practice midterm

While Loop Requirements in Python

A logical expression that is evaluated at the beginning of each loop.

Function Requirements in Python

All variables used in the function do not need to be declared at the beginning.

True Error Definition

True Value - Approximate Value.

When to Use Approximate Error

When the actual value is unknown.

Cause of Truncation Error

Approximating exact mathematical procedures

Matrix Indexing in NumPy A[:,1]

will take all rows and 2nd column (says 1 but starts at 0)

Machine Epsilon

The maximum possible ratio of the spacing between one number and the next compared to its magnitude.

Which of the following is not true of the first-order Taylor series approximation of f(x) at a?

its truncation error is always less than that of the zero-order approximation

Taylor Series Represents a function as an infinite sum of terms calculated from

values of the function's derivatives at a single point.

Will noy decrease Truncation Error in Taylor Series Approximations

Increasing the number of significant digits

Taylor Series Error Propagation formula for a function of two variables assumes that variation due to one variable

is independent of the variation due to another variable

Numerical Differentiation allows us to compute rates of change without know

the underlying function.

Numerical Integration involves evaluating a definite integral from

a set of values.

Simpson's 1/3 Rule Requirements

an even number of segments, an odd number of data points, evenly spaced segments