Numerical Methods for Engineers - 7th Edition - by Steven C. Chapra Dr., Raymond P. Canale - ISBN 9780073397924
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Numerical Methods for Engineers
7th Edition
Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
ISBN: 9780073397924

Solutions for Numerical Methods for Engineers

Book Details

This is the seventh edition of Chapra and Canale's Numerical Methods for Engineers that retains the instructional techniques that have made the text so successful. Chapra and Canale's unique approach opens each part of the text with sections called "Motivation," "Mathematical Background," and "Orientation." Each part closes with an "Epilogue" containing "Trade-Offs," "Important Relationships and Formulas," and "Advanced Methods and Additional References." Much more than a summary, the Epilogue deepens understanding of what has been learned and provides a peek into more advanced methods. Helpful separate Appendices. "Getting Started with MATLAB" and "Getting Started with Mathcad" which make excellent references. Numerous new or revised problems are drawn from actual engineering practice. The expanded breadth of engineering disciplines covered is especially evident in these exercises, which now cover such areas as biotechnology and biomedical engineering. Excellent new examples and case studies span all areas of engineering giving students a broad exposure to various fields in engineering.

Sample Solutions for this Textbook

We offer sample solutions for Numerical Methods for Engineers homework problems. See examples below:

4.6 Use zero- through fourth-order Taylor series expansions to predict x using a base point at....Given Information: The equation f(x)=−0.5x2+2.5x+4.5. Calculation: The graph of the function can be...5.3 Determine the real root of: (a) Graphically. (b) Using bisection to determine the root to....Determine the roots of f(x)=1221x+18x22.75x3 graphically. In addition, determine the first root of...Given: The function, f(x)=sin(x)−x. The initial condition, x0=0.5 and iterate until εa≤0.01%....6.2 Determine the highest real root of (a) Graphically. (b) Fixed-point iteration method...6.7 Locate the first positive root of Where x is in radians. Use four iterations of the secant...6.23 Determine the roots of the simultaneous nonlinear equations Use a graphical approach to...Given Information: Provided Polynomial is f(x)=x4−7.5x3+14.5x2+3x−20 and the monomial factor is x−2....Given Information: The given equation is, f(x)=x3+x2−4x−4 Use Müller’s method. Formula used: The...Use the program developed in Prob. 7.8 to determine the roots of the equations in Prob. 7.5.Given Information: For ethyl alcohol a=12.02,b=0.08407 and the temperature is T=375 K, the number of...Many fields of engineering require accurate population estimates. For example, transportation...8.44 Figure P8.44 shows three reservoirs connected by circular pipes. The pipes, which are made of...8.46 Repeat Prob. 8.45, but incorporate the fact that the friction factor can be computed with the...8.48 Determining the velocity of particles settling through fluids is of great importance of many...Given: The set of equations, 8=6x3+2x22−x1=x35x2+8x1=13 Consider the set of equations,...A number of matrices are defined as [A]=[415726][B]=[437127204][C]={361}[D]=94213675...9.21 Recall from Sec. 8.2 that determining the chemistry of water exposed to atmospheric can be...Given: The equations, [L][U]=[A] and [L]{D}={B}. Proof: Consider a linear equation represented in...10.3 (a) Solve the following system of equations by LU decomposition without pivoting (b) ...The following system of equations is designed to determine concentrations (thecsing/m3) in a series...Given: A tridiagonal system: 0.8−0.40−0.40.8−0.40−0.40.8{x1x2x3}={4125105} Formula used: (a) The...Use the Gauss-Seidel method (a) without relaxation and (b) with relaxation (=0.95) to solve the...11.13 Use the Gauss-Seidel method (a) without relaxation and (b) with relaxation to solve the...Given Information: Flow rates are provided as follows: Q01=6 Q15=3, Q12=4, Q31=1, Q03=8, Q25=1,...Chemical/Bio Engineering 12.10 An irreversible, first-order reaction takes place in four well mixed...Chemical/Bio Engineering 12.12 Figure P12.12 depicts a chemical exchange process consisting of a...Given Information: The air flow through the room with proper description is provided as follows:...Given Information: The function f(x) is given as, f(x)=−x2+8x−12 Calculation: Evaluate the first...Employ the following methods to find the maximum of f(x)=4x1.8x3+1.2x30.3x4 (a) Golden-section...Employ the following methods to find the maximum of the function from Prob. 13.7: (a) Golden-section...Given: The function f(x,y)=x2+2y2 at x=2 and y=2 in the direction of h=2i+3j. Formula used: The...14.5 Find the gradient vector and Hessian matrix for each of the following...Given Information: Product A and B are produced during a 40-hr of work week. Company has access to...Given Information: The factors are given as below, Resource Regular Premium Supreme Resource...Given Information: The volume of the cylinder is 0.5 m3. Formula used: Write the expression of...Given Information: Following data is given for a chemical plant that makes three products on a...Given Information: The Manning equation of flow Q (m3/s) can be written as Q=1nAcR2/3S1/2 where n is...Given Information: The parameters are given as Young’s modulus E is 2×1011Pa, Cross-sectional area A...Given Information: The data is, 8.8 9.5 9.8 9.4 10 9.4 10.1 9.2 11.3 9.4 10 10.4 7.9 10.4 9.8 