Ini dia Tugas Praktikum Aplikasi Komputer

Praktikum Aplikasi Komputer

1.     1. Plot permukaan didefinisikan oleh fungsi pada domain -2 ≤ x ≤ 2;

-2 ≤ y ≤ 2. Tentukan nilai-nilai dan lokasi dari maximum dan minimum fungsi

 Jawab:

Titik minimum (x, y, z)=(0.5000, 0.5000, -0.0920) dan (x, y, z)=(-0.5000, -0.5000,  -0.0920)

Titik maksimum (x, y, z)=(0.5000, -0.5000, 0.0920) dan (x, y, z)=(-0.5000, 0.5000,  0.0920)

Dalam command window langsung kita tuliskan :

>> f=inline('-x(1).*x(2).*exp(-2.*(x(1).^2+x(2).^2))');

>> x=-2:2;y=x;

>> [X,Y]=meshgrid(x,y);

>> Z=-X.*Y.*exp(-2.*(X.^2+Y.^2));

>> meshc(X,Y,Z)

Untuk mencari Titik minimum:

>> [x12min,fval]=fminsearch(f,[1,1])

x12min =

    0.5000    0.5000

fval =

   -0.0920

>> [x12min,fval]=fminsearch(f,[-1,-1])

x12min =

   -0.5000   -0.5000

fval =

   -0.0920

Untuk mencari Titik maksimum:

>> f1=inline('-(-x(1).*x(2).*exp(-2.*(x(1).^2+x(2).^2)))');

>> [x12min]=fminsearch(f1,[1,-1])

x12min =

    0.5000   -0.5000

>> Z2=f(x12min)

Z2 =

    0.0920

>> [x12min]=fminsearch(f1,[-1,1])

x12min =

   -0.5000    0.5000

>> Z3=f(x12min)

Z3 =

    0.0920

2.      2. Hitunglah integral terbatas berikut ini dengan metode trapezoid  (trapz) dan kuadratur (quad):

  

Jawab:

a. Dengan Metode trapezoid  (trapz):

Dalam command window kita tulis:

>> x =linspace(-10,10,50); % definisikan vektor x

>> y =sqrt(100-x.^2); % hitung nilai y

>> integral=trapz(x,y) % integralkan !

sehingga kita dapatkan:

integral =

  156.5954

b. Dengan Metode kuadratur (quad):

Dalam command window kita tulis:

>> int_y=quad(' sqrt(100-x.^2)',-10,10,00001)

kita dapatkan:

int_y =

  156.0646

3.     3. Hitunglah integral lipat-2 berikut ini:

   

Jawab:

a. Pertama, kita buat M-file untuk fungsi ini:

function z = fungsiku(x,y)

z =10-2*x.^2-y.^2;

b. kemudian dalam command window kita tulis:

>> Integral_dobel = dblquad('fungsiku',-4,4,-5,5)

kita dapatkan:

Integral_dobel =

  -720

4.      4. Hitunglah integral lipat-3 dari fungsi tiga variabel berikut ini:

            w(x, y, z)= x² + xy + yz + z²

    pada batas-batas -1 ≤ x ≤ 1, -1 ≤ y ≤ 1, -1 ≤ z ≤ 1.

Jawab:

a. Untuk mendapatkan nilai integral dari fungsi diatas, buat fungsi dalam script yaitu:

function w = funxyz(x,y,z)

w =(x.^2+x*y+y*z+z.^2);

b. Untuk contoh integral di atas, kita hitung dengan toleransi 0,001 dalam command window:

Integral_tripel = triplequad('funxyz', -1,1,-1,1,-1,1,0.001)

sehingga kita mendapat:

Integral_tripel =

    5.3333

The Aspect of Mathematics and How to Learn Them

The Aspect of Mathematics and How to Learn Them

At this fourth meeting, we were learning about the aspect of mathematics and how to learn them with Mr Marsigit M.A. Do you know the aspect of mathematics? I think this topic is very important for me as the candidate of mathematics teacher. So, listen to Mr Marsigit.

From time to time, since we born, we have many experiences about the aspect of mathematics. So, from the daily life to the academy life here at University, we can identify many aspect of mathematics. The aspects of mathematics are the application of mathematics and the concept of mathematics. Probably, it’s better for us and then to implement.

Mr marsigit ask to ours, since when we know about numbers or the concept of numbers? What kind activities that we are remember? How are remember since when and where? Then Mr marsigit ask again, when did you know the concept of distance? When did you know about far and near? When did you know about fraction? So, Mr marsigit said that please remember it and please tell me. We only silent and think hard to remember it, but we can’t remember since when we are know about it. If we now understand but we can’t remember it when we start understands, it is Intuition.

Mr marsigit giving question for ours again. Do you know about “laugh”? And then when you know about “Love”? Since when you are understand about love?  I try to remember it. When we know about “Sad”? If we remember, it is intuition, said He.

Do not Ignore about Intuition, because Intuition are very important. Learning language is intuition too. Intuitions do better our life. In order to empower intuition, we need to have many experiences. We must search experience that it’s good. Example: counting, measuring, listening, writing, etc. We must study hard to understand about something. Learning is not an obligation but learning is a necessity. We should study in overseas because it’s very important to get experience like Mr Marsigit and Mr Ilham. We are an adult, so we only know about the purpose, the benefit, and motivation to get our dreams. Intuition can keep healthy too, so we must understanding about intuition.

Mr Marsigit draws a pie, like a volcano or mount, such as:

Axiomatic Mathematics

Formal Mathematics

Abstract Mathematics

University Mathematics

 

                                     

Concrete Mathematics

Mathematics for younger student

We are learning at University need approach, we need:

1.      Read the definition, theorem, and example.

2.     Started to engage activity, such as:

a.       Read blog Mr Marsigit.

b.      Make a comment.

c.       Collect video about Mathematics Teaching.

Readiness contributes 90 % of our success, so work hard!!!

Learning and learning, confidence if we are can.