Introduction to Numerical Analysis, by Zhengsheng Wang，Science Press

Syllabus

NO. 0810110W

Numerical Analysis

Spring semester 2020

Instructor: Prof. Zhengsheng Wang

Email: wangzhengsheng@nuaa.edu.cn  

Lecture:  Wednesday 14:00-15:45，Friday  10:15-12:00

Online 【Jiangjun Road Campus，D3102】

Office Hours：Online & WeChat Group

【Tuesday 9:00AM-3:00PM，Room 358，Science Building】

Credit Hours:32   Credit: 2

Textbook: Introduction to Numerical Analysis，Science Press，2018

（by Zhengsheng Wang）

Language: English

Course webpage: https://mooc1.chaoxing.com/course/206173770.html

Prerequisites (Requirements for courses, ability and knowledge in advance):  Calculus，Linear Algebra，Fundamentals of Computer Programming

Grading Policy:

n Final Grade (100) = Presence, Class performance and Homework (30%) + Final Exam (70%)

n Final Examination: Closed-book exam

Course Topics and Objectives:

This course is an important basic course for specialty for undergraduate students of non-mathematical majors. This course mainly covers the classical theory and methods of numerical analysis, including Solution of Nonlinear Equations, Solution of Systems of Linear Equations, Approximation of Functions, Numerical Integration and Numerical Solution of Ordinary Differential Equations. It requires that students should master the basic discipline of numerical analysis, be able to carry out the classical numerical methods for some mathematical problems and have the basic knowledge and skills to use computers to solve mathematical problems and conduct research by both algorithm-designing and computer programming so that they are prepared with the necessary foundation for their future study and work.

Class Conduct:

All students are expected to be attentive in class. Please make every effort to arrive on time. It is the student’s responsibility to attend class, pay attention, respond to the teacher, and participate in discussions.

Contents

This course is divided into six chapters as follows.

Ch1 Introduction (4 hrs)

1.1 Numerical Analysis: What and Why？

1.2 Review of Calculus

1.3 Computer Arithmetic and Error Analysis

1.4 Algorithms and Convergence

1.5 An introduction to MATLAB

Ch2 Solution of Nonlinear Equations (6 hrs)

2.1 Introduction; Bisection method

2.2 Fixed point iteration

2.3 Newton's method

2.4 Secant method

Ch3 Solution of Systems of Linear Equations (10 hrs)

3.1 Introduction; Gaussian Elimination

3.2 LU factorization

3.3 Vector and matrix norms

3.4 Jacobi iterative method

3.5 Gauss-Seidel iterative method

Ch4 Approximation of function：Interpolation (4 hrs)

4.1 Introduction; Lagrange form

4.2 Newton's divided difference formula

Ch5 Numerical Integration (4 hrs)

5.1 Introduction; Numerical ...n based on interpolation

5.2 Trapezoid rule, Simpson’...Composite Trapezoid rule

5.3 Romberg Integration

Ch6 Solution of Ordinary Differential Equations (4 hrs)

6.1 Introduction; Euler's method

6.2 Taylor methods

6.3 Runge-Kutta methods

MATLAB

n MATLAB Demo

n MATLAB Programming

n Numerical Methods with MATLAB