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    교육학 >특수교육 >특수교육학
  • 강의학기
    2011년 2학기
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    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
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1. Introduction of the course, Applied Linear Algebra Four Special Matrices
2. Applied Linear Algebra Four Special Matrices
Differences, Derivatives, Boundary condition
URL
Applied Linear Algebra Differences, Derivatives, Boundary condition URL
3. Applied Linear Algebra Differences, Derivatives, Boundary condition
Elimination leads to K = LDL^T
URL
Applied Linear Algebra Elimination leads to K = LDL^T
Inverse and Delta function
URL
4. Applied Linear Algebra Inverse and Delta function URL
5. Applied Linear Algebra Inverse and Delta function
Eingenvalues and Eigenvectors
URL
Applied Linear Algebra Eingenvalues and Eigenvectors URL
6. Applied Linear Algebra (Eingenvalues and Eigenvectors) Part 1 : Ax = \lambda x and A^k x = \lambda^k x and Diagonalizing A URL
7. Applied Linear Algebra (Eingenvalues and Eigenvectors) Part 2 : Eigenvectors for Derivatives and Differences URL
Applied Linear Algebra (Eingenvalues and Eigenvectors, Positive Definite Matrices) Part 2 : Eigenvectors for Derivatives and Differences, What is Positive Definite? URL
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 URL
Applied Linear Algebra (Positive Definite Matrices, Numerical Linear Algebra: LU, QR, SVD) Three Essential Factorizations, Orthogonal Matrices, Orthogonalization A = QR, SVD URL
9. Applied Linear Algebra (Numerical Linear Algebra: LU, QR, SVD) SVD, The pseudoinverse, Condition Numbers and Norms URL
10. Applied Linear Algebra (Numerical Linear Algebra: LU, QR, SVD) Condition Numbers and Norms, Mass Spring System, Stiffness Matrix and Solution URL
A Framework for Applied Mathematics(Equilibrium and Stiffness Matrix) Fixed End and Free End, Minimum Principles URL
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) URL
12. A Framework for Applied Mathematics (Oscillation by Newtons Law) Key Example: Motion Around a Circle, Line of Masses and Springs URL
A Framework for Applied Mathematics (Oscillation by Newtons Law) Total Energy is Conserved, Applied Force and Resonance, Explicit Finite Differences, Stability and Instability URL
13. A Framework for Applied Mathematics (Oscillation by Newtons Law, Least Squares for Rectangular Matrices) Explicit Finite Differences, Stability and Instability Linear Algebra Interpretation URL
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 URL
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 URL
15. A Framework for Applied Mathematics (Graph Models and Kirchhoffs laws, Networks and Transfer Functions) KKT matrix, Impedance URL
16. A Framework for Applied Mathematics (Networks and Transfer Functions) Time Domain versus Frequency Domain, Transient Response and the Transfer Function, Underdamping and Overdamping URL
17. A Framework for Applied Mathematics (Graph Models and Kirchhoffs laws, Networks and Transfer Functions) KKT matrix, Impedance URL
A Framework for Applied Mathematics (Networks and Transfer Functions) Phase, Time Domain versus Frequency Domain, Transient Response and the Transfer Function URL
18. A Framework for Applied Mathematics (Networks and Transfer Functions) Time Domain versus Frequency Domain, Transient Response and the Transfer Function, Underdamping and Overdamping URL
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 URL
Boundary Value Problems (Differential Equations and Finite Elements) Galerkins Method, Comparison with Finite Difference, More accurate Finite Elements URL
20. Boundary Value Problems (Differential Equations and Finite Elements) Galerkins Method, Comparison with Finite Difference, More accurate Finite Elements URL
21. Boundary Value Problems (Cubic splines and Forth-Order Equations, Gradient and Divergence) Cubic Finite Elements, Finite Difference for (cu)=f, Gradient, Divergence URL
22. Boundary Value Problems (Gradient and Divergence) Gradient, Divergence, Curl, Two important identities URL
23. Boundary Value Problems (Gradient and Divergence) Two important identies, Converse of the Two Identities, Harmonic Function URL
Boundary Value Problems (Laplace Equation) Complex Plane, Analytic function, Derivative of complex valued function, Cauchy-Riemann Equation URL
24. Boundary Value Problems (Laplace Equation) Polar Coordinates: Laplace Equation in a Circle URL
25. Boundary Value Problems (Laplace Equation, Finite Differences and Fast Poisson Solver) Polar Coordinates: Laplace Equation in a Circle, Poissons Equation in a Square URL
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 URL
27. Boundary Value Problems (The Finite Element Method) Pyramid Functions, Element Matricers and Element Vectors URL
28. Boundary Value Problems(The Finite Element Method) Global Matrix K and F frome K_e and F_e, Element Matrix in Two Dimension URL
Boundary Value Problems(The Finite Element Method) Element Matrix in Two Dimension, Quadrilateral Elements URL

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