1. Lecture 1: Matlab Universe
Tom Rebold
ENGR 196.3

2. Course Overview

3. The Way the Class Works I lecture for 15 – 20 minutes
You do lab for 30 – 40 minutes
Labs link to extra Problems online for fast students
Everyone turn in a solution to the last problem they solve today
HOMEWORK: Bring in 3 Math problems to solve…medium, hard, impossible
We’ll have independent study time

4. To Buy Matlab Student Version, $100 Can purchase, download online
Link from ENGR196.3 class webpage
Bookstore does not stock
MATLAB retails for $1600, so it’s a pretty good deal

5. Why MATLAB Compared to other choices:
C++, Fortran, Java
Excel, MathCad, Mathematica, Labview
Matlab is a Very High Level Language
Designed for complex numerical calculations
Vast array of Toolboxes for different specialties
Excellent visualization tools
Symbolic math somewhat awkward
Simulink for modelling dynamic systems

6. Today’s Agenda MATLAB Overview Working in MATLAB’s Environment
Simple calculations, variables
Vectors, Matrices, Plotting
Applications—Problem Solving
Systems of equations
Analyzing a data file
3D Plotting

7. MATLAB’s ENVIRONMENT

8. Download week1.zip Follow instructions in Lab1 View toolbox demos
Experiment with workspace configuration

9. Numeric Data
At it’s most basic level, Matlab can be used as a simple calculator, by typing in an arithmetic expression and hitting enter. For example, at the command prompt, type:
>> 8/10
>>4 * 3
>>8/10 + 4*3
>>9^ (what does the ^ operator do? )

10. Arithmetic rules of precedence
>> 8 + 3*5
>> 8 + (3*5)
>> (8 + 3) * 5
>> 4^2 – 12
>> 8/4*2
>> 8/(4*2)
>> 3*4^2
>> (3*4)^2
>> 27^(1/3)
>> 27^1/3

11. built in functions
Matlab has hundreds of built in functions to do more complicated math
sqrt(9)
log10(1000)
log(10) pi
cos(pi) i
exp(i*pi)

12. Variables Usually we need to hang on to the result of a calculation
We need a way to name memory for storage
Variable--name of a place in memory where information is stored
r = 8/10 r
s=20*r
score = 4 * r + s
z = sqrt(1000)
z = sqrt(s)

13. Assignment Operator = means “gets” Translation: OK in Math
MATLAB: r = 8/10
ENGLISH: r “gets” the value 8/10
OK in Math
x + 2 = NOT OK IN MATLAB !!
(only variable on Left Side)

14. Expressing Math in MATLAB2
yx _______________ x-y
3x _______________ 2y

15. Saving Work in Matlab Script (.m) files
You’ll want to build up complex calculations slowly
Try, correct, try again, improve, etc
.m Files store your calculations
Can be edited in Matlab
Can be re-executed by typing the file name

16. Example .m file
Volume of a Cylinder. The volume of a cylinder is V= pr2h. A particular cylinder is 15 meters high with a radius of 8 meters. We want to construct another cylinder tank with a volume 20% greater, but with the same height. How large must its radius be? The session follows:
r = 8;
h = 15;
V = pi*r^2*h
V = V + 0.2*V  adds 20% to V
r = sqrt(V/ (pi * h))
Put this in a file called cyl_volume.m to save retyping

17. Finish Section IV
If you finish early, please follow the link to practice problems online

18. Vectors
Matlab has a very concise language for dealing with vectors (arrays of data)
scalar: x = 3
vector: x = [ ]
A vector is a series of data grouped together
Row Vectors and Column Vectors
Transpose operator
Functions and Arithmetic with vectors
Colon operator
Multiplication—cell by cell vs ‘dot product’

19. Finish Section V
If you finish early, please follow the link to practice problems online

20. Basic Plotting Experimental Results Mathematical Formulas
v = [20:10:70];
d = [46, 75, 128, 201, 292, 385];
plot(v, d);
Mathematical Formulas
x=[0:0.01:2];
y=exp(-3*x).*sin(8*pi*x);  .* is needed here
plot(x,y);
Both involve using plot( ) on vectors

21. Finish Section VI Play with multiple plots, linetypes, etc
If you finish early, please follow the link to practice problems online

22. VII Application: Polynomial Math
We can represent polynomials by vectors of coefficients, for example:
x3 – 9x2 + 2x represented by
[ ]
Matlab provides commands to calculate
Roots
Multiplication and division of polynomials
Example on structural resonance online
More problems online

23. VIII Matrices A matrix is a 2 dimensional vector Useful tools:
Useful tools:
Transpose
Cell address
Merging and extracting vectors
multiplication

24. IX Application: Systems of Equations
A common occurrence, need to solve 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

25. 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 32 20
120 * =

26. 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

27. The solution >> u = A\b u = 1.4497 ( 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

28. 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 32 10 22 * =

29. Application: Analyze Data from A Real Science Project

36. Data Files