Lecture1

Lecture 1 - IntroductionLecture 1 - Introduction

June 3, 2002

CVEN 302

Lecture’s GoalsLecture’s Goals

• General Introduction to CVEN 302 - Computer Applications in Engineering and Construction

• Introduction to Computer Lab• Why do you need to be able to write and

understand computer program and numerical methods?

• Matlab - Mathematical Laboratory

CVEN 302 CVEN 302 Computer Applications in Computer Applications in

Engineering and ConstructionEngineering and Construction

Text: Applied Numerical Analysis

Using MatLab

Author: Laurene V. Fausett

Software: Matlab Version 6.0

IntroductionIntroduction

Professor: Dr. E. Sandt

Office :207 CVEN Building

Phone: 458-4780

Office Hr: MWF 2:00 PM - 4:00 PM

Email: [email protected]

URL: http://stommel.tamu.edu/~esandt/

Grade Breakdown

Homework 25 %

Exam 1 20 %

Exam 2 20 %

Final 35 %

TopicsTopics

• Matlab - Mathematical Program (Vectors)

• Computer Errors - Recognition and solutions

• Roots f(x) = 0– Linear Methods– Nonlinear Methods

TopicsTopics

• Linear Systems - Setting up multiple sets of equations and solution techniques.

• LU Decomposition - Technique to decompose matrices

• Eigen-analysis - finding the eigenvalues and eigenvectors

TopicsTopics• Fitting Data

– Interpolation– Curve Fitting

• Numerical Differentiation

• Numerical Integration

TopicsTopics

• 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 Why do we need to know how to use numerical analysis and methods?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”.

ApplicationsApplications

• Signal Processing

• CFD (Computational Fluid Dynamics)

• Structural Analysis

• Finite Element Analysis

ApplicationsApplications

• Interpolation - Handling data

• Optimization - Design and estimation

• CAD (Computer Aided-Drafting)

• Data Collection

Numerical ErrorsNumerical Errors

Computers are only as good as theComputers are only as good as the

person running themperson running them.


• Precision Limits

• Stability

– Convergence

– Divergence

• Alaising


• Round-off Errors

• Truncation Errors - Code dependent

• Machine Precision

Computer Hardware TypesComputer Hardware Types

Personal Computer

Supercomputers

Vector Processors

Array Processors

Parallel Processor

SoftwareSoftware

Operating Systems (OS)

• Windows - NT, ME, Windows

• Unix

• VMS - VAX

• Linux

SoftwareSoftwareLanguages

– Fundamental Assembler (Bit manipulations)– Engineering Languages

• Fortran• Cobol• Pascal• C++ ( J++ )• Basic

– HTML and Java

SoftwareSoftwareHigher-Order Programming

– Maple - Mathematical Programming Language

– Mathematica - Mathematical Programming Language

– Java - Internet Programming Language

– Matlab - Matrix Laboratory

SoftwareSoftware

Tools– Word Processors– Spreadsheets– Database Management– Graphics– Mathematical Computer Codes

Matlab -Matrix LaboratoryMatlab -Matrix Laboratory

– 50 Licenses are available on the network with a wavelet tool box

– Student Version is available at the MSC ($120) without the tool boxes.

Currently Matlab 6.0 is available on CVEN Network

MatLabMatLab

You will need to obtain an account on the CVEN Network. You can obtain an account in the CVEN Lab. It will take a couple of days to get it setup.

The Matlab program can be run using command line, batch commands, and programs.

What is a program?What is a program?

Program consist of three main components:

• Input

• Main Program - Numerical methods and analysis and/or evaluation.

• Output - Results.

InputsInputs

• Numerical values

• Initialization of the variables

• Conditions

• Equations

Main ProgramMain Program

– Loops (for do while)– Conditions ( if then elseif etc.. )– Error Convergence (while )

Using flow charts, the programs can be designed to perform a task. Using:

OutputOutput

– Numerical Values– Decisions– Graphs and Plots

Outputs are the results of the program. They can go through a series of post-processing methods.

MatLabMatLab

Variable Types

– Integers

– Real Values (float and double)

– Complex Numbers (a + ib)• a - real value• b - imaginary value (“i” is the square root of -1)

MatlabMatlab

Data types– Numerical

• Scalars• Vectors• Matrices

– Logic Types– Alpha/Numerical Types

MatlabMatlab

• A scalar value is the simple number, a, 2, 3.14157…,

• A vector is a union of a

• Transpose vector

4321 ,,, xxxxx

4

3

2

1

T

x

x

x

x

x

MatlabMatlab• Matrix is a combination of vectors and

scalars. Scalar and vectors are subsets of matrices.

• Matlab uses matrix to do mathematical methods.

333231

232221

131211

aaa

aaa

aaa

A

MatlabMatlab

• Set of computer functions– Circular functions - sin(x),cos(x), tan(x),

asin(x), acos(x), atan(x)– Hyperbolic functions - sinh(x), cosh(x),

tanh(x)– Logarithmic functions - ln(x), log(x), exp(x)– Logic functions - abs(x), real(x), imag(x)

MatlabMatlab

• Simple commands– clc - clears window– clg - clear graphic window– clear - clears the workspace– who - variable list– whos - variable list with size– help - when doubt use it!

MatlabMatlab

• Simple commands and symbols – ^C - an escape from a loop– inf - infinity– NaN - No numerical value

Matlab - Scalar OperationsMatlab - Scalar Operations

• Addition - a + b

• Subtraction - a - b

• Multiplication - a * b

• Right Division - a / b

• Left Division - b \ a

• Exponential - a^b

Order of Precedence of Order of Precedence of Arithmetic OperationsArithmetic Operations

Precedence( 1 ) - Parenthesis

( 2 ) - Exponential from left to right

( 3 ) - Multiplication and division from left to right.

( 4 ) - Addition and subtraction from left to right.

HomeworkHomework

• Obtain an account on CVEN Network

• Find the Website (http:\\stommel.tamu.edu\~esandt)

• Play with Matlab

• Email me and say Hi! I

will need your email address to create an class email list.

Lecture1

Documents

Transcript of Lecture1