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 446
... др ду = a2z дудх and az дх and Q до a2z = дх дуду a2z дудх = 12 . = მთ ду and we know that дуду др до = ду дх Therefore , for dz to be an exact differential and this is the test we apply . Example 1 dz = ( 3x2 + 4y2 ) dx + 8xydy . If ...
... др ду = a2z дудх and az дх and Q до a2z = дх дуду a2z дудх = 12 . = მთ ду and we know that дуду др до = ду дх Therefore , for dz to be an exact differential and this is the test we apply . Example 1 dz = ( 3x2 + 4y2 ) dx + 8xydy . If ...
Page 737
... др [ [ ( ex - op ) dx dy = [ 2 [ dx ду 0 ( 1 - 2r sin 0 ) r dr de S π - 16 3 Complete it . 83 Here it is : до др dx - dy dx dy = x / 2 0 2 ( r - 2r2 sin 0 ) dr de = [ [ 2-232 sino ] ] = Cx / 2 16 0 de 이 2 15 sin e } do 16 16 20+ cos 0 ...
... др [ [ ( ex - op ) dx dy = [ 2 [ dx ду 0 ( 1 - 2r sin 0 ) r dr de S π - 16 3 Complete it . 83 Here it is : до др dx - dy dx dy = x / 2 0 2 ( r - 2r2 sin 0 ) dr de = [ [ 2-232 sino ] ] = Cx / 2 16 0 de 이 2 15 sin e } do 16 16 20+ cos 0 ...
Page 841
... др ду = до дх 17 for I1 = { ( x2 - y2 + 2y - 1 ) dx- ( 2xy - 2x ) dx } = S ( Pdx + Qdy ) др - . . P = x2 − y2 + 2y − 1 = 2y + 2 др ду = ду до Q = -2xy + 2x - = 2y + 2 дх до дх Similarly for 12 = { ( 2xy - 2x ) dx + ( x2 − y2 + 2y ...
... др ду = до дх 17 for I1 = { ( x2 - y2 + 2y - 1 ) dx- ( 2xy - 2x ) dx } = S ( Pdx + Qdy ) др - . . P = x2 − y2 + 2y − 1 = 2y + 2 др ду = ду до Q = -2xy + 2x - = 2y + 2 дх до дх Similarly for 12 = { ( 2xy - 2x ) dx + ( x2 − y2 + 2y ...
Contents
Theory of Equations Part 2 | 43 |
Partial Differentiation | 91 |
Integral Functions | 145 |
Copyright | |
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a₁ a²ƒ 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 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 дг дг ди ди др ду дг ду ди ду ду дх ду მა