Further Engineering Mathematics: Programmes and ProblemsThe purpose of this book is essentially to provide a sound second year course in mathematics appropriate to studies leading to BSc Engineering degrees. It is a companion volume to "Engineering Mathematics" which is for the first year. An ELBS edition is available. |
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Page 479
... { Pdx + Qdy ) and If I = C ( Pdx + Qdy ) is an exact differential , then Ic1 = Ic2 If we reverse the direction of c2 , then Ic1 = - - Ic2 0 i.e. X 1 Ic1 + Ic2 = 0 Hence , the integration taken round a closed curve is zero , provided ( Pdx ...
... { Pdx + Qdy ) and If I = C ( Pdx + Qdy ) is an exact differential , then Ic1 = Ic2 If we reverse the direction of c2 , then Ic1 = - - Ic2 0 i.e. X 1 Ic1 + Ic2 = 0 Hence , the integration taken round a closed curve is zero , provided ( Pdx ...
Page 481
... ( Pdx + Qdy ) is an exact differential ( a ) I J = ( Pdx + Qdy ) is independent of the path of integration ( b ) I = ( Pdx + Qdy ) is zero . On to the next frame . 64 Exact differentials in three independent variables A line integral in ...
... ( Pdx + Qdy ) is an exact differential ( a ) I J = ( Pdx + Qdy ) is independent of the path of integration ( b ) I = ( Pdx + Qdy ) is zero . On to the next frame . 64 Exact differentials in three independent variables A line integral in ...
Page 494
... ( Pdx + Qdy ) dy = f ( x , y ) 1+ dx . dx With parametric equations , x and y in terms of t , I : 2 dx dt dy dt 1 ... Pdx + Qdy is an exact differential ( a ) ap ду = до дх ( b ) I = ( Pdx + Qdy ) is independent of the path of integration ...
... ( Pdx + Qdy ) dy = f ( x , y ) 1+ dx . dx With parametric equations , x and y in terms of t , I : 2 dx dt dy dt 1 ... Pdx + Qdy is an exact differential ( a ) ap ду = до дх ( b ) I = ( Pdx + Qdy ) is independent of the path of integration ...
Contents
Theory of Equations Part 2 | 43 |
Partial Differentiation | 91 |
Integral Functions | 145 |
Copyright | |
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a₁ b₁ b₂ c₁ c₂ coefficients cosh cosine curl F curve curvilinear coordinates defined Determine dx dy dx² dy dx Evaluate exact differential Example expression F.dr Fourier series frame function f(x function values gives grad graph Green's theorem harmonic inverse transforms k₁ k₂ Laplace transform line integral matrix method nx dx obtain odd function parametric equations partial fractions Pdx Qdy periodic function plane polar coordinates programme region Revision Summary roots scalar sin nx sin² sinh solution Solve the equation stationary values substitute surface Test Exercise theorem U₁ variables vector field w-plane x₁ xy-plane Y₁ zero δε δυ бу дг дг ди ди др ду ди ду ду дф дф дх ду дг მა