計算數學

Computational Mathematics

學期

106-2

學分

3 學分

當期課號

1392

永久課號

DAM3201

開課單位

應用數學系

授課教師

林得勝

校區

光復

類別

必修

上課時間表

* 根據陽明交大上課時間表所列

概述

Weeks 1-6: Approximating functions Weeks 7-12: Solving system of linear equations Weeks 13-18: Solution of nonlinear equations

先修科目

Calculus I and II, Linear algebra

教學方式

There will be 6 hrs joint-lecture with ``Computational physics".

評分方式

Project 30%; Homework assignments 30%; Exams 40%.

週次計畫

週次	主題
第 2 週	Introduction and mathematical preliminaries
第 3 週	Approximating functions: Polynomial interpolation
第 3 週	Review of equations in general physics and quantum physics (Joint course with ``Comp. Phys.")
第 4 週	Taylor series, error analysis (Joint course with ``Comp. Phys.")
第 6 週	Approximating functions: Trigonometric interpolation
第 8 週	Matrix diagonalization (Joint course with ``Comp. Phys.")
第 9 週	Solving system of linear equations: LU, Cholesky factorization and power method
第 10 週	Overview of Physical problems in statistical physics, central limit theorem (Joint course with ``Comp. Phys.")
第 11 週	Solving system of linear equations: Solution of equations by iterative methods
第 13 週	Solution of nonlinear equations: Root finding methods
第 16 週	Solution of nonlinear equations: Homotopy and continuation methods

教科書

``Numerical Analysis: Mathematics of Scientific Computing" by David Kincaid and Ward Cheney

Office Hours