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# Solutions for Chapter 11: ORTHOGONAL FUNCTIONS AND FOURIER SERIES

## Full solutions for Differential Equations with Boundary-Value Problems | 7th Edition

ISBN: 9780495108368

Solutions for Chapter 11: ORTHOGONAL FUNCTIONS AND FOURIER SERIES

Solutions for Chapter 11
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##### ISBN: 9780495108368

Since 25 problems in chapter 11: ORTHOGONAL FUNCTIONS AND FOURIER SERIES have been answered, more than 14338 students have viewed full step-by-step solutions from this chapter. Differential Equations with Boundary-Value 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 Boundary-Value Problems, edition: 7. Chapter 11: ORTHOGONAL FUNCTIONS AND FOURIER SERIES includes 25 full step-by-step solutions.

Key Calculus Terms and definitions covered in this textbook
• 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.

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 x-axis

• 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.

• Half-plane

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 + an-1x n-1 + 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.

• Second-degree 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.

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