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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. |
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Root finding for Nonlinear Equations |
Root finding for nonlinear equations with Secent method, Fixed-Point Iteration method and Aitkens extrapolation formula. |
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3. |
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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. |
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Interpolation Theory (2) |
Interpolate and approximate |
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5. |
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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. |
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Approximation of functions |
We need to approximate a function which is difficult to calculate. There are several theorems we can use. |
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7. |
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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. |
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Numerical Integration (3) |
There are many functions which we cannot integrate. Then we use Numerical Integration methods to approximate a value. |
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9. |
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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. |
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Numerical Methods for Ordinary Differential Equations (2) |
Solve some examples of initial value problem. Theorem of the existence and uniqueness and stability. |
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11. |
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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. |
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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. |
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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. |
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Linear Algebra |
Eigenvalues and Canonical forms |
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Linear Algebra |
Eigenvalues and Canonical forms |
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15. |
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Numerical solution of systems of linear equations |
Gaussian elimination |
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16. |
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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. |
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Numerical solution of systems of linear equations |
Conjugate Gradient Method |
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18. |
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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. |
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The matrix eienvalue problem |
Stability of eigenvalues for nonsymmetric matrices |
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20. |
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The matrix eienvalue problem |
Power method |
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The matrix eienvalue problem |
QR-method, Least squares solution |
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