Matlab Untuk Guru Sma.pdf

MATLAB untuk GURU SMA/SMK

Hari Sutiksno SURABAYA, 10 OKTOBER 2018

SEKOLAH TINGGI TEKNIK SURABAYA

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Singkatan dari MATrix LABoratory • • • • •

Scientific programming environment Very good tool for the manipulation of matrices Great visualisation capabilities Loads of built-in functions Easy to learn and simple to use 2

STARTING MATLAB

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MATLAB

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OPERATOR

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MARI KITA MULAI % This is a comment >> ((1+2)*3 - 2^2 - 1)/2 ans: 2 % Use ; to suppress output (scripts and functions) >> ((1+2)*3 - 2^2 - 1)/2; No output

% You need to use the ... operator to wrap lines >> 1 + 2 + 3 + 4 + 5 ... +6+7+8+9 ans: 45 7

Logic and Assignment % Assignment with equality >> a = 5; No Output % Logical test like >, <, >=, <=, ~= >> a == 6 ans: 0 % 0 is false in Matlab >> a ~= 6 ans: 1 % 1 is true in Matlab not( a == 6 ) also works 8

Logical Operators % Short Circuited Logic >> true || (slow_function) ans: 1 % Evaluates Quickly >> true | (slow_function) ans: 1 % Evaluate slowly % Matrix logic >> matrix1 || matrix2 ans: Error >> matrix1 | matrix2 Pair wise logic 9

Round, Floor, Ceil, Fix Round

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Round

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Fix

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Ceil

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Mod and Rem

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rem >> rem(15,3) ans = 0 >> rem(15,4) ans = 3

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POLY, ROOTS, CONV >> poly([1 2 3]) ans = 1 -6 11 -6 >> roots([1 3 2]) ans = -2 -1

>> conv([1 3 2],[1 4]) ans = 1 7 14 8 16

Residue

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Complex Number >> a = 3i+6 a = 6.0000 + 3.0000i >> b = 5-2i b = 5.0000 - 2.0000i >> (a+2i)^3 ans = -2.3400e+002 +4.1500e+002i >> exp(pi*i/2) ans = 0.0000 + 1.0000i

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MATRIX % A simple array >> [1 2 3 4 5] ans: 1 2 3 4 5 >> [1,2,3,4,5] ans: 1 2 3 4 5 >> 1:5 ans: 1 2 3 4 5 >> 1:2:5 ans: 1 3 5 >> 5:-2:1 ans: 5 3 1

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Accessing Matrices Elements % Make a matrix >> A = [1 2 3; 4 5 6; 7 8 9] >> A(1,:) ans: 1 2 3 % Access Individual Elements >> A([1, 3, 5]) ans = 1 7 5 >> A( [1,3], 2:end ) ans = 2 3 8 9 % Semuanya adalah data yang sama >> [1 2 3; 4 5 6; 7 8 9] >> [1,2,3; 4,5,6; 7,8,9] >> [[1 2; 4 5; 7 8] [3; 6; 9]] >> [[1 2 3; 4 21

% Creating all ones, zeros, or identity matrices >> zeros( rows, cols ) >> ones( rows, cols ) >> eye( rows )

% Creating Random matrices >> rand( rows, cols ) >> rand(1,2) ans = 0.1419 0.9157 0.4218 0.7922 >> randi(10,4) ans = 6 7 8 5 3 2 1 5 8 4 10 5 2 7 8 4 22

% Make 3x5 with N(1, 4) entries >> 1 + 2 * randn(3,5) Ans: 2.0753 2.7243 0.1328 6.5389 2.4508 4.6678 1.6375 1.6852 -1.6998 0.8739 -3.5177 -1.6154 8.1568 7.0698 2.4295 randi(10,[4 3]) ans = 7 7 10 9 1 1 4 7 5 8 4 5 % Get the size >> Matrix=[4 3 5;2 1 8]; >> [baris, kolom]=size(Matrix) ans= ? 23

% Make a matrix >> A = [1 2 3; 4 5 6; 7 8 9] A= 1 4 7

2 5 8

3 6 9

4 5 6

7 8 9

>> A' ans = 1 2 3

>> A(:)’ ans: 1 4 7 2 5 8 3 6 9

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>> A=[1 2 3;4 6 7; 1 4 -8]

ans =

A= 1 4 1

>> inv(A)

2 6 4

3 7 -8

Columns 1 through 2

>> A'

-2.3750 0.8750 1.2188 -0.3438 0.3125 -0.0625

ans =

Column 3

1 2 3

4 6 7

1 4 -8

-0.1250 0.1563 -0.0625

>> det(A)

>> diag(A)

ans =

ans =

32

1 6 -8

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Carilah x , y dan z dari persamaan berikut:

x + 2 y - 5z = 1 3x - y + 4 z = 3 5 x + 3 y + 2 z = 23 >> A=[1 2 -5;3 -1 4;5 3 23]

>> inv(A)*B

A=

ans =

1 3 5

2 -1 3

-5 4 2

3.0000 2.0000 1.0000

>> B=[2;11;23] B= 2 11 23

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Menggambar GRAFIK

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PLOT sebuah grafik t = 0:pi/100:2*pi; y = sin(t);plot(t,y)

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PLOT 3 buah grafik >> t = 0:pi/100:2*pi; >> y2 = sin(t-0.25);y3 = sin(t-0.5);plot(t,y,t,y2,t,y3)

