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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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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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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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Interpolation Theory (2) | Interpolate and approximate | ![]() |
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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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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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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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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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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. | ||
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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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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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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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Linear Algebra | Eigenvalues and Canonical forms | ![]() |
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Linear Algebra | Eigenvalues and Canonical forms | ![]() |
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Numerical solution of systems of linear equations | Gaussian elimination | ![]() |
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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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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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Numerical solution of systems of linear equations | Conjugate Gradient Method | ![]() |
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The matrix eienvalue problem | Stability of eigenvalues for nonsymmetric matrices | ![]() |
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The matrix eienvalue problem | Power method | ![]() |
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The matrix eienvalue problem | QR-method, Least squares solution | ![]() |