Advanced Engineering Mathematics, 10th Edition

APPENDIX 3

Auxiliary Material

A3.1 Formulas for Special Functions

For tables of numeric values, see Appendix 5.

Exponential function e^x (Fig. 545)

Natural logarithm (Fig. 546)

ln x is the inverse of e^x, and e^lnx = x, e^{−ln x} = e^ln (1/x) = 1/x.

Logarithm of base ten log₁₀x or simply log x

log x is the inverse of 10^x, and 10^logx = x, 10^{−log x} = 1/x.

Sine and cosine functions (Figs. 547, 548). In calculus, angles are measured in radians, so that sin x and cos x have period 2π.

sin x is odd, sin (−x) = −sin x, and cos x is even, cos (−x) = cos x.

Fig. 545. Exponential function e^x

Fig. 546. Natural logarithm ln x

Fig. 547. sin x

Fig. 548. cos x

Fig. 549. tan x

Fig. 550. cot x

Tangent, cotangent, ...