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Numerical Analysis

10th Edition

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

Publisher: Cengage Learning

ISBN: 9781305253667

Chapter

Section

Problem 1ES:

Show that the following equations have at least one solution in the given intervals. a. x cos x 2x2...

Problem 2ES:

Show that the following equations have at least one solution in the given intervals. a. x cos x =...

Problem 3ES:

Find intervals containing solutions to the following equations. a. x 2x = 0 b. 2x cos(2x) (x + 1)2...

Problem 4ES:

Find intervals containing solutions to the following equations. a. x 3x = 0 b. 4x2 ex = 0 c. x3 ...

Problem 5ES:

Find maxaxb |f(x)| for the following functions and intervals. a. f(x) = (2 ex + 2x)/3, [0, 1] b....

Problem 6ES:

Find maxaxb | f(x)| for the following functions and intervals. a. f(x) = 2x/(x2 + 1), [0, 1] b. f(x)...

Problem 7ES:

Show that f(x) is 0 at least once in the given intervals. a. f(x) = 1 ex + (e 1) sin((/2)x), [0,...

Problem 8ES:

Suppose f C[a, b] and f (x) exists on (a, b). Show that if f (x) 0 for all x in (a, b), then there...

Problem 9ES:

Let f(x) = x3. a. Find the second Taylor polynomial P2(x) about x0 = 0. b. Find R2(0.5) and the...

Problem 10ES:

Find the third Taylor polynomial P3(x) for the function f(x)=x+1 about x0 = 0. Approximate...

Problem 11ES:

Find the second Taylor polynomial P2(x) for the function f(x) = ex cos x about x0 = 0. a. Use...

Problem 12ES:

Repeat Exercise 11 using x0 = /6. 11. Find the second Taylor polynomial P2(x) for the function f(x)...

Problem 13ES:

Find the third Taylor polynomial P3(x) for the function f(x) = (x 1) ln x about x0 = 1. a. Use...

Problem 14ES:

Let f(x) = 2x cos(2x) (x 2)2 and x0 = 0. a. Find the third Taylor polynomial P3(x) and use it to...

Problem 15ES:

Find the fourth Taylor polynomial P4(x) for the function f(x) = xex2 about x0 = 0. a. Find an upper...

Problem 16ES:

Use the error term of a Taylor polynomial to estimate the error involved in using sin x x to...

Problem 18ES:

Let f(x) = (1 x)1 and x0 = 0. Find the nth Taylor polynomial Pn(x) for f(x) about x0. Find a value...

Problem 19ES:

Let f(x) = ex and x0 = 0. Find the nth Taylor polynomial Pn(x) for f(x) about x0. Find a value of n...

Problem 21ES:

The polynomial P2(x)=112x2 is to be used to approximate f(x) = cos x in [12,12]. Find a bound for...

Problem 22ES:

Use the Intermediate Value Theorem 1.11 and Rolles Theorem 1.7 to show that the graph of f(x) = x3 +...

Problem 23ES:

A Maclaurin polynomial for ex is used to give the approximation 2.5 to e. The error bound in this...

Problem 24ES:

The error function defined by erf(x)=20xet2dt gives the probability that any one of a series of...

Problem 25ES:

The nth Taylor polynomial for a function f at x0 is sometimes referred to as the polynomial of...

Problem 26ES:

Prove the Generalized Rolles Theorem, Theorem 1.10, by verifying the following. a. Use Rolles...

Problem 27ES:

Example 3 stated that for all x we have | sin x| |x|. Use the following to verify this statement....

Problem 28ES:

A function f : [a, b] is said to satisfy a Lipschitz condition with Lipschitz constant L on [a, b]...

Problem 29ES:

Suppose f C[a, b] and x1 and x2 are in [a, b]. a. Show that a number exists between x1 and x2 with...

Chapter 1.1 - Review Of CalculusChapter 1.2 - Round-off Errors And Computer ArithmeticChapter 1.3 - Algorithms And ConvergenceChapter 2.1 - The Bisection MethodChapter 2.2 - Fixed-point IterationChapter 2.3 - Newton’s Method And Its ExtensionsChapter 2.4 - Error Analysis For Iterative MethodsChapter 2.5 - Accelerating ConvergenceChapter 3.1 - Interpolation And The Lagrange PolynomialChapter 3.2 - Data Approximation And Neville’s Method

Chapter 3.3 - Divided DifferencesChapter 3.4 - Hermite InterpolationChapter 3.5 - Cubic Spline InterpolationChapter 3.6 - Parametric CurvesChapter 4.1 - Numerical DifferentiationChapter 4.2 - Richardson’s ExtrapolationChapter 4.3 - Elements Of Numerical IntegrationChapter 4.4 - Composite Numerical IntegrationChapter 4.5 - Romberg IntegrationChapter 4.6 - Adaptive Quadrature MethodsChapter 4.7 - Gaussian QuadratureChapter 4.8 - Multiple IntegralsChapter 4.9 - Improper Integrals

This well-respected book introduces readers to the theory and application of modern numerical approximation techniques. Providing an accessible treatment that only requires a calculus prerequisite, the authors explain how, why, and when approximation techniques can be expected to work - and why, in some situations, they fail. A wealth of examples and exercises develop readers' intuition, and demonstrate the subject's practical applications to important everyday problems in math, computing, engineering, and physical science disciplines. Three decades after it was first published, Burden, Faires, and Burden's Numerical Analyses remains the definitive introduction to a vital and practical subject.

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