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Diffstat (limited to 'book/module2/error.tex')
| -rw-r--r-- | book/module2/error.tex | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/book/module2/error.tex b/book/module2/error.tex index 2646dc8..d515c4a 100644 --- a/book/module2/error.tex +++ b/book/module2/error.tex @@ -29,12 +29,12 @@ part of the computation}. An example of this could be using a finite number of terms from a Taylor Series expansion to approximate a function. -Approximating \(e^x\) by the first few terms of its Taylor series: +Approximating $e^x$ by the first few terms of its Taylor series: -\[e^x \approx 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!}\] +$e^x \approx 1 + x +\frac{x^2}{2!} + \frac{x^3}{3!}$ The error comes from \textbf{neglecting} all the higher order terms -(\(\frac{x^4}{4!}, \frac{x^5}{5!}\), \ldots). +($\frac{x^4}{4!}, \frac{x^5}{5!}$), \ldots). Truncation error occurs when using numerical methods such as approximating and calculating derivatives and integrals. A @@ -57,7 +57,7 @@ algorithms. Round-off error is caused by \textbf{the limited precision} with which computers represent numbers. Since computers cannot store an infinite number of digits, \textbf{they round off} after a certain number of -decimal or binary places. For example, instead of representing π with +decimal or binary places. For example, instead of representing pi with infinite decimal places it may be rounded off to approximately 16 digits depending on number of bits and the representation of the bits. |