New PDF release: A Course of Mathematics for Engineers and Scientists. Volume

By Brian H. Chirgwin and Charles Plumpton (Auth.)

ISBN-10: 0080159702

ISBN-13: 9780080159706

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Extra resources for A Course of Mathematics for Engineers and Scientists. Volume 2

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4. By Picard's method obtain an approximate solution in series, as far as the term in x7> of dy/dx = 1 - xy2, given that y = 0 when * = 0. Check the result by substituting this expansion in the differential equation. 5. By applying Picard's method to the equations find, as far as the term in x5, the series solution of the equation given that y = 0, dy/dx = 1 when x — 0. 6. By Picard's iterative method, or otherwise, obtain three terms of the solution of the equation dy/dx — (x2+y2)/x for which y — 0 when x = 0.

By Picard's method obtain the first four non-vanishing terms of a power series in x satisfying the equation with the condition that y — 2 when x = 0. 001 of the correct value. § 1 : 11] FIRST ORDER DIFFERENTIAL EQUATIONS 57 3. 3 with that obtained in (i). 4. By Picard's method obtain an approximate solution in series, as far as the term in x7> of dy/dx = 1 - xy2, given that y = 0 when * = 0. Check the result by substituting this expansion in the differential equation. 5. By applying Picard's method to the equations find, as far as the term in x5, the series solution of the equation given that y = 0, dy/dx = 1 when x — 0.

15. (i) Find the orthogonal trajectories of the system of curves whose equation in plane polar coordinates is (ii) Prove that the system of curves whose equation is is auto-orthogonal, and sketch the curves of the system. § 1 : 7] FIRST ORDER DIFFERENTIAL EQUATIONS 33 1:7 Application to dynamics—resisted motion Suppose a body moves along a straight line so that at time / its displacement from a fixed point O of the line is x, its velocity is v = dx/dt and its acceleration is a = dv/dt = d2x/dt2 = v dvjdx.

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A Course of Mathematics for Engineers and Scientists. Volume 2 by Brian H. Chirgwin and Charles Plumpton (Auth.)


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