Computational Physics PHYS3114

Syllabus for Computational Physics

PHYS3114

Current Lecturer

Prof. Tianyi CAI Email: caitianyi@suda.edu.cn

Course Description

Computational Physics is a course for students of engineering, science, mathematics, and computer science. The primary goal is to construct and explore algorithms for solving science and engineering problems. The second mission is to help the student locate these algorithms in a landscape of some potent and far-reaching principles.

Prerequisites

Calculus (00071012/13); Linear algebra (00071004)

Textbook

Timothy Sauer, Numerical analysis, 2nd Ed，Pearson, 机械工业出版社, 2012.

Main Contents

Week	Teaching Contents	Sessions	Objectives
1	Fundamentals	2	Evaluating a polynomial; Binary numbers; Floating point representation of real numbers; Loss of significance; Review of calculus
2	Solving Equations	2	Bisection Method; Fixed-point Iteration; Limits of Accuracy
3	Solving Equations	2	Newton’s Method; Root-Finding without Derivatives
4	Systems of Equations	2	Gaussian Elimination
5	Systems of Equations	2	The LU Factorization; Sources of Error
6	Systems of Equations	2	Iterative Methods; Methods for symmetric positive-definite matrices
7	Systems of Equations	2	Nonlinear systems of Equations
8	Interpolation	2	Data and Interpolating Functions; Interpolation Error
9	Mid-term exam	2
10	Interpolation	2	Chebyshev Interpolation; Cubic Interpolation; Bezier Curves
11	Least Squares	2	Least squares and the Normal Equations; a survey of Models
12	Least Squares	2	QR Factorization;
13	Least Squares	2	GMRES Methods; Nonlinear Least Squares
14	Numerical Differentiation	2	Numerical Differentiation
15	Numerical Differentiation	2	Newton-Cotes Formulas for numerical Integration
16	Numerical Integration	2	Romberg Integration; Adaptive Quadrature; Gaussian Quadrature
17	Review	2	Review all the lecture materials

Marking Scheme:

Homework	Attendance	Project	Final exam
10%	10%	20%	60%