Understanding Engineering Mathematics

(i) 10 12 (ii) 36 9 (iii) 7 3 × 2 5 (iv) 14 15 ÷ 5 7 (v) 1 2 + 1 4 (vi) 1 3 − 1 7 (vii) 21 5 − 7 10 (viii) 1− 1 2 + 1 3 (ix) 3 5 ...

(i) 2^223 (ii) 3^4 /3^2 (iii) 6^3 × 32 /4 (iv) 6^22 −^232 (v) 2^2 × 4 × 25 (vi) 5^6 /10^4 (vii) 3^4223 −^1 (viii) 49× 7 / 212 B. ...

C.Write the following numbers in scientific notation stating the mantissa and exponent (i) 21.3241 (ii) 429.003 (iii) −0.000321 ...

Thereciprocalof the equivalent resistance of two resistors inparallelis equal to the sum of their reciprocals: 1 R = 1 R 1 + 1 R ...

(x) 18 9 improper fraction which can be cancelled down to lowest terms as an integer 2. (xi) 0.0 – decimal representation, to ...

(iv) 24= 23 ×3(v)− 72 =− 1 × 23 × 32 (vi) 81= 34 (vii) 2−^1 × 33 × 7 −^1 (viii) 11× 13 (ix) 17× 23 (x) 5× 41 B. (i) 11 (ii) 4 (i ...

D.(i) 9 2 (ii) 13 6 (iii) 2 5 (iv) 14 1.3.6 Factorial and combinatorial notation A. (i) 120 (ii) 3628800 (iii) 301 (iv) 220320 ( ...

(iv) − 39 125 (v) 17 100 C. Scientific Given Notation Mantissa Exponent (i) 21.3241 2. 13241 × 10 2.13241 1 (ii) 429.003 4. 2900 ...

2 Algebra In this chapter we review the basic principles of algebra in some detail and introduce some more advanced topics. Ther ...

further mathematical topics and techniques such as integration, coordinate geom- etry, Laplace transforms solving systems of li ...

2.1.6 Roots and factors of a polynomial ➤^5276 ➤➤ A.Referring to 2.1.2(iii), what are the (i)factors and (ii)roots of the polyno ...

2.1.12 Powers and indices for algebraic expressions ➤^7078 ➤➤ Simplify the following (i) a^2 c^4 a−^3 b^2 c (ii) ( 3 x)^3 ( 2 y) ...

Another important example is aquadratic expression inxsuch as 2x^2 + 7 x−4, of general form ax^2 +bx+c wherea,b,care again ‘cons ...

Two very important special cases of products of linear expressions are (a−b)(a+b)=a^2 −b^2 (a+b)^2 =a^2 + 2 ab+b^2 You should kn ...

2.2.2 Polynomials ➤ 38 74 ➤ Amonomialis an algebraic expression consisting of a single term, such as 3x, while a binomialconsist ...

This can only be true if eitherx− 1 =0orx− 2 =0, yielding two possible values ofx: x= 1 , 2 Such solutions of a polynomial equat ...

This is fine, but it is much quicker if you notice that pairing off one of the(x− 1 )factors with the(x+ 1 )givesx^2 −1 and: (x− ...

When factorising more complicated polynomials it pays to remember that this is not always possible. For example, we cannot facto ...

of brackets is good, then you’ll be able to do this mentally: (x− 1 )(x+ 2 )=x^2 +x− 2 × (x+ 1 )(x− 2 )=x^2 −x− 2 √ So the facto ...

2.2.4 Simultaneous equations ➤ 38 75 ➤ We will say more about solving equations in Section 13.5, but here we need to cover some ...