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# Solutions for Chapter 7.1: Definition of the Laplace Transform

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

ISBN: 9780495108368

Solutions for Chapter 7.1: Definition of the Laplace Transform

Solutions for Chapter 7.1
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##### ISBN: 9780495108368

Chapter 7.1: Definition of the Laplace Transform includes 48 full step-by-step solutions. 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. Since 48 problems in chapter 7.1: Definition of the Laplace Transform have been answered, more than 15942 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.

Key Calculus Terms and definitions covered in this textbook
• Acceleration due to gravity

g ? 32 ft/sec2 ? 9.8 m/sec

• Arccotangent function

See Inverse cotangent function.

• Augmented matrix

A matrix that represents a system of equations.

• Constant of variation

See Power function.

• Direction angle of a vector

The angle that the vector makes with the positive x-axis

• Divergence

A sequence or series diverges if it does not converge

• Elimination method

A method of solving a system of linear equations

• Inequality

A statement that compares two quantities using an inequality symbol

• Intercept

Point where a curve crosses the x-, y-, or z-axis in a graph.

• Inverse composition rule

The composition of a one-toone function with its inverse results in the identity function.

• Inverse relation (of the relation R)

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

• Limit

limx:aƒ1x2 = L means that ƒ(x) gets arbitrarily close to L as x gets arbitrarily close (but not equal) to a

• nth root of a complex number z

A complex number v such that vn = z

• Odd function

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

• Paraboloid of revolution

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

• Position vector of the point (a, b)

The vector <a,b>.

• Rational expression

An expression that can be written as a ratio of two polynomials.

• Real number

Any number that can be written as a decimal.

• Slope

Ratio change in y/change in x

• Sum of a finite geometric series

Sn = a111 - r n 2 1 - r

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