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연세대학교
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페이스북 트위터 카카오톡 네이버밴드 링크복사

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자연과학 >수학ㆍ물리ㆍ천문ㆍ지리 >수학
강의학기

2012년 1학기

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This course is designed to acquaint students in mathematical and physical sciences and engineering with the fundamental theory of numerical analysis.

수강안내 및 수강신청
※ 수강확인증 발급을 위해서는 수강신청이 필요합니다

Preliminaries. Error:its sources, propagation, and analysis

차시별 강의

1.	Preliminaries. Error:its sources, propagation, and analysis	Introduce some mathematical preliminaries
	Root finding for Nonlinear Equations	This course introduce a well known root finding methods such as Bisection Method, Newtons Method
2.	Root finding for Nonlinear Equations	Root finding for nonlinear equations with Secent method, Fixed-Point Iteration method and Aitkens extrapolation formula.
3.	Systems of Nonlinear Equations	Introduce some methods to find a root of nonlinear equations
	Interpolation Theory (1)	Interpolate and approximate
4.	Interpolation Theory (2)	Interpolate and approximate
5.	Interpolation Theory (3)	Introduce an useful algorithm of Cubic Spline and B-spline
	Interpolation Theory and Approximation of functions	Introduce an useful algorithm of Cubic Spline and B-spline and compare both method.
6.	Approximation of functions	We need to approximate a function which is difficult to calculate. There are several theorems we can use.
7.	Numerical Integration (1)	There are many functions which we cannot integrate. Then we use Numerical Integration methods to approximate a value.
	Numerical Integration (2)	There are many functions which we cannot integrate. Then we use Numerical Integration methods to approximate a value.
8.	Numerical Integration (3)	There are many functions which we cannot integrate. Then we use Numerical Integration methods to approximate a value.
9.	Numerical Integration (4)	There are many functions which we cannot integrate. Then we use Numerical Integration methods to approximate a value.
	Numerical Methods for Ordinary Differential Equations (1)	Review of basic concept Ordinary Differential Equations
10.	Numerical Methods for Ordinary Differential Equations (2)	Solve some examples of initial value problem. Theorem of the existence and uniqueness and stability.
11.	Numerical Methods for Ordinary Differential Equations (3)	Existence, Uniqueness, and Stability Theory
	Numerical Methods for Ordinary Differential Equations (4)	Eulers method, Multistep methods
12.	Numerical Methods for Ordinary Differential Equations (5)	The Midpoint method, the Trapezoidal method
	Numerical Methods for Ordinary Differential Equations (6)	Runge-Kutta method
13.	Numerical Methods for Ordinary Differential Equations	Multistep methods, Convergence, Stability theory
	Numerical Methods for Ordinary Differential Equations , Linear Algebra	Convergence, Stability regions, Vector spaces, Matrices, Linear systems
14.	Linear Algebra	Eigenvalues and Canonical forms
	Linear Algebra	Eigenvalues and Canonical forms
15.	Numerical solution of systems of linear equations	Gaussian elimination
16.	Numerical solution of systems of linear equations	Error Analysis
	Numerical solution of systems of linear equations	Iteration method
17.	Numerical solution of systems of linear equations	Conjugate Gradient Method
18.	Numerical solution of systems of linear equations	Conjugate Gradient Method
	Numerical solution of systems of linear equations	Conjugate Gradient Method
19.	The matrix eienvalue problem	Stability of eigenvalues for nonsymmetric matrices
20.	The matrix eienvalue problem	Power method
	The matrix eienvalue problem	QR-method, Least squares solution