Flashcards
ADVANCE MATH 223ME LT1
Cards in this deck (28)
- 1are techniques by which mathematical problems are formulated so that they can be solved with arithmetic operationsNumerical methods
- 2Three phases of engineer problem solvingA: The precomputer and B: The computer era
1. Formulation
2. Solution
3. Interpretation - 3can be broadly defined as a formulation or equation that expresses the essential features of a physical system or process in mathematical terms.A mathematical model
- 4is a characteristic that usually reflects the behavior or state of the systemDep var = f( indep var, parameters, force func)
Dependent variable - 5are usually dimensions, such as time and space, along which the system’s behavior is being determinedDep var = f( indep var, parameters, force func)
Independent variables - 6are reflective of the system’s properties or compositionDep var = f( indep var, parameters, force func)
Parameters - 7are external influences acting upon the systemDep var = f( indep var, parameters, force func)
Forcing functions - 8The engineering problem-solving process.Problem Definition→
Mathematical Model(Theory or data)→
Numeric or Graphic Results→
Implementation - 9In statistics, an _____(or _____) is not a "mistake" but rather a difference between a computed, estimated, or measured value and the accepted true, specified, or theoretically correct value.Error (or residual)
- 10Two Forms of Numerical ErrorRound-off error
Truncation error - 11caused by the finite precision of computations involving floating-point values. Roundoff error is due to the fact that computers can represent only quantities with a finite number of digits.Round-off error
- 12the difference between the exact mathematical solution and the approximate solution. __________ is the discrepancy introduced by the fact that numerical methods may employ approximations to represent exact mathematical operations and quantities.Truncation error
- 13are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value.Significant figures
- 14refers to how closely a computed or measured value agrees with the true value.Accuracy
- 15is defined as systematic deviation from the truth.Inaccuracy (also called bias)
- 16refers to how closely individual computed or measured values agree with each other.Precision
- 17refers to the magnitude of the scatterImprecision (also called uncertainty)
Note: Error represents both the inaccuracy and the imprecision of our predictions. - 18formula for true errorEt = true value - approximation
Et = exact value of the error or true error - 19—where:
𝜀𝑡 = true percent relative error - 20—where:
𝜀𝑎 = approximate percent relative error
- 21Example Problem 1
- 22Example Problem 2
- 23Often, when performing computations, we may not be concerned with the sign of the error, but we are interested in whether the percent absolute value is lower than a prespecified percent tolerance, 𝜀𝑠 . For such cases, the computation is repeated until
- 24—
- 25—
- 26—
- 27Taylor series provides a means to predict a function value at one point in terms of the function value and its derivatives at another point. In particular, the theorem states that any smooth function can be approximated as a polynomial.
- 28In a similar manner, additional terms can be included to develop the complete Taylor series expansion:In a similar manner, additional terms can be included to develop the complete Taylor series expansion:
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- Flashcards on ADVANCE MATH 223ME LT1, created by BSME 2-E James Victor Abao on 02/02/2023.
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- BSME 2-E James Victor Abao
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