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 484
... x = 1 . ду дх ap aQ -- SSCOP --ƒƒ ( ~~ 20 ) dx dy = - R дх - R ( -1-1 ) dx dy But SS = - 2 [ fdx dy dx dy over any closed region gives . R the area of the figure 2A where A is the 484 Further Engineering Mathematics 68 Green's theorem.
... x = 1 . ду дх ap aQ -- SSCOP --ƒƒ ( ~~ 20 ) dx dy = - R дх - R ( -1-1 ) dx dy But SS = - 2 [ fdx dy dx dy over any closed region gives . R the area of the figure 2A where A is the 484 Further Engineering Mathematics 68 Green's theorem.
Page 486
... Green's theorem , so move on . 71 ( b ) By Green's theorem 1 = √ { ( 2x + y ) dx + ( 3x − 2y ) dy } P = 2x + y :: I = ӘР ду = = 1 ; Q 3x - 2y .. ap aQ dx dy dy дх R aQ дх = 3 Finish it off . I - for I = I = 2 = 1-3 ) dx urther ...
... Green's theorem , so move on . 71 ( b ) By Green's theorem 1 = √ { ( 2x + y ) dx + ( 3x − 2y ) dy } P = 2x + y :: I = ӘР ду = = 1 ; Q 3x - 2y .. ap aQ dx dy dy дх R aQ дх = 3 Finish it off . I - for I = I = 2 = 1-3 ) dx urther ...
Page 733
Programmes and Problems K. A. Stroud. Green's Theorem Green's theorem enables an integral over a plane area to be expressed in terms of a line integral round its boundary curve . We showed in Programme 9 that , if P and Q are two single ...
Programmes and Problems K. A. Stroud. Green's Theorem Green's theorem enables an integral over a plane area to be expressed in terms of a line integral round its boundary curve . We showed in Programme 9 that , if P and Q are two single ...
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