 11.1: In 16 fill in the blank or answer true or false without referring b...
 11.2: In 16 fill in the blank or answer true or false without referring b...
 11.3: In 16 fill in the blank or answer true or false without referring b...
 11.4: In 16 fill in the blank or answer true or false without referring b...
 11.5: In 16 fill in the blank or answer true or false without referring b...
 11.6: In 16 fill in the blank or answer true or false without referring b...
 11.7: Suppose the function f(x) x2 1, 0 x 3, is expanded in a Fourier ser...
 11.8: What is the corresponding eigenfunction for the boundaryvalue prob...
 11.9: Chebyshevs differential equation has a polynomial solution for n 0,...
 11.10: The set of Legendre polynomials {Pn(x)}, where P0(x) 1, P1(x) x, . ...
 11.11: Without doing any work, explain why the cosine series of is the fin...
 11.12: (a) Show that the set is orthogonal on the interval [0, L]. (b) Fin...
 11.13: Expand in a Fourier series.
 11.14: Expand in a Fourier series.
 11.15: Expand (a) in a cosine series (b) in a Fourier series.
 11.16: In 13, 14, and 15, sketch the periodic extension of f to which each...
 11.17: Discuss: Which of the two Fourier series of f in converges to on th...
 11.18: Consider the portion of the periodic function f shown in Figure 11....
 11.19: Find the eigenvalues and eigenfunctions of the boundaryvalue problem
 11.20: Give an orthogonality relation for the eigenfunctions in 19.
 11.21: Expand , in a FourierBessel series, using Bessel functions of orde...
 11.22: Expand , in a FourierLegendre series.
 11.23: Suppose the function y f(x) is defined on the interval . (a) Verify...
 11.24: The function f(x) ex is neither even or odd. Use to write f as the ...
 11.25: Suppose that f is an integrable 2pperiodic function. Prove that fo...
Solutions for Chapter 11: ORTHOGONAL FUNCTIONS AND FOURIER SERIES
Full solutions for Differential Equations with BoundaryValue Problems  7th Edition
ISBN: 9780495108368
Solutions for Chapter 11: ORTHOGONAL FUNCTIONS AND FOURIER SERIES
Get Full SolutionsSince 25 problems in chapter 11: ORTHOGONAL FUNCTIONS AND FOURIER SERIES have been answered, more than 14338 students have viewed full stepbystep solutions from this chapter. Differential Equations with BoundaryValue Problems was written by and is associated to the ISBN: 9780495108368. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Differential Equations with BoundaryValue Problems, edition: 7. Chapter 11: ORTHOGONAL FUNCTIONS AND FOURIER SERIES includes 25 full stepbystep solutions.

Absolute maximum
A value ƒ(c) is an absolute maximum value of ƒ if ƒ(c) ? ƒ(x) for all x in the domain of ƒ.

Addition principle of probability.
P(A or B) = P(A) + P(B)  P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

Compounded k times per year
Interest compounded using the formula A = Pa1 + rkbkt where k = 1 is compounded annually, k = 4 is compounded quarterly k = 12 is compounded monthly, etc.

Conversion factor
A ratio equal to 1, used for unit conversion

Direction angle of a vector
The angle that the vector makes with the positive xaxis

Exponential growth function
Growth modeled by ƒ(x) = a ? b a > 0, b > 1 .

Factoring (a polynomial)
Writing a polynomial as a product of two or more polynomial factors.

Halfplane
The graph of the linear inequality y ? ax + b, y > ax + b y ? ax + b, or y < ax + b.

Inverse relation (of the relation R)
A relation that consists of all ordered pairs b, a for which a, b belongs to R.

Nappe
See Right circular cone.

Paraboloid of revolution
A surface generated by rotating a parabola about its line of symmetry.

Parameter
See Parametric equations.

Polar coordinates
The numbers (r, ?) that determine a point’s location in a polar coordinate system. The number r is the directed distance and ? is the directed angle

Polynomial in x
An expression that can be written in the form an x n + an1x n1 + Á + a1x + a0, where n is a nonnegative integer, the coefficients are real numbers, and an ? 0. The degree of the polynomial is n, the leading coefficient is an, the leading term is anxn, and the constant term is a0. (The number 0 is the zero polynomial)

Random behavior
Behavior that is determined only by the laws of probability.

Regression model
An equation found by regression and which can be used to predict unknown values.

Sample space
Set of all possible outcomes of an experiment.

Scientific notation
A positive number written as c x 10m, where 1 ? c < 10 and m is an integer.

Seconddegree equation in two variables
Ax 2 + Bxy + Cy2 + Dx + Ey + F = 0, where A, B, and C are not all zero.

Upper bound test for real zeros
A test for finding an upper bound for the real zeros of a polynomial.