Mathematics for Physicists

Answers to selected problems

Problems 1

 1.1 (a) p = 124.68; (b) q = 400; (c) r = 0.04.

 1.2 (a) 756 = 2²3³7; (b) .

 1.3 (a) p = 1.246 × 10³; (b) − 1.57 × 10³; (c) 4.5 × 10^{− 3}.

 1.5 (a) 2^5/23^11/12; (b) 3^{− 1/6}5^12/5; (c) 7^7/32^{− 1/2}.

 1.6 (a) (b)

*1.7 (a) 10.31 = 1010.0101₂…; (b) 1101.01₂ = 13.25.

*1.8 (a) p × q = 32130₄; (b) (p − q) = 11₄.

 1.9 (a) ; (b) ; (c) 3^5/6a^{− 5/3}.

1.10 (a) identity; (b) equation.

1.11 (a) − 1 < x < 4; (b) − 4 < x < −2 or 2 < x < 4; (c) x > −2 or x < −4.

1.12 31.681.

1.13 − 9828a³b¹¹.

1.17 (a) (b) (c) x = y⁶ + 2.

1.18 

1.19 (a) (b) f^{− 1}(x) = 27x³ − 4.

1.20 (a) ...