# ## 주메뉴

### 수치해석 및 실습

• 한국기술교육대학교
• Manar Mohaisen • 주제분류
공학 >전기ㆍ전자 >전자공학
• 강의학기
2013년 2학기
• 조회수
10,779
•
This course is intended to undergraduate students where we study several numerical techniques and their implementation using matlab program. The practical aspects of systems are analyzed under imperfect conditions
math and numerical models #### 차시별 강의      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 #### 연관 자료 #### 사용자 의견

강의 평가를 위해서는 로그인 해주세요.

#### 이용방법

• 비디오 강의 이용시 필요한 프로그램 [바로가기]

※ 강의별로 교수님의 사정에 따라 전체 차시 중 일부 차시만 공개되는 경우가 있으니 양해 부탁드립니다.