수치해석1
- 연세대학교
- 이은정
페이스북
트위터
카카오톡
네이버밴드
링크복사
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- 주제분류
- 자연과학 >수학ㆍ물리ㆍ천문ㆍ지리 >수학
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- 강의학기
- 2012년 1학기
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- 조회수
- 18,474
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This course is designed to acquaint students in mathematical and physical sciences and engineering with the fundamental theory of numerical analysis.
- 수강안내 및 수강신청
- ※ 수강확인증 발급을 위해서는 수강신청이 필요합니다
Preliminaries. Error:its sources, propagation, and analysis
차시별 강의
| 1. | |
Preliminaries. Error:its sources, propagation, and analysis | Introduce some mathematical preliminaries |  |
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Root finding for Nonlinear Equations | This course introduce a well known root finding methods such as Bisection Method, Newtons Method | |
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| 2. | |
Root finding for Nonlinear Equations | Root finding for nonlinear equations with Secent method, Fixed-Point Iteration method and Aitkens extrapolation formula. | |
| 3. | |
Systems of Nonlinear Equations | Introduce some methods to find a root of nonlinear equations | |
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Interpolation Theory (1) | Interpolate and approximate | |
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| 4. | |
Interpolation Theory (2) | Interpolate and approximate | |
| 5. | |
Interpolation Theory (3) | Introduce an useful algorithm of Cubic Spline and B-spline | |
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Interpolation Theory and Approximation of functions | Introduce an useful algorithm of Cubic Spline and B-spline and compare both method. | |
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| 6. | |
Approximation of functions | We need to approximate a function which is difficult to calculate. There are several theorems we can use. | |
| 7. | |
Numerical Integration (1) | There are many functions which we cannot integrate. Then we use Numerical Integration methods to approximate a value. | |
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Numerical Integration (2) | There are many functions which we cannot integrate. Then we use Numerical Integration methods to approximate a value. | |
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| 8. | |
Numerical Integration (3) | There are many functions which we cannot integrate. Then we use Numerical Integration methods to approximate a value. | |
| 9. | |
Numerical Integration (4) | There are many functions which we cannot integrate. Then we use Numerical Integration methods to approximate a value. | |
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Numerical Methods for Ordinary Differential Equations (1) | Review of basic concept Ordinary Differential Equations | |
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| 10. | Numerical Methods for Ordinary Differential Equations (2) | Solve some examples of initial value problem. Theorem of the existence and uniqueness and stability. | ||
| 11. | |
Numerical Methods for Ordinary Differential Equations (3) | Existence, Uniqueness, and Stability Theory | |
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Numerical Methods for Ordinary Differential Equations (4) | Eulers method, Multistep methods | |
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| 12. | |
Numerical Methods for Ordinary Differential Equations (5) | The Midpoint method, the Trapezoidal method | |
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Numerical Methods for Ordinary Differential Equations (6) | Runge-Kutta method | |
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| 13. | |
Numerical Methods for Ordinary Differential Equations | Multistep methods, Convergence, Stability theory | |
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Numerical Methods for Ordinary Differential Equations , Linear Algebra | Convergence, Stability regions, Vector spaces, Matrices, Linear systems | |
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| 14. | |
Linear Algebra | Eigenvalues and Canonical forms | |
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Linear Algebra | Eigenvalues and Canonical forms | |
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| 15. | |
Numerical solution of systems of linear equations | Gaussian elimination | |
| 16. | |
Numerical solution of systems of linear equations | Error Analysis | |
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Numerical solution of systems of linear equations | Iteration method | |
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| 17. | |
Numerical solution of systems of linear equations | Conjugate Gradient Method | |
| 18. | |
Numerical solution of systems of linear equations | Conjugate Gradient Method | |
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Numerical solution of systems of linear equations | Conjugate Gradient Method | |
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| 19. | |
The matrix eienvalue problem | Stability of eigenvalues for nonsymmetric matrices | |
| 20. | |
The matrix eienvalue problem | Power method | |
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The matrix eienvalue problem | QR-method, Least squares solution | |
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