Numerical Analysis

Syllabuses on Computational Mathematics
and Applied Mathematics

Interpolation and approximation

Trigonometric interpolation and approximation, fast Fourier transform; approximations by rational functions; polynomial and spline interpolations and approximation; least-squares approximation. 

Nonlinear equation solvers

Convergence of iterative methods (bisection, Newton’s method, quasi-Newton’s methods and fixed-point methods)for both scalar equations and systems, finding roots of polynomials. 

Linear systems and eigenvalue problems

Classical and modern iterative method for linear systems and eigenvalue problems, condition number and singular value decomposition.

Numerical solutions of ordinary differential equations

Single step methods and multi-step methods, stability, accuracy and convergence; absolute stability, long time behavior; numerical methods for

stiff ODE’s.

Numerical solutions of partial differential equations

Finite difference method, finite element method and spectral method:  stability, accuracy

and convergence, Lax equivalence theorem.

References:

1. C. de Boor and S.D. Conte, Elementary Numerical Analysis, an algorithmic approach, McGraw-Hill, 2000.
2. G.H. Golub and C.F. van Loan, Matrix Computations, third edition, Johns Hopkins University Press, 1996.
3. E. Hairer, P. Syvert and G. Wanner, Solving Ordinary Differential Equations, Springer, 1993.
4. B. Gustafsson, H.-O. Kreiss and J. Oliger, Time Dependent Problems and Difference Methods, John Wiley Sons, 1995.
5. Lloyd N. Trefethen and David Bau, Numerical linear algebra, SIAM, 1997.
6. Susanne Brenner and Ridgway Scott, The Mathematical Theory of Finite Element Methods, Springer, 2010.

R.L. Burden and D. Faires, Numerical analysis, 7th edition, Thomson Learning。


J. Stoer and R. Bulirsch, An introduction to numerical analysis, Springer-Ver

lag,

《Introduction to Algorithms》Corman

C. de Boor and S.D. Conte, Elementary Numerical Analysis, an algorithmic approach, McGraw-Hill, 2000.

G.H. Golub and C.F. van Loan, Matrix Computations, third edition, Johns Hopkins University Press, 1996.

E. Hairer, P. Syvert and G. Wanner, Solving Ordinary Differential Equations, Springer, 1993.

B. Gustafsson, H.-O. Kreiss and J. Oliger, Time Dependent Problems and Difference Methods, John Wiley Sons, 1995.

G. Strang and G. Fix, An Analysis of the Finite Element Method, second edition, Wellesley-Cambridge Press, 2008.

228《数值分析:mathematics of scientific computing》(美)David Kincaid，Ward Cheney著

《数值逼近》李岳生，黄友谦

《数值分析方法》奚梅成

《数值计算方法》林成森

《数值逼近》王仁宏

《数值分析》李庆扬，王能超，易大义

《计算方法引论》徐萃薇，孙绳武

《数值分析基础》李庆扬，王能超，易大义

《数值逼近》蒋尔雄，赵风光

《数值分析引论》易大义

223《数值分析基础》关治，陆金甫著

225《数值方法》关治，陆金甫编著

229《计算方法典型例题分析》孙志忠编著

Numerical Linear Algebra & PDE

LeVeque, Randall J. Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2007. ISBN: 9780898716290.

Finite Volume Methods for Hyperbolic Problems. Cambridge texts in applied mathematics. Cambridge, UK: Cambridge University Press, 2002. ISBN: 9780521009249.

Fletcher, C. A. J. Computational Techniques for Fluid Dynamics. Fundamental and General Techniques Volume I. Springer series in computational physics. New York, NY: Springer-Verlag, 1996. ISBN: 9783540530589.

Buy at Amazon ———. Computational Techniques for Fluid Dynamics. Specific Techniques for Different Flow Categories Volume II. Springer series in computational physics. New York, NY: Springer-Verlag, 1991. ISBN: 9783540536017.

Buy at Amazon Canuto, Claudio S., M. Y. Hussaini, A. Quarteroni, and T. A. Zang. Spectral Methods Evolution to Complex Geometries and Applications to Fluid Dynamics. New York, NY: Springer-Verlag, 2007. ISBN: 9783540307273.

Buy at Amazon Trefethen, Lloyd N. Spectral Methods in MATLAB (Software, Environments, Tools). Philadelphia, PA: Society for Industrial and Applied Mathematics, 2001. ISBN: 9780898714654.

Buy at Amazon Evans, Lawrence C. Partial Differential Equations. Vol. 19. Graduate studies in mathematics. Providence, RI: American Mathematical Society, 1998. ISBN: 9780821807729.

《矩阵计算和方程求根》曹志浩，张德玉，李瑞遐

《矩阵数值分析》邢志栋

《微分方程数值解法》李荣华，冯果忱

《微分方程数值解法》余德浩，汤华中

《微分方程数值解法》李立康，於崇华，朱政华

《非线性方程组解法与最优化方法》王德人

《最优化理论与算法》陈宝林

《最优化理论与方法》袁亚湘，孙文瑜

《信息论基础》叶中行

专门为数学系写的信息论

《信息论，编码与密码学》Ranjan Bose

Numerical Analysis

Syllabuses on Computational Mathematics 
and Applied Mathematics

Interpolation and approximation

Trigonometric interpolation and approximation, fast Fourier transform; approximations by rational functions; polynomial and spline interpolations and approximation; least-squares approximation. 

