added old projects

MTH122/Numerical-Integration-Assignment/main.py

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+from tabulate import tabulate
+from trap import trap as t
+from midpoint import midpoint as m
+from simpson import simpson as s
+
+l = [[10,  t(0, 4, 10), m(0, 4, 10), s(0, 4, 10)],
+     [20,  t(0, 4, 20), m(0, 4, 20), s(0, 4, 20)],
+     [40,  t(0, 4, 40), m(0, 4, 40), s(0, 4, 40)],
+     [80,  t(0, 4, 80), m(0, 4, 80), s(0, 4, 80)],
+     [100, t(0, 4, 100), m(0, 4, 100), s(0, 4, 100)],
+    ]
+
+print(tabulate(l, headers=['n', 'trapezoidal', 'midpoint', 'simpsons'], tablefmt='orgtbl'))

MTH122/Numerical-Integration-Assignment/midpoint.py

@@ -0,0 +1,20 @@
+#midpoint.py
+from numpy import sin
+
+def function(x):
+    return sin(x*x)
+
+def midpoint(a, b, n):
+    deltaX = (b - a) / n
+    deltaXValues = []
+    integral = 0
+
+    for i in range (n+1):
+        xSubscriptI = round((a + i * deltaX),5)
+        deltaXValues.append(xSubscriptI)
+
+    for i in range (n):
+        input = (deltaXValues[i] + deltaXValues[i + 1]) / 2
+        integral += function(input)
+
+    return integral * deltaX

MTH122/Numerical-Integration-Assignment/simpson.py

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+#simpson.py
+from numpy import sin
+
+def function(x):
+    return sin(x*x)
+
+def multiple(m, n):
+    return True if m % n == 0 else False
+
+def simpson(a, b, n):
+    deltaX = (b - a) / n
+    deltaXValues = []
+    integral = 0
+
+    for i in range (n+1):
+        xSubscriptI = round((a + i * deltaX),5)
+        deltaXValues.append(xSubscriptI)
+
+    i = 0
+    for i in range (n+1):
+        if i == 0 or i == n:
+            integral += function(deltaXValues[i])
+        elif multiple(i, 2) == True:
+            integral = integral + (2 * function(deltaXValues[i]))
+        else:
+            integral = integral + (4 * function(deltaXValues[i]))
+    
+    integral = (deltaX/3) * integral
+    return integral

MTH122/Numerical-Integration-Assignment/trap.py

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+#trap.py
+from numpy import sin
+
+def function(x):
+    return sin(x*x)
+
+def trap(a, b, n):
+    deltaX = (b  -a) / n
+    deltaXValues = []
+    integral = 0
+
+    for i in range (n+1):
+        xSubscriptI = round((a + i * deltaX),5)
+        deltaXValues.append(xSubscriptI)
+
+    for i in range(n+1):
+        if i == 0 or i == n:
+            integral += function(deltaXValues[i])
+        else:
+            integral += 2 * function(deltaXValues[i])
+
+    integral = round((deltaX/2) * integral, 7)
+    return integral