9.8...Given these data 29.65 28.55 28.65 30.15 29.35 29.75 29.25 30.65 28.15 29.85 29.05 30.25 30.85 28.75...Given Information: The data is, x 0 2 4 6 9 11 12 15 17 19 y 5 6 7 6 9 8 7 10 12 12 Calculation: The...Given Information: The values, log8=0.9030900log12=1.0791812 Formula used: Linear interpolation...Use Newtons interpolating polynomial to determine y at x=8 to the best possible accuracy. Compute...18.14 Develop cubic splines for the data in Prob. 18.6 and (a) predict f (4) and f (2.5) and (b)...Given: The average value formula is f(x)¯=∫0xf(x)dxx and the results are, ∑sin(ω0t)N=0,...Given Information: The sawtooth wave shown as, Formula used: Consider f(t) is a periodic function...Given Information: The sawtooth wave given in the following figure, Formula used: Consider f(t) is a...Given Information: Data for specific growth rate k and available food f is given in the form of a...Given Information: The table is given as, Depth, m 0 0.5 1.0 1.5 2.0 2.5 3.0 Temperature, Celsius 70...Given Information: Consider the experimentally measured values of γ˙ and τ from a single blood...20.16 Soft tissue follows an exponential deformation behavior in uniaxial tension while it is in the...Given Information: The provided data is, i −2 −1 −0.5 0.5 1 2 V −637 −96.5 −20.5 20.5 96.5 637...Given Information: The data is, T 0 5 10 20 30 40 μ 1.787 1.519 1.307 1.002 0.7975 0.6529 Graph: The...Given Information: The data is provided as, x=0 x=2 x=4 x=6 x=8 y=0 100.00 90.00 80.00 70.00 60.00...Given: The integral, ∫0π2(6+3cosx)dx Formula used: ∫abf(x)dx=[F(x)]ab=F(b)−F(a) Here, F(x) is...21.2 Evaluate the following integral: (a) Analytically; (b) Single application of the...Given: Integral, ∫03xe2x dx. Formula used: (1) Formula for h is given by, h=b−an (2) Formula for...Given Information: The given integral is, ∫2∞1x(x+2)dx Formula used: Simpson’s 1/3 rule. I1=h3[...Given information: Function, y=cosx Step size, h=π12 The initial value of x, x=π4 Formula used:...Compute the first-order central difference approximations of O(h4) for each of the following...Use a Taylor series expansion to derive a centered finite-difference approximation to the third...Given Information: Write the value of the provided temperatures. T1=−150°C and T2=100°C Write the...Given Information: The given expressions are as follows,...24.36 Repeat Prob. 24.35, but use (a) Simpson’s rule, (b) Romberg integration to, and (c) Gauss...Given Information: The position of a Jet fighter on an aircraft carrier’s runway is, t,s 0 0.52 1.04...Given Information: The vertical velocity of the rocket is,...Given Information: The formula for the upward velocity of rocket is given as, v=uln(m0m0−qt)−gt...Given Information: The initial value problem dydt=yt2−1.1y where y(0)=1. Formula used: Tosolve an...Solve the following problem over the interval from x=0to1 using a step size of 0.25 where y(0)=1....Given Information: Differential equation, dydx=−200,000y+200,000e−x−e−x . Formula used: The...Given Information: Differential equation, dydt=−2yt, t=4 to t=5 with step size of 0.5 and initial...Given Information: A steady-state heat balance for a rod is represented as d2Tdx2−0.15T=0 where the...27.27 The following nonlinear, parasitic ODE was suggested by Hornbeck (1975): If the initial...A heated rod with a uniform heat source can be modeled with the Poisson equation, d2Tdx2=f(x) Given...27.29 Repeat Prob. 27.28, but for the following heat source: . Given Information: The differential equation for mass balance of single reactor is, Vdcdt=Qcin−Qc....Given information: The system of equations, dcadt=−10cacc+cbdcbdt=10cacc−cbdccdt=−10cacc+cb−2cc...Given Information: The series of first order, liquid phase reactions is, A→k1B→k2C The second order...Perform the same computation for the Lorenz equations in Sec. 28.2, but use (a) Eulers method, (b)...28.27 The basic differential equation of the elastic curve for a uniformly loaded beam (Fig. P28.27)...Given Information: The dynamic of a forced spring-mass-damper system is given as,...Given information: The upper boundary condition increased to 150°C and the left boundary insulated...Given Information: The fixed temperature at top and right boundary is 100 °C and the fixed...Given Information: The expression of the temperature distribution of long, thin rod is, l=10...Repeat Example 30.3, but for x=1cm.Given Information: Poisson’s equation: d2Tdx2=−f(x) Here, function f(x) is the heat source along the...Given Information: To develop nodal equations for the temperature and their gradients at each of the...Given Information: The distributed-parameter system depicts chemical modelling being subjected to...Given Information: Write the expression for D’Arcy’s law. qn=−Kdhdn Here, K is the hydraulic...

More Editions of This Book

Corresponding editions of this textbook are also available below:

NUMERICAL METHODS FOR ENGINEERS
8th Edition
ISBN: 9781260986198
NUMERICAL METH.F/ENGR. (LL)-W/CONNECT
8th Edition
ISBN: 9781264091454
NUMERICAL METHODS FOR ENGINEERS
8th Edition
ISBN: 9781264150113
NUMERICAL METH.F/ENGR.-EBOOK>I<
8th Edition
ISBN: 9781264150106
Numerical Methods for Engineering
8th Edition
ISBN: 9781260232073
Numerical Methods for Engineers
8th Edition
ISBN: 9781260484571
Connect Online Access for Numerical Methods for Engineers
8th Edition
ISBN: 9781260484533
Numerical Methods for Engineers
6th Edition
ISBN: 9780073401065
Numerical Methods For Engineers, 7 Ed
7th Edition
ISBN: 9789352602131
Numerical Methods For Engineers: With Software And Programming Applications
4th Edition
ISBN: 9780072431933