EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 8220100254147
Author: Chapra
Publisher: MCG
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Chapter 2, Problem 17P
Develop well-structured programs to (a) determine the square root of the sum of the squares of the elements of a two-dimensional array (i.e., a matrix) and (b) normalize a matrix by dividing each row by the maximum absolute value in the row so that the maximum element in each row is 1.
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3. Properties of Pump Systems - II
Learning Objectives: This problem builds on the pump examples we have been doing, but is meant to help
you learn to do proofs in a step by step fashion. Can you generalize intuition from a simple example?
We consider a system of reservoirs connected to each other through pumps. An example system is shown
below in Figure 1, represented as a graph. Each node in the graph is marked with a letter and represents a
reservoir. Each edge in the graph represents a pump which moves a fraction of the water from one reservoir
to the next at every time step. The fraction of water moved is written on top of the edge.
Figure 1: Pump system
We want to prove the following theorem. We will do this step by step.
Theorem: Consider a system consisting of k reservoirs such that the entries of each column in the system's
state transition matrix sum to one. If s is the total amount of water in the system at timestep n, then total
amount of water at timestep n +1 will also be…
Chapter 2 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 2 - 2.1 Write pseudocode to implement the flowchart...Ch. 2 - Prob. 2PCh. 2 - 2.3 Develop, debug, and document a program to...Ch. 2 - The sine function can be evaluated by the...Ch. 2 - 2.5 Develop, debug, and document a program for...Ch. 2 - The following algorithm is designed to determine a...Ch. 2 - The divide and average method, an old-time method...Ch. 2 - 2.8 An amount of money P is invested in an account...Ch. 2 - 2.9 Economic formulas are available to compute...Ch. 2 - 2.10 The average daily temperature for an area can...
Ch. 2 - Develop, debug, and test a program in either a...Ch. 2 - 2.12 The bubble sort is an inefficient, but...Ch. 2 - Figure P2.13 shows a cylindrical tank with a...Ch. 2 - 2.14 Two distances are required to specify the...Ch. 2 - Develop a well-structured function procedure that...Ch. 2 - Prob. 16PCh. 2 - Develop well-structured programs to (a) determine...Ch. 2 - 2.18 Piecewise functions are sometimes useful when...Ch. 2 - Develop a well-structured function to determine...Ch. 2 - 2.20 Develop a well-structured function to...Ch. 2 - 2.21 Manning’s equation can be used to compute the...Ch. 2 - 2.22 A simply supported beam is loaded as shown in...Ch. 2 - ThevolumeV of liquid in ahollow horizontal...Ch. 2 - 2.24 Develop a well-structured program to compute...Ch. 2 - The pseudocode in Fig. P2.25 computes the...Ch. 2 - 2.26 The height of a small rocket y can be...Ch. 2 - 2.27 As depicted in Fig. P2.27, a water tank...
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