华南师范大学：《数值计算方法》课程PPT教学课件（数值分析 Numerical Analysis）Introduction to Numerical Methods

善样花导 Introduction to Numerical Methods Introduction Course Overview

Introduction to Numerical Methods Introduction & Course Overview

Lecture's Goals Introduce computer methods for the solution of civil engineering problems,including: General Introduction to Computer Applications in Engineering and Construction Why do you need to be able to write and understand computer program and numerical methods? MATLAB -Mathematical Laboratory

Lecture’s Goals Introduce computer methods for the solution of civil engineering problems, including: ◼ General Introduction to Computer Applications in Engineering and Construction ◼ Why do you need to be able to write and understand computer program and numerical methods? ◼ MATLAB - Mathematical Laboratory

Topics MATLAB-Mathematical Program(Vectors) Computer Errors -Recognition and solutions ■Roots fx)=0 ▣Linear Methods ▣Nonlinear Methods

Topics ◼ MATLAB - Mathematical Program (Vectors) ◼ Computer Errors - Recognition and solutions ◼ Roots f(x) = 0 Linear Methods Nonlinear Methods

Topics Linear Systems-Setting up multiple sets of equations and solution techniques. LU Decomposition-Technique to decompose matrices Eigen-analysis -finding the eigenvalues and eigenvectors

Topics ◼ Linear Systems - Setting up multiple sets of equations and solution techniques. ◼ LU Decomposition - Technique to decompose matrices ◼ Eigen-analysis - finding the eigenvalues and eigenvectors

Topics ■Fitting Data ▣Interpolation Curve Fitting Numerical Differentiation Numerical Integration

Topics ◼ Fitting Data Interpolation Curve Fitting ◼ Numerical Differentiation ◼ Numerical Integration

Topics ODE's (ordinary differential equations) Initial Value Problems Systems of ODE's of IVP Boundary Value Problems Systems of ODE's of BVP Partial Differential Equations(PDE's)

Topics ◼ ODE’s (ordinary differential equations) Initial Value Problems Systems of ODE’s of IVP Boundary Value Problems Systems of ODE’s of BVP ◼ Partial Differential Equations (PDE’s)

Why do we need to know how to use numerical analysis and methods? You are not going to be given a nice neat exact solution in the "real world". ■Applications Numerical Errors ■Computer Types ■Computer Software

Why do we need to know how to use numerical analysis and methods? ◼ Applications ◼ Numerical Errors ◼ Computer Types ◼ Computer Software You are not going to be given a nice neat exact solution in the “real world

Applications ■Signal Processing CFD(Computational Fluid Dynamics) ■Structural Analysis Finite Element Analysis

Applications ◼ Signal Processing ◼ CFD (Computational Fluid Dynamics) ◼ Structural Analysis ◼ Finite Element Analysis

Applications Interpolation-Handling data Optimization-Design and estimation CAD (Computer Aided-Drafting) ■Data Collection

Applications ◼ Interpolation - Handling data ◼ Optimization - Design and estimation ◼ CAD (Computer Aided-Drafting) ◼ Data Collection

Numerical Errors Computers are only as good as the person running them

Numerical Errors Computers are only as good as the person running them