Course No.:S070104ZJ008
Course Category:Professional Basic Course
Period/Credits:40/2
Prerequisites:Higher calculation, linear algebra
Aims and Requirements:
This course is the basic course of computational mathematics and computer science as well as other needs numerical calculation of the postgraduates. This course covers the basic methods of numerical calculation, calculation methods and mathematical theoretical basis for the calculation of the relevant professional. Main contents include: error, interpolation, approximation theory, numerical differentiation and integration; matrix norm theory, the solution of linear equations direct and iterative methods, nonlinear equations, eigenvalues , vector calculus, ordinary differential equation solving and so on.
Through this course, students can master the basic theories and methods of numerical approximation.
Primary Coverage:
Chapter 1, concept of error, causes and reduction.
Chapter 2, concept of interpolation, polynomial interpolation, remainder of the interpolation polynomial and convergence, orthogonal polynomial, best square approximation, expanding by Chebyshev polynomial.
Chapter 3, consistent approximation in function space, existence and uniqueness, the approximate order, class of approximate functions.
Chapter 4, Numerical differentiation, numerical integration, difference, intepolation differentiation and integration, Newton-cotes integration.
Chapter 5, Normal of vectors and matrices, conditions of matrix, convergence matrix, QR decomposition.
Chapter 6, Solving linear and nonlinear equations, elimination method, LU decomposition, SVD method, iterative algorithm of Jacobi, Gauss-Seidel, Newton.
Chapter 7, Soving ODE, Euler formula, Runge-Kutta method, implicit iteration schemes
References:
1.Feicheng Xie, Numerical analysis, Press of University of Science and Technology of China, 1995.
2.Renhong Wang, Numerical approximation, High Education Press, 2003。
Author: Liyong Shen
Date: June,2009