Consider the Problem Replace $\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } }$

question 11

Multiple Choice

Consider the problem $c ^ { 2 } \frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } = \frac { \partial ^ { 2 } u } { \partial t ^ { 2 } } , u ( 0 , t ) = 0 , u ( 1 , t ) = 0 , u ( x , 0 ) = \sin ( \pi x ) , u _ { t } ( x , 0 ) = g ( x )$ . Replace $\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } }$ with a central difference approximation with $h = 1 / 4$ and $\frac { \partial ^ { 2 } u } { \partial t ^ { 2 } }$ with a central difference approximation with $k = 1 / 3$ The resulting equation is

• A) \(c ^ { 2 } [ u ( x + h , t ) - 2 u ( x , t ) + u ( x - h , t ) ] / h ^ { 2 } = ( u ( x , t + k ) - u ( x , t ) + u ( x , t - k ) ) / k ^ { 2 }\)
• B) \(c ^ { 2 } [ u ( x + h , t ) - 2 u ( x , t ) + u ( x - h , t ) ] / h ^ { 2 } = ( u ( x , t + k ) - 2 u ( x , t ) + u ( x , t - k ) ) / k ^ { 2 }\)
• C) \(c ^ { 2 } [ u ( x + h , t ) - 2 u ( x , t ) + u ( x - h , t ) ] / h ^ { 2 } = ( u ( x , t + k ) - u ( x , t ) ) / k ^ { 2 }\)
• D) \(c ^ { 2 } [ u ( x + h , t ) - 2 u ( x , t ) + u ( x - h , t ) ] / h ^ { 2 } = ( u ( x , t + k ) + u ( x , t ) ) / k\)
• E) \(c ^ { 2 } [ u ( x + h , t ) - 2 u ( x , t ) + u ( x - h , t ) ] / h ^ { 2 } = ( u ( x , t + k ) - u ( x , t ) ) / k\)

Gain knowledge on the acquisition, valuation, and disposal processes of intangible assets and property, plant, and equipment (PP&E).

Differentiate between capital and revenue expenditures related to tangible and intangible assets.

Understand the legal aspects and life span of patents and copyrights and their impact on financial statements.

Practice the computation of financial ratios related to asset management, including asset turnover.

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Definitions:

Vertical Axis

The y-axis in a chart or graph, which often represents the range of the dependent variable.

Slope

The rate at which a line inclines or declines, showing the relationship between two variables in a graph, calculated as the rise over the run.

Graph

A graph is a visual representation of data, showing relationships between variables typically through lines, bars, or points.

Relationship

How two or more thoughts, entities, or persons are associated, or the status of being associated.