Lecture 1 - Introduction June 3, 2002 CVEN 302

Lecture’s Goals General Introduction to CVEN 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 Computer Applications in Engineering and Construction Text:Applied Numerical Analysis Using MatLab Author:Laurene V. Fausett Software:Matlab Version 6.0

Introduction Professor: Dr. E. Sandt Office :207 CVEN Building Phone: Office Hr:MWF 2:00 PM - 4:00 PM URL:

Grade Breakdown Homework 25 % Exam 120 % Exam 220 % Final35 %

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 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)

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 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 person running them.

Numerical Errors Precision Limits Stability –Convergence –Divergence Alaising

Numerical Errors Round-off Errors Truncation Errors - Code dependent Machine Precision

Computer Hardware Types Personal Computer Supercomputers Vector Processors Array Processors Parallel Processor

Software Operating Systems (OS) Windows - NT, ME, Windows Unix VMS - VAX Linux

Software Languages –Fundamental Assembler (Bit manipulations) –Engineering Languages Fortran Cobol Pascal C++ ( J++ ) Basic –HTML and Java

Software Higher-Order Programming –Maple - Mathematical Programming Language –Mathematica - Mathematical Programming Language –Java - Internet Programming Language –Matlab - Matrix Laboratory

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

Matlab -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

MatLab 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? Program consist of three main components: Input Main Program - Numerical methods and analysis and/or evaluation. Output - Results.

Inputs Numerical values Initialization of the variables Conditions Equations

Main 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:

Output –Numerical Values –Decisions –Graphs and Plots Outputs are the results of the program. They can go through a series of post-processing methods.

MatLab 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)

Matlab Data types –Numerical Scalars Vectors Matrices –Logic Types –Alpha/Numerical Types

Matlab A scalar value is the simple number, a, 2, …, A vector is a union of a Transpose vector

Matlab Matrix is a combination of vectors and scalars. Scalar and vectors are subsets of matrices. Matlab uses matrix to do mathematical methods.

Matlab 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)

Matlab 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!

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

Matlab - 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 Arithmetic 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.

Homework Obtain an account on CVEN Network Find the Website ( Play with Matlab me and say Hi! I will need your address to create an class list.