[Numeth] Intro to Numeth Flashcards
(26 cards)
a characteristic that shows the behavior or state of the system
Dependent Variable
In the pre-computer era, cite 3 ways in which problem solving was approached
Analytical/Exact Methods, Graphical Solutions, and Calculators/Slide Rules
The following numbers are NOT significant:
leading zeros, trailing zeros without decimal, 10 and x in sci. notation (N x 10^x)
indicates the dimensions, such as time and space, along with the system’s behavior
Independent Variable
broadly defined as a formulation or equation that expresses the essential features of a physical system or process.
Mathematical Model
“Engineering Problem Solving in the computer era:
Formulation: ___
Solution: ____
Interpretation: ____”
In-depth exposition of relationship of problem to fundamental laws
Easy-to-use computer method
Ease of calculations allow holistic thoughts and intuition to develop; system sensitivity and behavior can be studied
those that can be used with confidence. They correspond to the number of certain digits + 1 estimated digit
significant digits
true fractional relative error formula
εt = ( true error / true value ) x 100%
“true” error formula
Et = true value - approx.
refers to how closely a computed or measured value agrees with the true value
Accuracy
Engineering Problem Solving in the pre-computer era:
Formulation: ___
Solution: ____
Interpretation: ____
Fundamental Laws explained briefly
elaborate and complicated methods to make the problem tractable
in-depth analysis limited by time-consuming solutions
involves the study of methods of computing numerical data
Numerical analysis
Representation of a Mathematical Model
Dep. var = f(indep. var, parameters, forcing functions)
techniques used in the formulation of mathematical problems so that they can be solved with arithmetic operations.
Numerical Methods
2 implications of sig figs
Specify confidence in the approximate result and Approximates specific quatities (like pi or e)
When multiplying/dividing two numbers, the result will show the same number of sig figs as the number with the _____significant figures.
least
reflective of the system’s properties or composition
Parameters
When adding/subtracting two numbers, the result will show the number of decimal places as the number with the ____ decimal places
least
Reasons why we should study numerical methods:
Useful for non-linear equations and complex geometries
Computer programs involve numerical methods
can be applied in designing programs
Efficient vehicles for learning to use computers
Strengthens understanding of math
external influences acting upon the system
forcing functions
With the development of computers, the role of numeth in solving engineering problems ____ dramatically in recent years
increased
issues to consider in using numeth for problem solvign
rate of conergence, accuracy of answer, completeness of response
2 major forms of numerical error
round-off error and truncation error
satisfies the original DE, but there are many mathematical models that cannot be solved exactly
Analytical/Exact Solution
