[NA] Finished project

3 files changed, 231 insertions, 42 deletions

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+0.02`],Scaled[0.02`]},{Scaled[0.05`],Scaled[0.05`]}},PlotRangeClipping -> True,ImagePadding -> All,DisplayFunction -> Identity,AspectRatio -> NCache[
+Power[GoldenRatio,-1],0.6180339887498948`],Axes -> {True,True},AxesLabel -> {None,None},AxesOrigin -> {0,0},RuleDelayed[
+DisplayFunction,Identity],Frame -> {{False,False},{False,False}},FrameLabel -> {{None,None},{None,None}},FrameTicks -> {{Automatic,Automatic},{Automatic,Automatic}},GridLines -> {None,None},GridLinesStyle -> Directive[
+GrayLevel[0.5`,0.4`]],Method -> CompressedData["1:eJzlUstOwzAQbMv7wlscuPENfAAqLYVKFKqm6t1N1u0K1xt5bYnw2/wAtqs+CbkgTkRKtPbuzuxM9mZMA7lXq9V413+eka1sLE4DpyC59EEbpHDK3pPTmTBFYgsFfOQTTWdpJiymW03Xq6ZHI/IpptzVFoxILZKWOxV8Bz4YgWFfZ27j83m3VXLug6HHeuuRY+gTY0RtrKPGYGgccBDXEYqhhOhBSkgtVw4UdD7hZKr8a2W9ojIwGe8GYbjfSh6vw/QJ9S+wwkhtQ7lCDbypu8QqaQAkmVnLGSbTowyW5pTg5kqkMANtK3HD6O9JsK2pVEmuSMLxhfQ2xelqM3rA07hKcyPOAtiYSTkL0Z8EPwD3v6sPEEkqvPhJx+m4Ucw/0F35oEVkMtTCAg+J1GseOyrlnYQpkb0XxYJiPuRhWKbFzSZCyJcULW+6mTcVbbH67Ykii/UNgX1hbEkBLsH/jKFkzS6ieTlCNhLKwX9y4gucBRzd"],PlotRange -> {{-6.5`,12},{0.`,154268.84721448677`}},PlotRangeClipping -> True,PlotRangePadding -> {{Scaled[
+0.02`],Scaled[0.02`]},{Scaled[0.02`],Scaled[0.02`]}},Ticks -> {Automatic,Automatic}}],
+StandardForm],"Output",CellLabel -> "Out[258]= ",ExpressionUUID -> "67ca15e8-5e60-49a6-b7fc-0eb3c6603724"]},
+Open],ExpressionUUID -> "4aa4a658-6ba2-4db8-90d4-d6f69981eb09"],Cell[
+BoxData[""],
+"Input",ExpressionUUID -> "3e162c5d-1476-44de-8499-dd1295e3f297"]},StyleDefinitions -> "Default.nb",
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\ No newline at end of file
diff --git a/Year 3/Numerical analysis/Project NA.pdf b/Year 3/Numerical analysis/Project NA.pdf
new file mode 100644
index 0000000..b5a4036
--- /dev/null
+++ b/Year 3/Numerical analysis/Project NA.pdf
diff --git a/Year 3/Numerical analysis/Project.wl b/Year 3/Numerical analysis/Project.wl
index a3ac02a..9eb49f7 100644
--- a/Year 3/Numerical analysis/Project.wl
+++ b/Year 3/Numerical analysis/Project.wl
@@ -1,82 +1,74 @@
 (*----------
-* 1 задача
-*----------*)
+ * 1 задача
+ *----------*)
 ApproxIntegral[M_, a_, b_, f_] := With[
   {
     h=(b-a)/(2M),
-    xk=Function[k, a+k*(b-a)/(2M)]
+    xk=Function[k,a+k*(b-a)/(2M)]
   },
-  (h/3)(f[a]+f[b]) +
-  (2h/3)Sum[f[xk[2k]], {k, 1, M-1}]+
-  (4h/3)Sum[f[xk[2k-1]], {k, 1, M}]
+   (h/3) (f[a] + f[b]) +
+  (2h/3) Sum[f[xk[2k]],   {k, 1, M-1}] +
+  (4h/3) Sum[f[xk[2k-1]], {k, 1, M}]
 ]
 
