Numerical Analysis（数值分析）

王正盛

目录

  • 1 Introduction
    • 1.1 Course Videos
    • 1.2 Learning Objectives
    • 1.3 Lecture Notes
  • 2 Ch2 Solution of Nonlinear Equations
    • 2.1 Learning Objectives
    • 2.2 Course Videos
    • 2.3 Lecture Notes
  • 3 Ch3 Solution of Systems of Linear Equations
    • 3.1 Learning Objectives
    • 3.2 Course Videos-Gauss-LU
    • 3.3 Course Video-Norms-Iterative
    • 3.4 Course Videa-Jacobi Iterative Method
    • 3.5 Course Video-G-S Iterative Method
    • 3.6 Lecture Notes
  • 4 Ch4 Approximation of function：Interpolation
    • 4.1 Learning Objectives
    • 4.2 Introduction-Video
    • 4.3 Lagrange Interpolation Polynomial-Video
    • 4.4 Newton's Divided Difference Polynomial-Video
    • 4.5 Lecture Notes
  • 5 Ch5 Numerical Integration
    • 5.1 Learning Objectives
    • 5.2 Introduction; Numerical integration based on interpolation
    • 5.3 Trapezoid rule Simpson’s rule
    • 5.4 Composite Rule
    • 5.5 Lecture Notes
  • 6 Ch6 Solution of Ordinary Differential Equations
    • 6.1 Learning Objectives
    • 6.2 Introduction
    • 6.3 Euler-Taylor-RK
    • 6.4 Lecture Notes
  • 7 Numerical Methods with MATLAB
    • 7.1 Learning Objectives
    • 7.2 Lecture Notes
Learning Objectives

The Objectives of Chapter 1: Introduction

The primary objective of this chapter is to provide you with a concrete idea of what numerical analysis (numerical methods) are and how they relate to engineering and scientific problem solving. Also, it is to acquaint you with the major sources of errors involved in numerical methods.

Specific objectives and topics covered are

n  Understanding how numerical analysis afford a means to generate solutions in manner that can be implemented on a digital computer.

n  Learning how to quantify error.

n  Learning how error estimates can be used to decide when to terminate an iterative calculation.

n  Understanding how round-off errors occur because digital computers have a limited ability to represent numbers.

n  Recognizing that truncation errors occur when exact mathematical formulations are represented by approximations.