| 1. | |
math and numerical models | In this lecture, we introduce for numerical analysis by comparing between analytical and numerical models |  |
|
matlab (handling scalar variables) | Introduction to matlab environment and handling scalar variables and several basic operations on them | |
|
| 2. | |
matlab (handling vector variables) | handling vector variables in matlab and several basic operations on them including functions and plotting | |
| 3. | |
matlab (handling matrices variables) | handling vector variables in matlab and several basic operations on them including functions and plotting | |
| 4. | |
programming with matlab | introduction to more advanced topic in matlab such as plotting, inline functions, handling complex equations etc. | |
| 5. | |
Roundoff and Truncation Errors : Matlab hints | analyze sources of errors in computations with focus on reducing the errors | |
|
Roots: Bracketing methods : Introduction & Bracketing methods | introducing bracketing methods for finding the intervals of roots | |
|
|
Roots: Bracketing methods : open methods & matlab hints | introducing open methods for finding the intervals of roots | |
|
|
Linear algebraic equations : Introduction to matrices | introduce simple linear systems and several special matrices and their use | |
|
|
Linear algebraic equations : matrices operaions | Introduce several simple matrix-matrix and matrix-vector operations | |
|
|
Linear algebraic equations : singular value decomposition | Shed light o singular valus and their use in analyzing the stability of systems | |
|
| 7. | |
Gauss elimination: Cramer's rule & Naive Gauss elimination | Introduce Cramer's rule and Gausse elimiation as methods to solve linear algebraic systems | |
|
LU decomposition and Cholesky decomposition: Gauss elimination | Introduce LU and Cholesky decompositoon methods and introdce for matrix inversion | |
|
| 8. | |
Matrix inversion using LU decomposition | Due to its low complexity and stability, LU is used as a matrix inversion technique | |
|
Error analysis and system condition | In presence of noise, the system performance is analyzed using already studied algorithms including matrix inversion. Also, the idea and implementation of the maximum likelihood are investigated | |
|
| 9. | |
Iterative method - Gauss-seidel method | introduce iterative methods to solve linear systems - Gauss-Seidel method | |
|
Iterative method - newton-raphson method | introduce nonlinear systems and introduce the newton-raphson method | |
|
|
Introduce EVD & SVD | Introduction to singular value decomposition and eigen value decomposition | |
|
|
EVD (eigen value decompositon) | Introduce the characteristic polynomial and how to obtain the eigen values and relation with trace and det of a matrix | |
|
|
Power method | Introduce the power method to numerically obtain the minimum eigenvalue of a matrix | |
|
|
EVD vs. SVD | introduce points of similarity and difference between eigenvalues and singular values | |
|
| 10. | |
Introduction & overview | introduce curve fitting | |
|
Liner least-squares regression | introduce the linear least squares regression and the derivation of the line parameters | |
|
|
Linearization of nonliner models | linearization of power, exponential and saturation rate nonlinear models | |
|
|
Practice explanation | A practice on the linear curve fitting and the linearization of nonlinear models | |
|
| 11. | |
introduction (and reply to twitter questions) | more examples of linear curve fitting and linearization of nonlinear models | |
|
polynomial regression - single variable | introduce the polynomial regression (nonlinearregression) and the derivation of the polynomial parameters | |
|
|
polynomial regression - 2 variables | apply the nonlinear regression to the case of two independent variables | |
|
| 12. | |
Introduction (~ slide 6) | Introduction to interpolation | |
|
Newton interpolation polynomial | introduce the newton interpolation polynomial and discuss accuracy of this method | |
|
|
Lagrange interpolation polynomial | introduce the lagrange interpolation polynomial and discuss accuracy of this method | |
|
|
Extrapolation | introduce the idea behind extrapolation and the danger of this technique specially when using high order polynomials | |
|
| 13. | |
Integration and Newton-Cotes Formulas | Introduce the basic idea of numerical integration and the newton-cotes method that replaces the function with an interpolation function over which the integration is performed | |
|
Integration: The Trapezoidal/composite Trapezoidal rule | Introduce the Trapezoidal method which consists of integration over a line and a method of improving the result via several integration over several several intervals | |
|
|
Simpson's rules | Introduce the simpson's 1/3 and 3/8 rules which consist of integration over second order and third order polynomials, respectively | |
|
|
Richardson Extrapolation | Introduce the Richardson method which consists of using two less accurate integrals to obtain a more accurate result | |
대구광역시 동구 동내로 64(동내동 1119) 우)41061
COPYRIGHT keris. all rights reserved
페이스북
트위터
카카오톡
네이버밴드
링크복사