-Integrand[x_] := 1/((1+2x^2)^5)
-m15 := N[ApproxIntegral[15, -1, 1, Integrand], {Infinity, 20}]
-m50 := N[ApproxIntegral[50, -1, 1, Integrand], {Infinity, 20}]
-correct  := N[Integrate[Integrand[x], {x, -1, 1}], {Infinity, 20}]
+Integrand[x_] := 1/((1 + 2x^2)^5)
+m15 := N[ApproxIntegral[15, -1, 1, Integrand], {Infinity,20}]
+m50 := N[ApproxIntegral[50, -1, 1, Integrand], {Infinity,20}]
+correct := N[Integrate[Integrand[x], {x, -1, 1}], {Infinity,20}]
 
 Print["1 задача)"]
 Print["При M=15:        ", m15]
-Print["Разлика с точен: ", N[correct-m15, {Infinity, 20}]]
+Print["Разлика с точен: ", N[correct-m15,{Infinity,20}]]
 Print["При M=50:        ", m50]
-Print["Разлика с точен: ", N[correct-m50, {Infinity, 20}]]
+Print["Разлика с точен: ", N[correct-m50,{Infinity,20}]]
+Print["Точна стойност:  ", correct]
 
 (*----------
-* 2 задача
-*----------*)
+ * 2 задача
+ *----------*)
 
 (* Намиране Pn *)
 Pncoeff [xs_, f_] := With[
   {
-    k=Length[xs],
-    x0=First[xs],
-    xk=Last[xs]
+    k  = Length[xs],
+    x0 = First[xs],
+    xk = Last[xs]
   },
   Piecewise[{
     {
       f[xk],
-      k==1
+      k == 1
     },
     {
-      (Pncoeff[Drop[xs, 1], f]-Pncoeff[Drop[xs, -1], f])/(xk-x0),
-      x0!=xk
+      (Pncoeff[Drop[xs, 1], f] - Pncoeff[Drop[xs, -1], f])/(xk - x0),
+      x0 != xk
     },
     {
-      (D[f[x], {x, k-1}]/.x->x0)/((k-1)!),
-      x0==xk
+      (D[f[y], {y, k-1}] /. y->x0)/((k-1)!),
+      x0 == xk
     }}]
 ]
 
-Pn[f_, xsWithDup_] := With[
+Pn[f_,xsWithDup_] := With[
   { xs = xsWithDup },
-  Function[x, Sum[
-    FullSimplify[Pncoeff[Take[xs, i], f]*
-    Product[x-xs[[j]], {j, 1, i-1}]],
+  Function[x,Sum[
+    Pncoeff[Take[xs, i], f] *
+    Product[x - xs[[j]], {j, 1, i-1}],
     {i, 1, Length[xs]}
   ]]
 ]
 
-f[x_] := Piecewise[{
-  {Cos[3x], x<=Pi},
-  {x-Pi-1, x>Pi}
-}]
+f[x_]:= Piecewise[{
+    {Cos[3x],    x <= Pi},
+    {x - Pi - 1, x > Pi}
+  }]
 values := {9Pi/10, 9Pi/10, 9Pi/10, 10Pi/11, 10Pi/11, 11Pi/10}
-
-
 newtonpolyn := Pn[f, values]
 
 Print["2 задача)"]
-Print["Полином: ", newtonpolyn[x]]
-
-(*
-InterpolatingPolynomial[{
-  {9Pi/10, f[9Pi/10]},
-  {10Pi/11, f[10Pi/11]},
-  {11Pi/10, f[11Pi/10]}
-}, x]
-*)
+Print["Полином: ", Simplify[newtonpolyn[x]]]
+(* InterpolatingPolynomial[{{9Pi/10, f[9Pi/10]}, {10Pi/11, f[10Pi/11]}, {11Pi/10, f[11Pi/10]}}, x] *)
 
 (* Графика разлика *)
 Print["Графика на разлика:"]
-Plot[Abs[f[z]-newtonpolyn[z]], {z, -2Pi, 2Pi}]
+Plot[Abs[f[z] - newtonpolyn[z]], {z, -6.5, 12}]