Mastodawn

Alright, future engineers!
**Round-off Error:** Error from finite precision number representation in computers.
Ex: 1/3 stored as 0.33333333 has round-off error.
Pro-Tip: Accumulates significantly with many computations, so be aware!
#NumericalMethods #ErrorAnalysis #STEM #StudyNotes

kipriyanovich May 25

Alright, future engineers!
**Truncation Error:** The error from stopping an infinite process (like a series or iteration) after a finite number of steps.
Ex: Approximating `e^x` with only a few terms of its Taylor series.
Pro-Tip: More terms/steps reduce truncation error, but beware of round-off error increasing!
#NumericalMethods #ErrorAnalysis #STEM #StudyNotes

kipriyanovich Apr 19

Alright, future engineers!
**Truncation Error** occurs when an exact mathematical procedure is replaced by an approximation, often by cutting off an infinite series.
Ex: Using only the first few terms of a Taylor series for `e^x`.
Pro-Tip: This error is *predictable* and *controllable* by refining your approximation!
#NumericalMethods #ErrorAnalysis #STEM #StudyNotes

kipriyanovich Apr 16

Alright, future engineers!
**Relative Error:** Quantifies how much an approximation deviates, *relative to the true value*. Ex: `RE = |(Approx - True) / True|`. Pro-Tip: Essential for evaluating precision and setting engineering tolerances!
#NumericalMethods #ErrorAnalysis #STEM #StudyNotes

kipriyanovich Apr 14

Alright, future engineers!

**Truncation Error** is the inaccuracy from ending an infinite math process (like a series or integral) at a finite step. Ex: `e^x` approximated by `1+x`. Pro-Tip: You can *control* it by adjusting step size or terms, unlike round-off error!

#NumericalMethods #ErrorAnalysis #STEM #StudyNotes

kipriyanovich Apr 6

**Truncation Error** is the error from approximating an infinite mathematical process with a finite one. Ex: Using a finite Taylor series sum. Pro-Tip: It typically decreases with smaller step sizes (h) or more terms (N)!
#NumericalMethods #ErrorAnalysis #STEM #StudyNotes

kipriyanovich Mar 30

Condition Number measures how sensitive a problem's output is to tiny input changes. Large condition number = huge output errors! Pro-Tip: It's key for understanding solution reliability; high values mean your problem is ill-conditioned and results are unreliable!
#NumericalMethods #ErrorAnalysis #STEM #StudyNotes