1. Introduction to Matlab

2. What is Matlab? Matlab Assembly
Matlab is basically a high level language which has many specialized toolboxes for making things easier for us.
How high?
Assembly
High Level
Languages such as
C, Pascal etc.
Matlab

3. Matlab Screen Command Window type commands Current Directory
View folders and m-files
Workspace
View program variables
Double click on a variable
to see it in the Array Editor
Command History
view past commands

4. Variables No need for types. i.e.,
All variables are created with double precision unless specified and they are matrices.
After these statements, the variables are 1x1 matrices with double precision
int a;
double b;
float c;
Example:
>>x=5;
>>x1=2;

5. Sym, syms, and vpa Sym Create the symbolic variables Ex: Syms
x = sym('x');
y = sym('y','positive');
Syms
Shortcut for creating symbolic variables and functions
syms x y
syms x y real
*SYM and SYMS are essentially the same; SYMS is often used in the command form, while SYM is often used in the function form.

6. Vpa
Variable-precision arithmetic
Ex:
>> vpa(pi)
ans =
>> vpa(pi,4)
3.142

7. Exponential and Logarithmic
exp(x)
sqrt(x)
Ex:
>> y=exp(x)
>> y=sqrt(x)
Logarithmic
log(x) natural logarithm ln
log10(x)
>> log10(x)= log(x) / log(10)
log2(x)
>> log2(x)=  log(x) / log(2)

8. ceil, and floor ceil(x) round to nearest integer towards + Ex:
ans = 4
floor(x) round to nearest integer towards –
>> floor(3.2) 3

9. Round and abs round(x) round to nearest integer Ex: >>round(2.4)
ans= 2
>>round(2.6) 3
abs(x) absolute value
>>abs(-5) 5

10. Trigonometric and their inverse
cos(x) acos(x)
sin(x) asin(x)
tan(x) atan(x)
cot(x) acot(x)
csc(x) acsc(x)
sec(x) asec(x)
All trigonometric functions require the use of radians and not degrees
degtorad
Ex:
>>x=degtorad(45)
x =
0.7854
>> cos(x)
ans =
0.7071
*Inverse of trigonometric returns real values in the interval [0,pi].

11. Array, Matrix a vector x = [1 2 5 1]
a matrix x = [1 2 3; 5 1 4; ]
transpose y = x’ y = 1 2 5

12. Inverse x = [1 2; 5 1] Determinant x = [1 2; 5 1] y=inv(x) y =
Determinant x = [1 2; 5 1]
A=det(x)
A = -9

13. t =1:10
t =
k =2:-0.5:-1
k =
B = [1:4; 5:8]
x =

14. zeros(M,N) MxN matrix of zeros
ones(M,N) MxN matrix of ones
rand(M,N) MxN matrix of uniformly distributed random
numbers on (0,1)
x = zeros(1,3)
x =
x = ones(1,3)
x = rand(1,3)

15. Matrix Index The matrix indices begin from 1 (not 0 (as in C))
The matrix indices must be positive integer
A(-2), A(0)
Error: ??? Subscript indices must either be real positive integers or logicals.
A(4,2)
Error: ??? Index exceeds matrix dimensions.

16. x = [1 2], y = [4 5], z=[ 0 0] A = [ x y] 1 2 4 5 B = [x ; y] 1 2 4 5
B = [x ; y]
1 2
4 5
C = [x y ;z]
Error:
??? Error using ==> vertcat CAT arguments dimensions are not consistent.

17. Operators (arithmetic)
+ addition - subtraction * multiplication / division ^ power

18. Given A and B:
Addition
Subtraction
Product
Transpose

19. Operators (Element by Element)
.* element-by-element multiplication ./ element-by-element division .^ element-by-element power

21. A = [1 2 3; 5 1 4; 3 2 1]
A =
b = x .* y b=
c = x . / y c=
d = x .^2 d=
x = A(1,:) x=
y = A(3 ,:) y=

22. Factor, Expand, and Simplify
factor(f)
>>syms x
>>f=x^3-6*x^2+11*x-6;
>>y=factor(f) y=
(x-1)*(x-2)*(x-3)
expand
>> expand((x-1)*(x-2))
ans =
x^2 - 3*x + 2

23. simplify
Algebraic simplification
>>syms x
>>f1=sin(x)^2 + cos(x)^2 +log(x);
>> simplify(f1)
ans=
1+log(x)

24. Solve and dsolve solve Solve equations and systems >>syms x
>>solve(x^2-3*x+2)
ans = 1 2

25. >>S = solve('x + y = 1','x - 11*y = 5') S = x: [1x1 sym]
>>syms x y
>>S = solve('x + y = 1','x - 11*y = 5')
S =
x: [1x1 sym]
y: [1x1 sym]
>>S = [S.x S.y]
[ 4/3, -1/3]

26. dsolve
Ordinary differential equation
>>dsolve('Dx = -a*x')
ans =
C2*exp(-a*t)

27. Differentiation and Integration
Differences and approximate derivatives
>> x=[ ];
>> diff(x)
ans =
>> diff(sym('x^3+2*x^2-x+1'))
3*x^2 + 4*x - 1

28. int
Integrate symbolic expression
>>int(sym('x'))
ans =
x^2/2

29. limit
Compute limit of symbolic expression
>>syms x
>>limit(sin(x)/x)
ans= 1

30. Sum of series Symsum Sum of series S= 1+2^2+3^2+…+n^2 = >>syms k
>>symsum(k^2, 1, 10)
ans =
385

31. Questions ?