Nonlinear equation solvers

Convergence of iterative methods (bisection, Newton’s method, quasi-Newton’s methods and fixed-point methods)for both scalar equations and systems, finding roots of polynomials .

Linear systems and eigenvalue problems

Classical and modern iterative method for linear systems and eigenvalue problems, condition number and singular value decomposition.

Numerical solutions of ordinary differential equations

Single step methods and multi-step methods, stability, accuracy and convergence; absolute stability, long time behavior; numerical methods for

stiff ODE ‘s .

Numerical solutions of partial differential equations

Finite difference method, finite element method and spectral method: stability, accuracy

and convergence, Lax equivalence theorem.

References:

1. C. de Boor and S.D. Conte, Elementary Numerical Analysis, an algorithmic approach, McGraw-Hill, 2000.

2. G.H. Golub and C.F. van Loan, Matrix Computations, third edition , Johns Hopkins University Press, 1996.

3. E. Hairer, P. Syvert and G. Wanner, Solving Ordinary Differential Equations, Springer, 1993.

4. B. Gustafsson, H.-O. Kreiss and J. Oliger, Time Dependent Problems and Difference Methods, John Wiley Sons, 1995.

5. Lloyd N. Trefethen and David Bau, Numerical linear algebra , SIAM, 1997.

6. Susanne Brenner and Ridgway Scott, The Mathematical Theory of Finite Element Methods , Springer, 2010.

R.L. Burden and D. Faires, Numerical analysis, 7th edition, Thomson Learning 。 


J. Stoer and R. Bulirsch, An introduction to numerical analysis, Springer-Ver

lag,

《 Introduction to Algorithms 》 Corman

C. de Boor and S.D. Conte, Elementary Numerical Analysis, an algorithmic approach, McGraw-Hill, 2000.

G.H. Golub and C.F. van Loan, Matrix Computations, third edition, Johns Hopkins University Press, 1996.

E. Hairer, P. Syvert and G. Wanner, Solving Ordinary Differential Equations, Springer, 1993.

B. Gustafsson, H.-O. Kreiss and J. Oliger, Time Dependent Problems and Difference Methods, John Wiley Sons, 1995.

G. Strang and G. Fix, An Analysis of the Finite Element Method, second edition, Wellesley-Cambridge Press, 2008.

228 The numerical analysis :mathematics of scientific computing 》 ( The United States ), David Kincaid , Ward Cheney The

The numerical approximation of Li Yuesheng, Huang Youqian

Of the numerical analysis method for Xi Meicheng

Of the numerical method of the forest forest

The numerical approximation of Wang Renhong

The numerical analysis of Li Qingyang, Wang nengchao, da Yi

Introduction to the calculation method of Xu Cui Wei, Sun Shengwu

Numerical analysis of Li Qing-Yang, Wang nengchao, da Yi

The numerical approximation of Jiang erxiong, Zhao scenery

An introduction to numerical analysis of righteousness

223 Numerical analysis on basic Kanji, Lu jinfu with

225 The numerical methods for Kanji, written by Lu jinfu

229 Written by Sun Zhizhong of the calculation method of typical analysis examples

Numerical Linear Algebra & PDE

LeVeque, Randall J. Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2007. ISBN: 9780898716290.

Finite Volume Methods for Hyperbolic Problems. Cambridge texts in applied mathematics. Cambridge, UK: Cambridge University Press, 2002. ISBN: 9780521009249.

Fletcher, C. A. J. Computational Techniques for Fluid Dynamics. Fundamental and General Techniques Volume I. Springer series in computational physics. New York, NY: Springer-Verlag, 1996. ISBN: 9783540530589.

Buy at Amazon ———. Computational Techniques for Fluid Dynamics. Specific Techniques for Different Flow Categories Volume II. Springer series in computational physics. New York, NY: Springer-Verlag, 1991. ISBN: 9783540536017.

Buy at Amazon Canuto, Claudio S., M. Y. Hussaini, A. Quarteroni, and T. A. Zang. Spectral Methods Evolution to Complex Geometries and Applications to Fluid Dynamics. New York, NY: Springer-Verlag, 2007. ISBN: 9783540307273.

Buy at Amazon Trefethen, Lloyd N. Spectral Methods in MATLAB (Software, Environments, Tools). Philadelphia, PA: Society for Industrial and Applied Mathematics, 2001. ISBN: 9780898714654.

Buy at Amazon Evans, Lawrence C. Partial Differential Equations. Vol. 19. Graduate studies in mathematics. Providence, RI: American Mathematical Society, 1998. ISBN: 9780821807729.

The matrix calculations and equations Cao Zhihao, Zhang Deyu, Li Ruixia

Numerical analysis of the matrix of Xing Zhidong

The numerical solution of differential equations Li ronghua, Feng guochen

Galerkin approximations of the numerical solution of differential equations, soup Central

The numerical solution of differential equations Li likang, yuchonghua, Zhu Zhenghua

The solution of systems of nonlinear equations and optimization method of Wang Deren

Of the optimization theory and algorithms for Chen Baolin

Of the theory and method of optimal Yuan yaxiang, Sun wenyu

The characteristic of ye Zhong-XING

Specifically written for the Department of mathematics of information theory

The information theory, coding and Cryptography Ranjan Bose