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PLOT 3 grafik dengan tanda berbeda >> t = 0:pi/100:2*pi; >> y2 = sin(t-0.25);y3 = sin(t-0.5);plot(t,y,t,y2,t,y3) >> plot(t,y,'',t,y2,'--',t,y3,':')

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SKALA SEMILOG VERTIKAL >> x=1:100; >> semilogy(x)

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SKALA SEMILOG HORIZONTAL >> x=1:100; >> semilogx(x)

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SKALA LOG-LOG >> x=1:100; >> loglog(x,x.^2)

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>> Y = [5 2 18 7 39 8 65 5 54 3 2]; >> bar(Y)

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>> Y = [5 2 18; 7 39 8; 65 5 54; 100 3 2]; >> bar3(Y)

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>> t=0:10:100; >> x=t.^2; >> stem(t,x,'fill')

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Contoh: >> t = 1:60; >> x = linspace(0,2*pi,60); >> a = sin(x);b = cos(x) >> stem(t,a+b); >> hold on >> plot(t,[a' b']) >> legend('a + b','a = sin(x)','b =cos(x)') >> xlabel('Time in \musecs') >> ylabel('Magnitude'); >> title('Linear Combination of Two Functions') 37

Hasil

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MATLAB SYMBOLIC MATH TOOLBOX

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MATLAB Symbolic Math Toolbox q q q q q q q q

Symbolic Objects Kalkulus (Diferensial, limit, integral dan deret Taylor) Penyederhanaan fungsi Penyelesaian Persamaan Linier/Nonlinier Penyelesaian Persamaan Diferensial Variable-precision arithmetic Transformasi Fourier, Laplace, dan z Grafik

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1. SYMBOLIC OBJECTS Symbolic objects present symbolic variables, symbolic numbers, symbolic expressions and symbolic matrices.

• Symbolic Variables To declare variables x and y as symbolic objects use the syms command: Contoh 1:

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• Symbolic Numbers Contoh 2:

• Symbolic expressions Contoh 3:

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• Symbolic Matrices Contoh 4:

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• Symvar

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Contoh 5:

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2. Calculus 2.1. Diferensial

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Contoh 5:

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Contoh 6:

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Contoh 7:

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Contoh 8:

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Rangkuman Diferensial

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2.2. Limit

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Contoh 9:

Jawab 9a:

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Jawab 9b:

Jawab 9c:

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Jawab 9d:

Jawab 9e:

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Rangkuman Limit

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2.3. Integral

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Contoh 10. Indefinite Integral

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Contoh 11. Indefinite Integral

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Contoh 12. Definite Integral

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Contoh 13. Definite Integral

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Rangkuman Integral

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2.4. Deret Taylor

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Contoh 14:

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Contoh 15:

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Rangkuman Deret Taylor

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3. Simplication

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3.1. Coeffs

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Contoh 16 :

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3.2. Collect

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Contoh 17 :

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3.3. Expand

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Contoh 18 :

Contoh 19 :

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Contoh 20 :

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3.4. Factor

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Contoh 21:

Contoh 22:

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Contoh 23:

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3.5. Simplify

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Contoh 24:

Contoh 25:

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Contoh 26:

Contoh 27:

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Contoh 28:

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3.6. Simple

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Contoh 29:

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Contoh 30:

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Contoh 31:

Contoh 32:

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3.7. Subexpr

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Contoh 33:

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3.8. Subs

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Contoh 34:

Contoh 35:

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Contoh 36:

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4. Solution of Equations 4.1. Compose

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Contoh 37:

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Contoh 38 :

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Contoh 39 :

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4.2. Solve

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Contoh 40:

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Contoh 41:

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Contoh 42:

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Contoh 43:

x=2 y=5 99

4.3 Dsolve

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Contoh 44:

y = Ae

-2 x

+ Be

-4 x

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Contoh 45:

Contoh 46:

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Contoh 47:

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4.4 Finverse

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Contoh 48:

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5. Variable Precision Arithmetic

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Contoh 49:

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Contoh 50:

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6. TRANSFORMASI INTEGRAL 6.1. Transormasi Fourier

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Contoh 51:

Contoh 52:

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Contoh 53:

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6.2 Inverse Fourier Transform

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Contoh 54:

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6.3. Transformasi Laplace

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Contoh 55:

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6.4. Inverse Transformasi Laplace

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Contoh 56:

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6.5. Transformasi z

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Contoh 57:

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Contoh 58:

1 z Z [( ) k ] = 1 2 z2 120

6.6. Inverse Transformasi Laplace

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Contoh 59:

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7. Tambahan 7.1. Jacobian

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Contoh 60:

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7.2. pretty(f)

Contoh 61:

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7.3. int8, int16, int32, dan int64

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Contoh 62:

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7.4. uint8, uint16, uint32, dan uint64

Contoh 63:

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8.Grafik 8.1. ezplot(f)

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Contoh 64:

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Contoh 65:

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Contoh 66:

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Contoh 67:

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8.2. ezsurf

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Contoh 68:

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Contoh 69:

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8.3. ezsurfc

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Contoh 70:

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Contoh 71:

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8.3 ezpolar

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Contoh 72:

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Contoh Aplikasi Contoh 73:Optimasi

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Contoh 74:Rangkaian Listrik

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