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 670
... grad At ( 2 , 4 , 1 ) , 89 We have and then the div of the result . div grad V. ( V ) = = • div grad = 6 4 = xyz - 2y2z + x2z2 Φ Оф = i + j + k ax ду dz grad = V = = ( yz + 2xz2 ) i + ( xz − 4yz ) j + ( xy − 2y2 + 2x2z ) k .. At ( 2 ...
... grad At ( 2 , 4 , 1 ) , 89 We have and then the div of the result . div grad V. ( V ) = = • div grad = 6 4 = xyz - 2y2z + x2z2 Φ Оф = i + j + k ax ду dz grad = V = = ( yz + 2xz2 ) i + ( xz − 4yz ) j + ( xy − 2y2 + 2x2z ) k .. At ( 2 ...
Page 673
... grad = V. ( V ) · = ( i : = a a + i + k дф 08 Әф a i + j + . k дх ду dz дх ду dz a2ð2ð2 + + dx2 дуг Əz2 .. div grad = V. ( V6 ) = ð2ð2ð2 ¢ + + dx2 dy2 dz2 This result is sometimes denoted by V2 . So these general results are ( a ) curl grad ...
... grad = V. ( V ) · = ( i : = a a + i + k дф 08 Әф a i + j + . k дх ду dz дх ду dz a2ð2ð2 + + dx2 дуг Əz2 .. div grad = V. ( V6 ) = ð2ð2ð2 ¢ + + dx2 dy2 dz2 This result is sometimes denoted by V2 . So these general results are ( a ) curl grad ...
Page 675
... Grad ( gradient of a scalar function ) аф Оф Әф = i + j + k ax ду az grad 6 = Vo a a ' del ' = operator V = + j + k ду dz dф ( a ) Directional derivative = â . grad o = â . Vo where â is a ds unit vector in a stated direction . Grad ...
... Grad ( gradient of a scalar function ) аф Оф Әф = i + j + k ax ду az grad 6 = Vo a a ' del ' = operator V = + j + k ду dz dф ( a ) Directional derivative = â . grad o = â . Vo where â is a ds unit vector in a stated direction . Grad ...
Contents
coefficients and roots | 33 |
Theory of Equations Part 2 | 43 |
Partial Differentiation | 91 |
Copyright | |
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a₁ b₁ b₂ c₁ c₂ coefficients cos² cosh cosine curl F curve curvilinear coordinates defined 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 i+ j+ 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 δι δυ аф бу дг ду ди ду ду дх ду дхду Оф მა