INFORMATION I. Algebraic Identities 2 2 2 3 3 2 2 3 (a+b) = a +2ab+b (a +b) = a + 3a b + 3ab +b 2 2 2 3 3 2 2 3 (a -b) = a -2ab +b (a -b) = a -3a b + 3ab -b 4 4 3 2 2 3 4 (a + b) = a + 4a b + 6a b + 4ab + b 4 4 3 2 2 3 4 (a -b) = a -4a b + 6a b -4ab + b 2 3 3 2 2 2 a-b = (a -b)(a +b) a -b = (a -b)(a +ab +b ) 3 3 2 2 a +b = (a+b)(a -ab+b ) II. Trigonometrical Identities 2 2 2 2 (1) sin 0 + cos 0 = 1; sec 0 = 1 + tan 0; 2 2 cosec 0 = 1 + cot 0 (2) sin (A + B) = sin A cos B + cos A sin B sin (A - B) = sin A cos B -cos A sin B cos (A + B) = cos A cos B -sin A sin B cos (A - B) = cos A cos B + sin A sin B tanA+tanB tan(A+B) 1-tanA tanB tanA-tanB tan(A -B) = 1 + tanA tan B (3) Let A = B = 0.: .
A must-have to understand applications with minimal theory and no proofs. Continues from where the first volume ends with more advanced topics including optimization processes and advanced differential calculus. Really for engineers, but physicists and pure mathematicians that are starting out as first-year undergrads will gain a lot by working through the exercises as they begin from the fundamentals to the most challenging, in a step-by-step build up. Brilliant.