Introduction to Matlab What is Matlab Matlab is

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? Matlab High Level Languages such as C, Pascal etc. Assembly

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

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

Sym, syms, and vpa Sym Create the symbolic variables Ex: x = sym('x'); y = sym('y', 'positive'); Syms Shortcut for creating symbolic variables and functions Ex: 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.

Vpa Variable-precision arithmetic Ex: >> vpa(pi) ans = 3. 1415926535897932384626433832795 >> vpa(pi, 4) ans = 3. 142

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

ceil, and floor ceil(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 abs round(x) round to nearest integer Ex: >>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) sin(x) tan(x) cot(x) csc(x) sec(x) acos(x) asin(x) atan(x) acot(x) acsc(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].

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

Inverse x = [1 2; 5 1] y=inv(x) y = -0. 1111 0. 5556 Determinant A=det(x) A = -9 0. 2222 -0. 1111 x = [1 2; 5 1]

t t =1: 10 = 10 k 1 x = 3 4 1 0. 5 5 6 7 8 k =2: -0. 5: -1 = 2 2 B 1 1. 5 0 -0. 5 = [1: 4; 5: 8] 5 2 6 3 4 7 8 -1 9

zeros(M, N)Mx. N matrix of zeros x = zeros(1, 3) x = 0 0 0 ones(M, N) Mx. N matrix of ones x = ones(1, 3) x = 1 1 1 rand(M, N) Mx. N matrix of uniformly distributed random x = rand(1, 3) numbers on (0, 1) x = 0. 9501 0. 2311 0. 6068

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.

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 x = A(1, : ) x= y = A(3 , : ) y= 1 2 3 3 4 -1 b = x. * y c=x. /y d = x. ^2 b= c= 0. 33 0. 5 -3 d= 3 8 -3 1 4 9

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 >>syms x >> expand((x-1)*(x-2)) ans = x^2 - 3*x + 2

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

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

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

dsolve Ordinary differential equation >>dsolve('Dx = -a*x') ans = C 2*exp(-a*t)

Differentiation and Integration diff Differences 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

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

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

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

Questions ? ? ?