Numerical Methods for Engineers

7th Edition

ISBN: 9780073397924

Author: Steven C. Chapra Dr., Raymond P. Canale

Publisher: McGraw-Hill Education

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Textbook Question

Chapter 23, Problem 16P

Evaluate ∂ f / ∂ x , ∂ f / ∂ y , and ∂ f / ( ∂ x ∂ y ) for the following function at x = y = 1

(a) Analytically and

(b) Numerically Δ x = Δ y = 0.0001 ,

f ( x , y ) = 3 x y + 3 x − x 3 − 3 y 3

Expert Solution & Answer

Chapter 23 Solutions

Numerical Methods for Engineers

Ch. 23 - 23.1 Compute forward and backward difference...Ch. 23 - 23.2 Repeat Prob. 23.1, but for evaluated at...Ch. 23 - 23.3 Use centered difference approximations to...Ch. 23 - Use Richardson extrapolation to estimate the first...Ch. 23 - Repeat Prob. 23.4, but for the first derivative of...Ch. 23 - 23.6 Employ Eq. (23.9) to determine the first...Ch. 23 - 23.7 Prove that for equispaced data points, Eq....Ch. 23 - Compute the first-order central difference...Ch. 23 - Prob. 9P Ch. 23 - Develop a user-friendly program to apply a Romberg...

Ch. 23 - 23.11 Develop a user-friendly program to obtain...Ch. 23 - 23.12 The following data are provided for the...Ch. 23 - 23.13 Recall that for the falling parachutist...Ch. 23 - The normal distribution is defined as f(x)=12ex2/2...Ch. 23 - 23.15 The following data were generated from the...Ch. 23 - Evaluate f/x,f/y, and f/(xy) for the following...Ch. 23 - 23.17 Evaluate the following integral with...Ch. 23 - 23.18 Use the diff command in MATLAB and compute...Ch. 23 - The objective of this problem is to compare...Ch. 23 - Use a Taylor series expansion to derive a centered...Ch. 23 - Use the following data to find the velocity and...Ch. 23 - 23.22 A plane is being tracked by radar, and data...Ch. 23 - 23.23 Develop an Excel VBA macro program to read...Ch. 23 - Use regression to estimate the acceleration at...Ch. 23 - You have to measure the flow rate of water through...Ch. 23 - The velocity y (m/s) of air fl owing past a flat...Ch. 23 - Chemical reactions often follow the model:...Ch. 23 - 23.28 The velocity profile of a fluid in a...Ch. 23 - 23.29 The amount of mass transported via a pipe...

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Evaluate ∂ f / ∂ x , ∂ f / ∂ y , and ∂ f / ( ∂ x ∂ y ) for the following function at x = y = 1 (a) Analytically and (b) Numerically Δ x = Δ y = 0.0001 , f ( x , y ) = 3 x y + 3 x − x 3 − 3 y 3

Solution Summary: The author analyzes the function f(x,y) = 3xy+3x-x3-3y.

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Chapter 23 Solutions