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# Solutions for Chapter 1.1: Fundamentals of Differential Equations 8th Edition

## Full solutions for Fundamentals of Differential Equations | 8th Edition

ISBN: 9780321747730

Solutions for Chapter 1.1

Solutions for Chapter 1.1
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##### ISBN: 9780321747730

This textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8. Chapter 1.1 includes 17 full step-by-step solutions. Since 17 problems in chapter 1.1 have been answered, more than 122133 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Fundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730.

Key Calculus Terms and definitions covered in this textbook
• Absolute value of a real number

Denoted by |a|, represents the number a or the positive number -a if a < 0.

• Algebraic expression

A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots

• Arithmetic sequence

A sequence {an} in which an = an-1 + d for every integer n ? 2 . The number d is the common difference.

• De Moivre’s theorem

(r(cos ? + i sin ?))n = r n (cos n? + i sin n?)

• Equal complex numbers

Complex numbers whose real parts are equal and whose imaginary parts are equal.

• Factored form

The left side of u(v + w) = uv + uw.

• First quartile

See Quartile.

• Lemniscate

A graph of a polar equation of the form r2 = a2 sin 2u or r 2 = a2 cos 2u.

• Length of an arrow

See Magnitude of an arrow.

• Major axis

The line segment through the foci of an ellipse with endpoints on the ellipse

• Median (of a data set)

The middle number (or the mean of the two middle numbers) if the data are listed in order.

• Odd function

A function whose graph is symmetric about the origin (ƒ(-x) = -ƒ(x) for all x in the domain of f).

• Partial fractions

The process of expanding a fraction into a sum of fractions. The sum is called the partial fraction decomposition of the original fraction.

• Power rule of logarithms

logb Rc = c logb R, R 7 0.

• Probability distribution

The collection of probabilities of outcomes in a sample space assigned by a probability function.

• Quartic function

A degree 4 polynomial function.

• Singular matrix

A square matrix with zero determinant

• Solve an equation or inequality

To find all solutions of the equation or inequality

• Tangent line of ƒ at x = a

The line through (a, ƒ(a)) with slope ƒ'(a) provided ƒ'(a) exists.

• Third quartile

See Quartile.