10th Edition

ISBN: 9781305253667

Author: Richard L. Burden, J. Douglas Faires, Annette M. Burden

Publisher: Cengage Learning

Concept explainers

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These…

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are…

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) ge…

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.

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Textbook Question

Chapter 4.7, Problem 1DQ

Describe the differences and similarities between Gaussian quadrature and the adaptive Gaussian quadrature method known as Gauss-Kronrod quadrature.

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Chapter 4.7, Problem 14ES

Chapter 4.7, Problem 2DQ

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Chapter 4 Solutions

Numerical Analysis

Ch. 4.1 - Use the forward-difference formulas and...Ch. 4.1 - The data in Exercise 1 were taken from the...Ch. 4.1 - Use the most accurate three-point formula to...Ch. 4.1 - Use the most accurate three-point formula to...Ch. 4.1 - The data in Exercise 5 were taken from the...Ch. 4.1 - The data in Exercise 6 were taken from the...Ch. 4.1 - Prob. 9ES Ch. 4.1 - Use the formulas given in this section to...Ch. 4.1 - The data in Exercise 9 were taken from the...Ch. 4.1 - Prob. 12ES

Ch. 4.1 - Use the following data and the knowledge that the...Ch. 4.1 - Prob. 14ES Ch. 4.1 - Prob. 15ES Ch. 4.1 - Prob. 16ES Ch. 4.1 - Prob. 17ES Ch. 4.1 - Prob. 18ES Ch. 4.1 - Prob. 19ES Ch. 4.1 - Prob. 20ES Ch. 4.1 - Prob. 21ES Ch. 4.1 - In a circuit with impressed voltage (t) and...Ch. 4.1 - In Exercise 9 of Section 3.4, data were given...Ch. 4.1 - Derive an O(h4) five-point formula to approximate...Ch. 4.1 - Use the formula derived in Exercise 24 and the...Ch. 4.1 - a. Analyze the round-off errors, as in Example 4,...Ch. 4.1 - Derive a method for approximating f (x0) whose...Ch. 4.1 - Consider the function e(h)=h+h26M, where M is a...Ch. 4.1 - Prob. 1DQ Ch. 4.1 - Prob. 2DQ Ch. 4.2 - Apply the extrapolation process described in...Ch. 4.2 - Add another line to the extrapolation table in...Ch. 4.2 - The following data give approximations to the...Ch. 4.2 - Prob. 6ES Ch. 4.2 - Prob. 7ES Ch. 4.2 - The forward-difference formula can be expressed as...Ch. 4.2 - Prob. 9ES Ch. 4.2 - Prob. 10ES Ch. 4.2 - Prob. 11ES Ch. 4.2 - Prob. 12ES Ch. 4.2 - Prob. 13ES Ch. 4.3 - Approximate the following integrals using the...Ch. 4.3 - Approximate the following integrals using the...Ch. 4.3 - Find a bound for the error in Exercise 1 using the...Ch. 4.3 - Prob. 4ES Ch. 4.3 - Repeat Exercise 1 using Simpsons rule. 1....Ch. 4.3 - Prob. 6ES Ch. 4.3 - Prob. 7ES Ch. 4.3 - Prob. 8ES Ch. 4.3 - Prob. 9ES Ch. 4.3 - Prob. 10ES Ch. 4.3 - Prob. 11ES Ch. 4.3 - Prob. 12ES Ch. 4.3 - The Trapezoidal rule applied to 02f(x)dx gives the...Ch. 4.3 - Prob. 14ES Ch. 4.3 - Approximate the following integrals using formulas...Ch. 4.3 - Prob. 17ES Ch. 4.3 - Suppose that the data of Exercise 17 have...Ch. 4.3 - Prob. 19ES Ch. 4.3 - Prob. 20ES Ch. 4.3 - The