페이스북
트위터
카카오톡
네이버밴드
링크복사
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- 주제분류
- 자연과학 >수학ㆍ물리ㆍ천문ㆍ지리 >수학
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- 등록일자
- 2010.10.01
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- 조회수
- 7,899
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This course is intended for graduate students (or undergraduate) who need a rapid and uncomplicated introductions to the field of applied mathematics involving computational linear algebra and differential equations. The lecture has two themes-how to understand equations, and how to solve them . This course include numerical linear algebra(QR,SVD, singular system), Newton’s method for minimization, Equilibrium and stiffness matrix, Least squares, Nonlinear problems, Covariances and Recursive Least squares, Differential equations and finite elements, Finite Difference and Fast Poisson, Boundary value problems in Elasticity and Solid mechanics
- 수강안내 및 수강신청
- ※ 수강확인증 발급을 위해서는 수강신청이 필요합니다
Graph models and Kirchhoffs laws 1
차시별 강의
| 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 |
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