From e461df7573c2b7b7e26c965d8cf2d8e175d67378 Mon Sep 17 00:00:00 2001
From: Nguyễn Gia Phong <vn.mcsinyx@gmail.com>
Date: Mon, 16 Dec 2019 21:31:18 +0700
Subject: [usth/MATH2.2] Numerical Methods

The future starts now.
---
 usth/MATH2.2/final/EX1.m | 36 ++++++++++++++++++++++++++++++++++++
 usth/MATH2.2/final/EX2.m | 38 ++++++++++++++++++++++++++++++++++++++
 usth/MATH2.2/final/EX3.m | 16 ++++++++++++++++
 3 files changed, 90 insertions(+)
 create mode 100644 usth/MATH2.2/final/EX1.m
 create mode 100644 usth/MATH2.2/final/EX2.m
 create mode 100644 usth/MATH2.2/final/EX3.m

(limited to 'usth/MATH2.2/final')

diff --git a/usth/MATH2.2/final/EX1.m b/usth/MATH2.2/final/EX1.m
new file mode 100644
index 0000000..354aa2f
--- /dev/null
+++ b/usth/MATH2.2/final/EX1.m
@@ -0,0 +1,36 @@
+disp ("Question 1:");
+disp ("(a)");
+printf ("11^3 + 12^3 - 7^3 = %d\n", 11^3 + 12^3 - 7^3);
+printf ("15! = %d\n", factorial (15));
+
+disp ("(b)");
+A = [1 2 3
+     4 5 6
+     7 8 9];
+B = eye (3);
+
+disp ("(b.i)");
+disp ("A + B = ");
+disp (A + B);
+
+disp ("(b.ii)");
+disp ("A' = ");
+disp (A');
+
+disp ("(b.iii)");
+disp ("A^-1 = ");
+disp (inv (A));
+
+disp ("(c.i)");
+printf ("x^2 = 19  ->  x = %g\n", sqrt (19));
+disp ("(c.ii)");
+printf ("x^4 = 55  ->  x = %g\n", sqrt (sqrt (19)));
+
+disp ("(d)");
+X = 0 : 30;
+Y = X * 2 + 3;
+plot (X, Y);
+xlabel ("x");
+ylabel ("y = 2x + 3");
+disp ("Press any key to continue...");
+kbhit;
diff --git a/usth/MATH2.2/final/EX2.m b/usth/MATH2.2/final/EX2.m
new file mode 100644
index 0000000..9b8c95e
--- /dev/null
+++ b/usth/MATH2.2/final/EX2.m
@@ -0,0 +1,38 @@
+disp ("Question 2:");
+disp ("(a)");
+pkg load symbolic;
+syms x real;
+solve (sqrt (x) - x + 1 == 0)
+% ans = (sym)
+%   √5   3
+%   ── + ─
+%   2    2
+pkg unload symbolic;
+disp ("To get numerical solutions we can use fzero");
+disp ("With the initial guess of 0, fzero (@(x) sqrt (x) - x + 1, 0) returns");
+fzero (@(x) sqrt (x) - x + 1, 0)
+
+disp ("(b)");
+hold on;
+ezplot (@(x) exp (-x));
+ezplot (@(x) sin (x));
+hold off;
+disp ("Press any key to continue...");
+kbhit;
+
+disp ("(c)");
+s = 0;
+for k = 1 : 1000
+  s += k^3;
+endfor
+printf ("The cubic sum of integers from 1 to 1000 is %d\n", s);
+
+disp ("(d)");
+A = [2 1 4
+     1 2 -5
+     3 -2 4];
+b = [10 1 8]';
+disp ("Using mldivide, [x y z] = ");
+disp (mldivide (A, b)');
+disp ("Using inv, [x y z] = ");
+disp ((inv (A) * b)');
diff --git a/usth/MATH2.2/final/EX3.m b/usth/MATH2.2/final/EX3.m
new file mode 100644
index 0000000..99240f8
--- /dev/null
+++ b/usth/MATH2.2/final/EX3.m
@@ -0,0 +1,16 @@
+disp ("Question 3:");
+disp ("(a)");
+function y = f (x)
+  y = 2 + x.^2 + exp(x.*2 + 1);
+endfunction
+h = 0.005;
+printf ("By forward difference with h = 0.05, f'(1.35) = %g\n",
+        (f (1.35 + h) - f (1.35)) / h);
+
+disp ("(b)");
+disp ("I am unsure if diff is different on Matlab, but on octave,");
+disp ("it's simply taking differences between consecutive elements.");
+x = [1.35, 1.35+h];
+printf ("Using diff with h = 0.05, we get same result, f'(1.35) = %g\n",
+        (diff (f (x)) / h));
+disp ("Using symbolical methods, f'(1.35) = 83.5946 which is quite close.");
-- 
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