Introduction to Matlab

What is Matlab?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

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

VariablesNo 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;

Sym, syms, and vpaSymCreate the symbolic variablesEx:

x = sym('x'); y = sym('y','positive');

SymsShortcut for creating symbolic variables and

functionsEx:

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.

VpaVariable-precision arithmeticEx:

>> vpa(pi) ans = 3.1415926535897932384626433832795 >> vpa(pi,4) ans = 3.142

Exponential and LogarithmicExponential

exp(x) sqrt(x)Ex:

>> y=exp(x)>> y=sqrt(x)

Logarithmiclog(x) natural logarithm lnlog10(x)Ex:

>> log10(x)= log(x) / log(10)log2(x)Ex:

>> log2(x)=  log(x) / log(2)

ceil, and floorceil(x) round to nearest integer towards

+Ex:

ceil(3.2)ans = 4

floor(x) round to nearest integer towards –

Ex:>> floor(3.2)ans = 3

Round and absround(x) round to nearest integerEx:

>>round(2.4)ans= 2>>round(2.6)ans= 3

abs(x) absolute value Ex:

>>abs(-5)ans= 5

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 degreesdegtoradEx:

>>x=degtorad(45)x = 0.7854>> cos(x)ans = 0.7071

*Inverse of trigonometric returns real values in the interval [0,pi].

Array, Matrixa vector x = [1 2 5 1]

x = 1 2 5 1

a matrix x = [1 2 3; 5 1 4; 3 2 -1]

x = 1 2 3 5 1 4 3 2 -1

transpose y = x’ y = 1

2 5

1

Inverse x = [1 2; 5 1]y=inv(x)y =

-0.1111 0.2222 0.5556 -0.1111

Determinant x = [1 2; 5 1]A=det(x)

A = -9

t =1:10

t = 1 2 3 4 5 6 7 8 9 10

k =2:-0.5:-1

k = 2 1.5 1 0.5 0 -0.5 -1

B = [1:4; 5:8]

x = 1 2 3 4 5 6 7 8

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 =

0 0 0

x = ones(1,3)

x =

1 1 1

x = rand(1,3)

x =

0.9501 0.2311 0.6068

Matrix IndexThe 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.

x = [1 2], y = [4 5], z=[ 0 0]

A = [ 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.

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

Given A and B:

Addition

Subtraction

Product Transpose

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

A = [1 2 3; 5 1 4; 3 2 1] A = 1 2 3 5 1 4 3 2 -1

y = A(3 ,:)

y= 3 4 -1

b = x .* y

b= 3 8 -3

c = x . / y

c= 0.33 0.5 -3

d = x .^2

d= 1 4 9

x = A(1,:)

x= 1 2 3

Factor, Expand, and Simplifyfactor(f)

>>syms x>>f=x^3-6*x^2+11*x-6;>>y=factor(f)y=(x-1)*(x-2)*(x-3)

expand>>syms x>> expand((x-1)*(x-2))

ans = x^2 - 3*x + 2

simplifyAlgebraic simplification

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

Solve and dsolvesolveSolve equations and systems

>>syms x>>solve(x^2-3*x+2)ans =

12

>>syms x y>>S = solve('x + y = 1','x - 11*y =

5')S = x: [1x1 sym]y: [1x1 sym]>>S = [S.x S.y]S =[ 4/3, -1/3]

dsolveOrdinary differential equation

>>dsolve('Dx = -a*x')ans = C2*exp(-a*t)

Differentiation and IntegrationdiffDifferences and approximate derivatives

>> x=[2 5 9 1 3];>> diff(x)ans = 3 4 -8 2>> diff(sym('x^3+2*x^2-x+1'))ans =

3*x^2 + 4*x - 1

intIntegrate symbolic expression

>>int(sym('x')) ans = x^2/2

limitCompute limit of symbolic expression

>>syms x>>limit(sin(x)/x)ans=1

Sum of seriesSymsumSum of seriesS= 1+2^2+3^2+…+n^2 =

>>syms k >>symsum(k^2, 1, 10)ans = 385

Questions?????