dirivatives, boundary conditions / Elimination leads to k = LDL^T | Properties of four special of matrices : K,C,T,B Gaussian elimination and.LU decomposition. |
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24. | Elimination leads to k = LDL^T | Sysmmetry convert K = LU to K = LDL^T The determinant of Kn |
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25. | Inverse and dalta functions | Delta functions and Greens function | ||
26. | Inverse and dalta functions / Eigenvalaue and Eigenvectors | Discrete vectors: Load and Step and Ramp Greens function and the inverse matrix Diagonalizing a Matrix |
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27. | Eigenvalaue and Eigenvectors | Ax = λx and A^k x = λ^k x and diagonalizing A | ||
28. | Eigenvalaue and Eigenvectors | The power of matrix Application to vector differential equations Eigenvectors and derivatives and differences |
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29. | Eigenvalaue and Eigenvectors | Eigenvectors of Kn :Discrete Sines Eigenvectors of Bn :Discrete Cosines |
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30. | Eigenvalaue and Eigenvectors / Positive Definite Matrices | Eigenvectors of Cn The Fourier Matrix Energy or quadratic form |
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31. | Positive Definite Matrices (1) | Minimum Problem in n dimensions Newtons Method for Minimization |
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32. | Positive Definite Matrices (2) | Minimum Problem in n dimensions Newtons Method for Minimization |
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33. | Numerical Linear Algebra: LU, QR, SVD 1 | Orthogonal Matrices Orthogonalization A = QR Singular Value Decomposition |
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34. | Numerical Linear Algebra: LU, QR, SVD 2 | Singular value Decomposition The Pseudoinverse Condition numbers |
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35. | Numerical Linear Algebra: LU, QR, SVD 3 | Condition numbers and Norms | ||
36. | Equilibrium and the Stiffness Matrix | Stiffness matrix and solution Minimum principle |
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37. | Oscillation by Newtons Law (1) | One mass and One Spring Motion around a circle Line of masses and spring |
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38. | Oscillation by Newtons Law (2) | M - orthogonality Total energy is conserved Applied force and resonance |
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39. | Least squares for rectangular matrices | Least squares by calculus Least squares by linear algebra Computational Least squares |