Glossary

Accumulation Problem

Criticality: 3

A type of problem that involves finding the total amount or net change of a quantity over an interval, typically by integrating its given rate of change function.

Example:

Calculating the total amount of water that has flowed into a reservoir over a specific week, given the rate of inflow, is an accumulation problem.

Definite Integral

Criticality: 3

A mathematical operation that calculates the total accumulation of a quantity over a specified interval, often representing the signed area under the curve of a function.

Example:

To find the total distance a car travels from $t=0$ to $t=10$ seconds, you would compute the definite integral of its speed function over that interval.

Displacement

Criticality: 2

The net change in position of an object, calculated by integrating its velocity function over a given time interval. It considers the direction of movement.

Example:

If a runner moves 5 miles east and then 2 miles west, their displacement is 3 miles east, which can be found by integrating their velocity.

Initial Condition

Criticality: 2

A known value of a quantity at a specific starting point in time or at a particular state, used to determine the total accumulated amount by adding it to the net change.

Example:

If a tank initially contains 50 gallons of water at $t=0$ , this is the initial condition needed to find the total volume at a later time after water has flowed in or out.

Net Change

Criticality: 3

The total change in a quantity over an interval, found by evaluating the definite integral of its rate of change function over that interval.

Example:

If the rate of snow falling is $S(t)$ and melting is $M(t)$ , the net change in snow depth from morning to evening is $\int_{t_{start}}^{t_{end}} (S(t) - M(t)) dt$ .

Rate of Change Function

Criticality: 3

A function that describes how one quantity changes with respect to another, often representing a derivative of the accumulated quantity.

Example:

If the number of people entering a park is given by $E(t)$ people per hour, then $E(t)$ is the rate of change function for the total number of people in the park.

Glossary

Accumulation Problem

Criticality: 3

A type of problem that involves finding the total amount or net change of a quantity over an interval, typically by integrating its given rate of change function.

Example:

Calculating the total amount of water that has flowed into a reservoir over a specific week, given the rate of inflow, is an accumulation problem.

Definite Integral

Criticality: 3

A mathematical operation that calculates the total accumulation of a quantity over a specified interval, often representing the signed area under the curve of a function.

Example:

To find the total distance a car travels from $t=0$ to $t=10$ seconds, you would compute the definite integral of its speed function over that interval.

Displacement

Criticality: 2

The net change in position of an object, calculated by integrating its velocity function over a given time interval. It considers the direction of movement.

Example:

If a runner moves 5 miles east and then 2 miles west, their displacement is 3 miles east, which can be found by integrating their velocity.

Initial Condition

Criticality: 2

A known value of a quantity at a specific starting point in time or at a particular state, used to determine the total accumulated amount by adding it to the net change.

Example:

If a tank initially contains 50 gallons of water at $t=0$ , this is the initial condition needed to find the total volume at a later time after water has flowed in or out.

Net Change

Criticality: 3

The total change in a quantity over an interval, found by evaluating the definite integral of its rate of change function over that interval.

Example:

If the rate of snow falling is $S(t)$ and melting is $M(t)$ , the net change in snow depth from morning to evening is $\int_{t_{start}}^{t_{end}} (S(t) - M(t)) dt$ .

Rate of Change Function

Criticality: 3

A function that describes how one quantity changes with respect to another, often representing a derivative of the accumulated quantity.

Example:

If the number of people entering a park is given by $E(t)$ people per hour, then $E(t)$ is the rate of change function for the total number of people in the park.