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

ISBN-10: 0080159702

ISBN-13: 9780080159706

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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. 2. Draw the isoclinals and the inflexion locus for the equation where a, b are constants and 0 < a < e, b > 0. Prove that an integral curve which touches the inflexion locus does so at the point x = 2/b + 2a/e2, y = 2.

A particle moves in a medium in which the resistance to its motion is kv* per unit mass, where v is the velocity of the particle and k is a constant. If no forces other than the resistance act on the particle, find the time in which the velocity is reduced from an initial value Kto the value v. Show that the particle moves through a distance 3(kV)~1 whilst its velocity falls to the value V/4. 38 A COURSE OF MATHEMATICS 5. A particle of mass m moves in a straight line against a resistance av+bv2 where v is the velocity and a and b are positive constants.

It is shown in books on analysis that this process is convergent if a domain D can be found in the x-y plane which includes the point (x0, yo) and in which/(x, y) is single-valued and continuous, and if for any two points (x, y{) and (x, y2) on the same arbitrary ordinate inside D the condition where K is a constant, is satisfied. (This is called a Lipschitz condition) Example 1. Use Picard's method to obtain the solution in powers of x as far as the term in x7 of the differential equation where y = 0 when x = 0.

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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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