The Gaussian error function is defined as the following:
The Gaussian Error Function is used with semi-infinite solid analysis. The Gaussian Distribution (aka Normal Distribution) appears in heat transfer purely by coincidence. Shown in 7A - 2nd Class Notes the equation for the Gaussian distribution appears while preforming a similarity transformation. We end up needed to find the area under the distribution over some arbitrary bounds, as it happens an easy (non-calculus) way to find this area already exists in the form of the error function.
The complementary error is defined as the following function:
Table B.2 Gaussian Error Function from the textbook:
w |
erf w |
w |
erf w |
w |
erf w |
0.00 |
0.00000 |
0.36 |
0.38933 |
1.04 |
0.85865 |
0.02 |
0.02256 |
0.38 |
0.40901 |
1.08 |
0.87333 |
0.04 |
0.04511 |
0.40 |
0.42839 |
1.12 |
0.88679 |
0.06 |
0.06762 |
0.44 |
0.46622 |
1.16 |
0.89910 |
0.08 |
0.09008 |
0.48 |
0.50275 |
1.20 |
0.91031 |
0.10 |
0.11246 |
0.52 |
0.53790 |
1.30 |
0.93401 |
0.12 |
0.13476 |
0.56 |
0.57162 |
1.40 |
0.95228 |
0.14 |
0.15695 |
0.60 |
0.60386 |
1.50 |
0.96611 |
0.16 |
0.17901 |
0.64 |
0.63459 |
1.60 |
0.97635 |
0.18 |
0.20094 |
0.68 |
0.66378 |
1.70 |
0.98379 |
0.20 |
0.22270 |
0.72 |
0.69143 |
1.80 |
0.98909 |
0.22 |
0.24430 |
0.76 |
0.71754 |
1.90 |
0.99279 |
0.24 |
0.26570 |
0.80 |
0.74210 |
2.00 |
0.99532 |
0.26 |
0.28690 |
0.84 |
0.76514 |
2.20 |
0.99814 |
0.28 |
0.30788 |
0.88 |
0.78669 |
2.40 |
0.99931 |
0.30 |
0.32863 |
0.92 |
0.80677 |
2.60 |
0.99976 |
0.32 |
0.34913 |
0.96 |
0.82542 |
2.80 |
0.99992 |
0.34 |
0.36936 |
1.00 |
0.84270 |
3.00 |
0.99998 |