2 1 F M m r G F = GMm r 2 (1.1) (1.1) (r = r ) F = GMmr r 3 (1.2) a F m F = kma k 1 F = ma (1.3) (1.2) (1.3) ma = GMmr r 3 (1.4)
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2 2 1 F M m r G F = GMm r 2 (1.1) (1.1) (r = r ) F = GMmr r 3 (1.2) a F m F = kma k 1 F = ma (1.3) (1.2) (1.3) ma = GMmr r 3 (1.4)
3 1.1 3 M m r a a = d2 r dt 2 (1.4) r d 2 r dt 2 = GM r 3 r (1.5) r (1.5)
4 (1.6) x 2 = cos x (1.6) y = x 2 y = cos x
5 1.2 5 x = x (1.6) ( ) (1.7)
6 6 1
7 du dt = f(t, u) (2.1) f f(t, u) = u + t (2.2) u t (2.1) u t f (2.2) (2.1) u = e t t 1 u = 2e t t 1 (2.3) C u = Ce t t 1 (2.4) C t u t = 0 u = 1
8 8 2 (2.4) 1 = C 1 C = 2 (2.3) (2.1) (2.1) f u t f(t, u) = (cos e ut + sin t log u) t+u t u (2.4) (2.3) t u t u (t, u) 2.1 u t t u t u t u t du dt = lim u(t + t) u(t) t 0 t du dt u(t + t) u(t) t (2.5) (2.6) 2.2 (2.6) (2.1) u(t + t) = u(t) + tf(t, u(t)) (2.7)
9 (2.7) u(t) u(t + t) 2.2 (2.6) u(0) (2.7) u(0) u( t) u(2 t) u(3 t) (2.8) t u (2.1) (2.2) u(0) = 1 t = 0.1 (2.8) (2.7) u(t + t) = u(t) + t(u(t) + t) = (1 + t)u(t) + t t
10 10 2 u(0.1) = ( )u(0) = 1.1 u(0.2) = ( ) = 1.22 u(0.3) = ( ) = (2.3) u(0.1) u(0.2) t = 0.1 t = t = 0.1 t
11 t = 0.01 t t t
12 12 2 (2.1) t t t 0 t 1 t 2 t = t n u u n u n = u(t n ) (2.9) t n+1 = t n + t (2.7) t = t n u n+1 = u n + tf(t n, u n ) (2.10) 2.10 (2.1) u 0 u 1 u 2 (2.1) F(T,U) T0 0 U0 DT = t TMAX N (2.10)
13 Option Explicit Function F(T, U) F = U + T End Function Sub Program() End Sub Dim T0 As Double, U0 As Double, DT As Double, TMAX As Double Dim T As Double, U As Double, N As Integer, I As Integer With Worksheets(" ") T0 =.Range("_T ").Value U0 =.Range("_ ").Value DT =.Range("_T ").Value TMAX =.Range("_T ").Value End With T = T0 U = U0 N = (TMAX - T0) / DT + DT With Worksheets(" ") Do Until.Shapes.Count = 0.Shapes(1).Delete Loop.Cells.Delete For I = 1 To N U = U + DT * F(T, U) T = T + DT.Cells(I, 1).Value = T.Cells(I, 2).Value = U Next Charts.Add ActiveChart.ChartType = xlxyscatterlines ActiveChart.HasLegend = False ActiveChart.SetSourceData.Range(.Cells(1, 1),.Cells(N, 2)), xlcolumns ActiveChart.Location Where:=xlLocationAsObject, Name:=" " End With
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