Intro to Matlab 1.Using scalar variables 2.Vectors, matrices, and arithmetic 3.Plotting 4.Solving Systems of Equations Can be found at:

New Class--for Engineers ENGR196.3 SPECIAL TOPICS: INTRODUCTION TO MATLAB Description: Fundamentals of MATLAB programming applied to problems in science and mathematics. Solving systems of equations, basic scripting, functions, vectors, data files, and graphics. (Credit course for grade or CR/NC)

Why use Matlab? Drawbacks: Slow (execution) compared to C or Java Advantages: Handles vector and matrices very nice Quick plotting and analysis EXTENSIVE documentation (type ‘help’) Lots of nice functions: FFT, fuzzy logic, neural nets, numerical integration, OpenGL (!?) One of the major tools accelerating tech change

A tour of Matlab’s features Click on Help>Full Product Family Help: Check out Fuzzy Logic Genetic Algorithms Symbolic Math

Scalars The First Time You Bring Up MATLAB MATLAB as a Calculator for Scalars Fetching and Setting Scalar Variables MATLAB Built-in Functions, Operators, and Expressions Problem Sets for Scalars

3-1 The First Time You Bring Up MATLAB Basic windows in MATLAB are: Command - executes single-line commands Workspace - keeps track of all defined variables Command History - keeps a running record of all single line programs you have executed Current Folder - lists all files that are directly available for MATLAB use Array Editor - allows direct editing of MATLAB arrays Preferences - for setting preferences for the display of results, fonts used, and many other aspects of how MATLAB looks to you

3-2 MATLAB as a Calculator for Scalars A scalar is simply a number… In science the term scalar is used as opposed to a vector, i.e. a magnitude having no direction. In MATLAB, scalar is used as opposed to arrays, i.e. a single number. Since we have not covered arrays (tables of numbers) yet, we will be dealing with scalars in MATLAB.

3-3 Fetching and Setting Scalar Variables Think of computer variables as named containers. We can perform 2 types of operations on variables: we can set the value held in the container: x = 22 we can set the value held in the container: x = 22 we can look at the value held in the container: x

The Assignment Operator (=) The equal sign is the assignment operator in MATLAB. >> x = 22 places number 22 in container x How about: >> x = x + 1 Note the difference between the equal sign in mathematics and the assignment operator in MATLAB!

Useful Constants Inf infinity NaN Not a number (div by zero) epsmachine epsilon ansmost recent unassigned answer pi …. i and jMatlab supports imaginary numbers!

Using the Command History Window

3-4 MATLAB Built-in Functions, Operators, and Expressions MATLAB comes with a large number of built-in functions (e.g.. sin, cos, tan, log10, log, exp) A special subclass of often-used MATLAB functions is called operators –Assignment operator (=) –Arithmetic operators (+, -, *, /, ^) –Relational operators ( =, >) –Logical operators (&, |, ~)

Example – Arithmetic Operators Hint: the function exp(x) gives e raised to a power x

Example – Relational and Logical Operators

Vector Operations Chapter 5

Vector Operations Vector Creation Accessing Vector Elements Row Vectors and Column Vectors, and the Transpose Operator Vector Built-in Functions, Operators, and Expressions

Vectors and Matrices Can be to command line or from *.m file scalar:x = 3 vector: x = [1 0 0] 2D matrix:x = [1 0 0; 0 1 0; 0 0 1] arbitrarily higher dimensions (don’t use much) Can also use matrices / vectors as elements: x = [1 2 3] y = [ x 4 5 6]

2-D Plotting and Help in MATLAB Chapter 6

2-D Plotting and Help in MATLAB Using Vectors to Plot Numerical Data Other 2-D plot types in MATLAB Problem Sets for 2-D Plotting

6-2 Using Vectors to Plot Numerical Data Mostly from observed data - your goal is to understand the relationship between the variables of a system. Determine the independent and dependent variables and plot: speed = 20:10:70; stopDis = [46,75,128,201,292,385]; plot(speed, stopDis, '-ro') % note the ‘-ro’ switch Don’t forget to properly label your graphs: title('Stopping Distance versus Vehicle Speed', 'FontSize', 14) xlabel('vehicle speed (mi/hr)', 'FontSize', 12) ylabel('stopping distance (ft)', 'FontSize', 12) grid on Speed (mi/hr) Stopping Distance (ft)

Sample Problem – Plotting Numerical Data

3D Plotting 3D plots – plot an outer product x = 1:10 y = 1:10 z = x’ * y mesh(x,y,z) Single quote ‘ means transpose (can’t cut and paste though…)

Flow Constructs IF block if ( ) elseif end WHILE block while ( ) end Conditions same as C, ( ==, >=, <=) except != is ~=

More Flow Constructs FOR block for i = 1:10 end SWITCH statement switch case, otherwise, end

Other Language Features Matlab language is pretty sophisticated –Functions Stored in a *.m file of the same name: function = ( ) –Structs point.x = 2;point.y = 3;point.z = 4; –Even has try and catch (never used them)

Solving Systems of Equations Consider a system of simultaneous equations 3x + 4y + 5z = 32 21x + 5y + 2z = 20 x – 2y + 10z = 120 A solution is a value of x, y, and z that satisfies all 3 equations In general, these 3 equations could have 1 solution, many solutions, or NO solutions

Using Matlab to Solve Simultaneous Equations Set up the equation in matrix/vector form: A = [3 4 5; ; ] u = [ x y z]’ b = [ ]’ In other words, A u = b (this is linear algebra) x y z * =

The solution uses matrix inverse If you multiply both sides by 1/A you get u = 1/A * b In the case of matrices, order of operation is critical (WRONG: u = b/A ) SO we have “Left division” u = A \ b (recommended approach) OR use inv( ) function: u = inv(A) * b

The solution >> u = A\b u = ( value of x) ( value of y) ( value of z) You can plug these values in the original equation test = A * u and see if you get b

Caution with Systems of Eqs Sometimes, Matrix A does not have an inverse: This means the 3 equations are not really independent and there is no single solution (there may be an infinite # of solns) Take determinant det(A) if 0, it’s singular x y z * =