Page 169 - Essentials of applied mathematics for scientists and engineers

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Appendix A: The Roots of Certain

Transcendental Equations

TABLE A.1: The first six roots, † α n ,of

α tan α + C = 0.
C α 1 α 2 α 3 α 4 α 5 α 6

0 0 3.1416 6.2832 9.4248 12.5664 15.7080
0.001 0.0316 3.1419 6.2833 9.4249 12.5665 15.7080
0.002 0.0447 3.1422 6.2835 9.4250 12.5665 15.7081
0.004 0.0632 3.1429 6.2838 9.4252 12.5667 15.7082
0.006 0.0774 3.1435 6.2841 9.4254 12.5668 15.7083

0.008 0.0893 3.1441 6.2845 9.4256 12.5670 15.7085
0.01 0.0998 3.1448 6.2848 9.4258 12.5672 15.7086
0.02 0.1410 3.1479 6.2864 9.4269 12.5680 15.7092
0.04 0.1987 3.1543 6.2895 9.4290 12.5696 15.7105

0.06 0.2425 3.1606 6.2927 9.4311 12.5711 15.7118
0.08 0.2791 3.1668 6.2959 9.4333 12.5727 15.7131
0.1 0.3111 3.1731 6.2991 9.4354 12.5743 15.7143
0.2 0.4328 3.2039 6.3148 9.4459 12.5823 15.7207

0.3 0.5218 3.2341 6.3305 9.4565 12.5902 15.7270
0.4 0.5932 3.2636 6.3461 9.4670 12.5981 15.7334
0.5 0.6533 3.2923 6.3616 9.4775 12.6060 15.7397
0.6 0.7051 3.3204 6.3770 9.4879 12.6139 15.7460

0.7 0.7506 3.3477 6.3923 9.4983 12.6218 15.7524
0.8 0.7910 3.3744 6.4074 9’5087 12.6296 15.7587