Course No.：S070100XJ013
Course Category：Basic course of subject
Period/Credits：40/2
Prerequisites：calculus, linear algebra, ordinary differential equation, elementary functional analysis
Aims & Requirements：
This is one of the speciality foundation courses for master degree candidates majoring in computational mathematics and applied mathematics, and it can also be taken as an elective course for those majoring in physics, mechanics, chemistry and engineering fields. It mainly includes: 1. Basic theories of interpolation and numerical quadrature 2. Basic methods for linear and non-linear equation systems；3. Linear and non-linear eigenvalue problems；4.Introduction to numerical methods for ordinary differential equations and finite element methods.
Participants of this course are expected to have a command of fundamental theories and methods of numerical analysis, to be able to employ the methods in practical computations, and to lay the foundation for future scientific and engineering. computation
Primary Coverage：
Chapter 1 Interpolation and numerical quadrature
Polynomial interpolation; triangular function and spline interpolation；Newton -Cotes
quadratureformula；Gaussian quadrature formula.
Chapter 2 Basic methods for linear and non-linear equation systems
Gauss elimination ; Cholesky decomposition; conjugate gradient method; Lanczos methods；Newton’s method；multi-mesh methods.
Chapter 3 Basic methods for linear and non-linear eigenvalue problems
QR algorithm；power and inverse power method；subspace iteration methods；
predictor-corrector methods for regular solutions；continuity method.
Chapter 4 Numerical methods for ordinary differential equations (ODEs)
Basic theories of ODEs；one-step and multi-step method；introduction to stiff ODEs；
Shooting method.
Chaper 5 Introduction to variational principle and finite element methods
Variational principle; Euler equation；Ritz-Galerkin methods；introduction to finite element methods.
References：
1.J. Stoer, R. Bulirsch，Introduction to Numerical Analysis, Second Edition,
Springer-Verlag, 1991.
2．H. R. Schwarz，Numerical Analysis， A Comprehensive Introduction: With a
Contribution by J. Waldvogel， Chichester: Wiley，1989.
3．Cai Dayong, Bai fengshan, Advanced Numerical Analysis，Tsinghua University Press,Beijing, 1998.
Author：Wang Lijin (School of Mathematical Science of GUCAS)
Date ：June, 2010
