## 주메뉴

### 기초계산과학공학

• 연세대학교
• 정윤모 • 주제분류
교육학 >특수교육 >특수교육학
• 강의학기
2011년 2학기
• 조회수
6,634
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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
Applied Linear Algebra #### 차시별 강의      1. Introduction of the course, Applied Linear Algebra Four Special Matrices 2. Applied Linear Algebra Four Special MatricesDifferences, Derivatives, Boundary condition  Applied Linear Algebra Differences, Derivatives, Boundary condition 3. Applied Linear Algebra Differences, Derivatives, Boundary conditionElimination leads to K = LDL^T  Applied Linear Algebra Elimination leads to K = LDL^TInverse and Delta function 4. Applied Linear Algebra Inverse and Delta function 5. Applied Linear Algebra Inverse and Delta functionEingenvalues and Eigenvectors  Applied Linear Algebra Eingenvalues and Eigenvectors 6. Applied Linear Algebra (Eingenvalues and Eigenvectors) Part 1 : Ax = \lambda x and A^k x = \lambda^k x and Diagonalizing A 7. Applied Linear Algebra (Eingenvalues and Eigenvectors) Part 2 : Eigenvectors for Derivatives and Differences  Applied Linear Algebra (Eingenvalues and Eigenvectors, Positive Definite Matrices) Part 2 : Eigenvectors for Derivatives and Differences, What is Positive Definite? 8. Applied Linear Algebra (Positive Definite Matrices) Examples and Energy-based Definition, Positive definiteness, Minimum Problem in n Dimensions, Test for a Minmimum, Newtons Method  Applied Linear Algebra (Positive Definite Matrices, Numerical Linear Algebra: LU, QR, SVD) Three Essential Factorizations, Orthogonal Matrices, Orthogonalization A = QR, SVD 9. Applied Linear Algebra (Numerical Linear Algebra: LU, QR, SVD) SVD, The pseudoinverse, Condition Numbers and Norms 10. Applied Linear Algebra (Numerical Linear Algebra: LU, QR, SVD) Condition Numbers and Norms, Mass Spring System, Stiffness Matrix and Solution  A Framework for Applied Mathematics(Equilibrium and Stiffness Matrix) Fixed End and Free End, Minimum Principles 11. A Framework for Applied Mathematics (Oscillation by Newtons Law) One Mass and One Spring, Key Example: Motion Around a Circle (Four Finite Difference Methods) 12. A Framework for Applied Mathematics (Oscillation by Newtons Law) Key Example: Motion Around a Circle, Line of Masses and Springs  A Framework for Applied Mathematics (Oscillation by Newtons Law) Total Energy is Conserved, Applied Force and Resonance, Explicit Finite Differences, Stability and Instability 13. A Framework for Applied Mathematics (Oscillation by Newtons Law, Least Squares for Rectangular Matrices) Explicit Finite Differences, Stability and Instability Linear Algebra Interpretation 14. A Framework for Applied Mathematics (Least Squares for Rectangular Matrices, Graph Models and Kirchhoffs laws) Linear Algebra Interpretation, Computation of Least Squares, The Incident Matrix  A Framework for Applied Mathematics (Graph Models and Kirchhoffs laws) The Graph Laplacian Matrix A^T*A, Inputs b, f and Matrices A, C, A^T, Assembling the Matrix K = A^T*C*A 15. A Framework for Applied Mathematics (Graph Models and Kirchhoffs laws, Networks and Transfer Functions) KKT matrix, Impedance 16. A Framework for Applied Mathematics (Networks and Transfer Functions) Time Domain versus Frequency Domain, Transient Response and the Transfer Function, Underdamping and Overdamping 17. A Framework for Applied Mathematics (Graph Models and Kirchhoffs laws, Networks and Transfer Functions) KKT matrix, Impedance  A Framework for Applied Mathematics (Networks and Transfer Functions) Phase, Time Domain versus Frequency Domain, Transient Response and the Transfer Function 18. A Framework for Applied Mathematics (Networks and Transfer Functions) Time Domain versus Frequency Domain, Transient Response and the Transfer Function, Underdamping and Overdamping 19. Boundary Value Problems (Differential Equations and Finite Elements) The Framework A^TCA for a Hanging Bar, General Solution and Examples, The Transpose A = d/dx  Boundary Value Problems (Differential Equations and Finite Elements) Galerkins Method, Comparison with Finite Difference, More accurate Finite Elements 20. Boundary Value Problems (Differential Equations and Finite Elements) Galerkins Method, Comparison with Finite Difference, More accurate Finite Elements 21. Boundary Value Problems (Cubic splines and Forth-Order Equations, Gradient and Divergence) Cubic Finite Elements, Finite Difference for (cu)=f, Gradient, Divergence 22. Boundary Value Problems (Gradient and Divergence) Gradient, Divergence, Curl, Two important identities 23. Boundary Value Problems (Gradient and Divergence) Two important identies, Converse of the Two Identities, Harmonic Function  Boundary Value Problems (Laplace Equation) Complex Plane, Analytic function, Derivative of complex valued function, Cauchy-Riemann Equation 24. Boundary Value Problems (Laplace Equation) Polar Coordinates: Laplace Equation in a Circle 25. Boundary Value Problems (Laplace Equation, Finite Differences and Fast Poisson Solver) Polar Coordinates: Laplace Equation in a Circle, Poissons Equation in a Square 26. Boundary Value Problems (Finite Differences and Fast Poisson Solver, The Finite Element Method) Elimination and Fill-in, Solver Using Eigenvalues, Fast Poisson Solvers, Trial and Test Functions: Galerkins method 27. Boundary Value Problems (The Finite Element Method) Pyramid Functions, Element Matricers and Element Vectors 28. Boundary Value Problems(The Finite Element Method) Global Matrix K and F frome K_e and F_e, Element Matrix in Two Dimension  Boundary Value Problems(The Finite Element Method) Element Matrix in Two Dimension, Quadrilateral Elements #### 연관 자료 #### 사용자 의견

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