EBK NUMERICAL METHODS FOR ENGINEERS
EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 8220100254147
Author: Chapra
Publisher: MCG
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Chapter 2, Problem 22P

A simply supported beam is loaded as shown in Fig. P2.22. Using singularity functions, the displacement along the beam can be expressed by the equation:

u y ( x ) = 5 6 [ x 0 4 x 5 4 ] + 15 6 x 8 3 + 75 x 7 2 + 57 6 x 3 238.25 x

By definition, the singularity function can be expressed as follows:

x a n = { ( x a ) n when  x > a 0 when  x a }

Develop a program that creates a plot of displacement versus distance along the beam x. Note that x = 0 at the left end of the beam.

Chapter 2, Problem 22P, 2.22	A simply supported beam is loaded as shown in Fig. P2.22. Using singularity functions, the

FIGURE P2.22

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Determine whether each function is an injection and determine whether each is a surjection.The notation Z_(n) refers to the set {0,1,2,...,n-1}. For example, Z_(4)={0,1,2,3}.  f: Z_(6) ->  Z_(6) defined by f(x)=x^(2)+4(mod6). g: Z_(5) ->  Z_(5) defined by g(x)=x^(2)-11(mod5). h: Z*Z  ->  Z defined by h(x,y)=x+2y. j: R-{3} -> R defined by j(x)=(4x)/(x-3).
Determine whether each function is an injection and determine whether each is a surjection.
Let A = {a, b, c, d}, B = {a,b,c}, and C = {s, t, u,v}. Draw an arrow diagram of a function for each of the following descriptions. If no such function exists, briefly explain why. (a) A function f : AC whose range is the set C. (b) A function g: BC whose range is the set C. (c) A function g: BC that is injective. (d) A function j : A → C that is not bijective.

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EBK NUMERICAL METHODS FOR ENGINEERS

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