Course Name Year Term Period Faculty / Graduate School All Instructors Credits
35260:Numerical Algorithms (G1) 2019 Fall Mon5 College of Information Science and Engineering BAI YANG 2

Campus

BKC

Class Venue

Forest102

Language

English

Course Outline and Method

This course brings an introduction to the numerical analysis. The goal of the course is to develop a basic understanding of numerical algorithms, as well as to train skills for selecting and applying feasible algorithms in solving “real world” problems. Specifically, this course covers numerical root finding problems, interpolation and approximation problems, numerical differentiation and integration, as well as problems of solving a system of equations numerically, and so on.

Student Attainment Objectives

After this course, students will be able to understand the principle that how computers are dealing with mathematical problems, such as solving differentiation and integration problems, differential equations, and optimization problems. Also, they will learn the basic terms in numerical mathematics and the techniques for the analysis of numerical algorithms. Based on these techniques, students are expected to be able to solve concrete problems by selecting or even devising feasible algorithms.

Recommended Preparatory Course

Calculus, Linear Algebra, basic programming skills

Course Schedule

Lecture/Instructor（When there are multiple instructors) Theme
Keyword, References and Supplementary Information
1

Preliminaries of Computing

Basic concepts: round-off errors, floating point arithmetic, convergence
2

Root Finding

Bisection method, fixed-point iteration, Newton’s method, error analysis for iterative methods
3

Interpolation

Lagrange polynomial, divided differences, Hermite interpolation
4

Numerical Differentiation and Integration (1)

Numerical differentiation: Richardson’s extrapolation, etc.
5

Numerical Differentiation and Integration (2)

Numerical integration: Trapezoidal rule, etc., Gaussian quadrature and Euler-Maclaurin formula
6

Numerical Solutions to System of Equations (1)

Direct methods for solving linear systems of equations: pivoting strategies, Linear Algebra and Matrix Inversion
7

Numerical Solutions to System of Equations (2)

Iterative methods for solving linear systems of equations: Jacobi and Gauss-Siedel iterative techniques, etc.
8

Numerical Solutions to System of Equations (3)

Solving nonlinear systems of equations: fixed points for functions of several variables, Newton’s method
9

Mid-term Exam

Lasts 90 min. and covers topics of Weeks 1 through 8
10

Solving Differential Equations (1)

IVP problems for ODE: Euler’s, Taylor, Runge-Kutta, and multistep methods, stability
11

Solving Differential Equations (2)

BVP problems for ODE: shooting methods, finite-difference methods
12

Solving Differential Equations (3)

Partial Differential Equations: an introduction to the finite-element method
13

Approximation Theory (1)

Orthogonal polynomials and least Squares approximation, Chebyshev polynomials
14

Approximation Theory (2)

Approximating Eigenvalues: Power method, Householder’s method
15

Course Overview

Covers topics of Weeks 1 through 14

Class Format

Recommendations for Private Study

Students are recommended to read relevant chapters before class. This will be helpful for them to better and faster understand the contents of the lecture. Homework will be assigned within each lecture and is due on the next lecture. Collaboration on homework is encouraged because discussion with other students is an efficient way of solving challenging problems. However, it is not allowed to copy solutions from other students directly.

Grade Evaluation Method

Kind Percentage Grading Criteria etc.
Final Examination (Written) 50

Ability to solve the questions provided in the final exam
Report Examination
(A report to be submitted by the unified deadline)

Exams and/or Reports other than those stated above, and Continuous Assessment　
(Evaluation of Everyday Performance in Class)		 50

Attendance, assignments and the mid-term exam

Grade Evaluation Method （Note）

Algorithms involving matrices and vectors are recommended to be implemented by Matlab or Python.

Advice to Students on Study and Research Methods

Students are recommended to review the contents of the lecture after each class. Although the slides used in the lecture will be provided, taking notes is considered to be necessary, since the slides may not cover everything in the lecture. The algorithms learned during the class are recommended to be implemented by programming based on suitable code libraries or numerical programming environments.

Textbooks

Title Author Publisher ISBN Code Comment
Numerical Analysis 9th Ed. Richard L. Burden, J. Douglas Faires Brooks/Cole 978-0-538-73351-9

Textbooks （Frequency of Use, Note）

Reference Books

Title Author Publisher ISBN Code Comment
Numerical Recipes 3rd Ed. William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery Cambridge University Press 978-0-538-73351-9

Reference Books （Frequency of Use, Note）

Web Pages for Reference

How to Communicate with the Instructor In and Out of Class(Including Instructor Contact Information)

Talk with Students

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