A Course of Mathematics for Engineers and Scientists. Volume - download pdf or read online

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

ISBN-10: 0080159702

ISBN-13: 9780080159706

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In calculating both y2(x) and yz(x) we only included terms in the integrand which increased the highest power of / by two over the highest power in the preceding line. The next step gives as required. § 1 : 10] FIRST ORDER DIFFERENTIAL EQUATIONS 55 Example 3. By obtaining an approximate solution of the simultaneous differential equations in terms of powers of x, given that y = 1 and z — \ when x = 0, find the values of y and of z, each correct to four decimal places, when x = | . To apply Picard's method to this problem we must keep the solutions going in step.

Given the differential equation (y-Qz) dy/dx = 1, sketch the isoclinals which cross the y-axis at unit intervals from y = 0 to y = 3, and indicate the corresponding values of dy/dx. Show that the inflexion locus is y = e^+e*"*, and sketch the integral curve which passes through the point (0, 2). § 1 : 10] FIRST ORDER DIFFERENTIAL EQUATIONS 51 4. Sketch the integral curves of the differential equation by the method of isoclinals. 5. For the differential equation draw the isoclinals that cut the x-axis at equal intervals of 0-25 between x = - 2 and x=2.

This inflexion curve is plotted also in Fig. 6. We can integrate the differential equation by writing z = y2, so that The solution of this linear equation is The integral curve which passes through (0, 1) has the equation This curve is also shown on the diagram. Exercises 1:9 1. 2, using y as the horizontal coordinate. 5. Show that the isoclinals for the above extreme values of the gradient satisfy the condition for an inflexion locus. Find the formal solution of the differential equation and compare the values of y at x = 2 obtained from the two solutions.

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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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