quadrature formula...Ch. 4.3 - The quadrature formula...Ch. 4.3 - Find the constants c0, c1, and x1 so that the...Ch. 4.3 - Find the constants x0, x1, and c1 so that the...Ch. 4.3 - Prob. 25ES Ch. 4.3 - Prob. 26ES Ch. 4.3 - Prob. 27ES Ch. 4.3 - Derive Simpsons Three-Eighths rule (the closed...Ch. 4.3 - Prob. 1DQ Ch. 4.3 - Prob. 2DQ Ch. 4.4 - Use the Composite Trapezoidal rule with the...Ch. 4.4 - Prob. 2ES Ch. 4.4 - Use the Composite Simpsons rule to approximate the...Ch. 4.4 - Prob. 4ES Ch. 4.4 - Prob. 5ES Ch. 4.4 - Prob. 6ES Ch. 4.4 - Prob. 7ES Ch. 4.4 - Prob. 8ES Ch. 4.4 - Prob. 9ES Ch. 4.4 - Prob. 10ES Ch. 4.4 - Determine the values of n and h required to...Ch. 4.4 - Repeat Exercise 11 for the integral 0x2cosxdx. 11....Ch. 4.4 - Determine the values of n and h required to...Ch. 4.4 - Repeat Exercise 13 for the integral 12xlnxdx. 13....Ch. 4.4 - Prob. 15ES Ch. 4.4 - Prob. 17ES Ch. 4.4 - A car laps a race track in 84 seconds. The speed...Ch. 4.4 - Prob. 19ES Ch. 4.4 - Prob. 20ES Ch. 4.4 - Prob. 21ES Ch. 4.4 - Prob. 23ES Ch. 4.4 - Prob. 24ES Ch. 4.4 - Prob. 25ES Ch. 4.4 - Prob. 26ES Ch. 4.4 - Prob. 1DQ Ch. 4.4 - Prob. 2DQ Ch. 4.5 - Use Romberg integration to compute R3, 3 for the...Ch. 4.5 - Use Romberg integration to compute R3, 3 for the...Ch. 4.5 - Prob. 3ES Ch. 4.5 - Prob. 4ES Ch. 4.5 - Use the following data to approximate 15f(x)dx as...Ch. 4.5 - Prob. 9ES Ch. 4.5 - Prob. 10ES Ch. 4.5 - Prob. 11ES Ch. 4.5 - Romberg integration for approximating 01f(x)dx...Ch. 4.5 - Prob. 15ES Ch. 4.5 - Prob. 18ES Ch. 4.5 - Prob. 19ES Ch. 4.5 - Prob. 1DQ Ch. 4.5 - Prob. 4DQ Ch. 4.6 - Prob. 1ES Ch. 4.6 - Prob. 2ES Ch. 4.6 - Prob. 11ES Ch. 4.6 - Prob. 12ES Ch. 4.6 - Could Romberg integration replace Simpsons rule in...Ch. 4.7 - Approximate the following integrals using Gaussian...Ch. 4.7 - Approximate the following integrals using Gaussian...Ch. 4.7 - Repeat Exercise 1 with n = 3. 1. Approximate the...Ch. 4.7 - Repeat Exercise 2 with n = 3. 2. Approximate the...Ch. 4.7 - Repeat Exercise 1 with n = 4. 1. Approximate the...Ch. 4.7 - Repeat Exercise 2 with n = 4. 2. Approximate the...Ch. 4.7 - Repeat Exercise 1 with n = 5. 1. Approximate the...Ch. 4.7 - Repeat Exercise 2 with n = 5. 2. Approximate the...Ch. 4.7 - Describe the differences and similarities between...Ch. 4.7 - Prob. 2DQ Ch. 4.8 - Prob. 1DQ Ch. 4.8 - Prob. 2DQ Ch. 4.8 - Prob. 3DQ Ch. 4.8 - Prob. 4DQ Ch. 4.9 - Suppose a body of mass m is traveling vertically...Ch. 4.9 - The Laguerre polynomials {L0(x), L1(x) ...} form...Ch. 4.9 - Prob. 7ES Ch. 4.9 - Prob. 8ES Ch. 4.9 - Prob. 9ES Ch. 4.9 - Prob. 1DQ Ch. 4.9 - Prob. 2DQ

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Describe the differences and similarities between Gaussian quadrature and the adaptive Gaussian quadrature method known as Gauss-Kronrod quadrature.

Solution Summary: The author explains the differences and similarities between Gaussian quadrature and Adaptive Quadratures. The nodes and coefficients are chosen to minimize the expected error.

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