Root Finding
Integration
Numerical Integration
Trapezoidal Rule
100
A general category of root finding methods that requires two points on either side of a single root to start.
What is a bracket method?
100
Integration is also known as this...
What is the area under a curve?
100
This is a reason why an engineer might need a numerical integration method.
What is when there is a function, but it is too complicated to analytically integrate?
100
In plain English, this is the formula for integration using the trapezoidal rule between two points.
What is I = width x average height?
200
A general category of root finding methods that requires only a single starting value or two starting values that do not necessarily bracket the root.
What is an open method?
200
In dynamics, this is the integration of a force in the direction of a displacement.
What is work?
200
This is another reason for numerical integration methods.
What is having experimental data points and no function?
200
The error of the Trapezoidal Rule depends upon this characteristic of the function.
What is the second derivative or curvature?
300
This root finding method is guaranteed to converge to a solution so long as the initial guesses bracket the root.
What is the bisection method?
300
In dynamics, this is the integration of acceleration with time.
What is velocity?
300
This numerical integration strategy entails replacing a complicated function or tabulated data with a polynomial that is easy to integrate.
What are Newton-Cotes formulas?
300
This is a way to improve the accuracy of the trapezoidal rule over a domain from a to b.
What is dividing the integration interval into a number of segments and then applying the trapezoidal rule to each segment.
400
This open method demonstrates quadratic convergence.
What is the Newton-Raphson Method?
400
In thermodynamics, this is the integration of pressure with volume.
What is work?
400
This Newton-Cotes formula involves replacing the function at hand with a first order polynomial.
What is the Trapezoidal Rule?
400
The error in the composite trapezoidal rule is quartered when this happens.
What is the number of segments is doubled?
500
Under this condition, the fixed-point iteration method is guaranteed to converge to a solution.
What is |g'| < 1 ?
500
This is the calculus definition of the average of a function.
What is f_avg = ... ?
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