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Lecture 1 - Introduction. June 3, 2002 CVEN 302. Lecture’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? - PowerPoint PPT Presentation
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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.
Numerical ErrorsNumerical Errors
• Precision Limits
• Stability
– Convergence
– Divergence
• Alaising
Numerical ErrorsNumerical Errors
• 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.