Advanced Construction Mathematics

Surinder Virdi

• Publisher: Routledge
• Year: 2019
• eBook ISBN: 9780429683602
• Edition: 1
• Topic: Mathematics
• Subtopic: Arithmetic
• Index: Mathematics

Advanced Construction Mathematics covers the range of topics that a student must learn in order to achieve success in Level 3 and 4 mathematics for the Pearson BTEC National and BTEC HNC/HND in Construction, Building Services, and Civil Engineering.

Packed with easy to follow examples, its 18 chapters cover algebra (equations, transposition and evaluation of formulae), differentiation, integration, statistics and numerous other core concepts and their application in the construction/civil engineering field. The book explains technical processes before applying mathematical techniques to solve practical problems which gradually build in complexity. Each chapter contains self-test exercises and answers and numerous illustrations to simplify the essential maths required at Levels 3 and 4. The book is also a useful recap or primer for students on BSc or non-cognate MSc Construction and Civil Engineering degrees.

CHAPTER 1

Introduction to some basic techniques

Topics covered in this chapter:

• Order of operations, rounding off numbers: rounding off numbers to the nearest whole number, truncation, significant figures, decimal places

• Estimation of answers, absolute and relative errors

• Indices

1.1 Introduction

In this chapter some of the basic techniques are explained. Most of these do not involve any complexity, but it is very important to solve a number of problems and to show the answer in an acceptable format.

1.2 Order of operations

In mathematics and other analytical subjects, the calculations may involve one or more of:

multiplication, division, addition, subtraction and brackets.

There is a definite order of operations in algebra that needs to be followed to get accurate solutions. For example, in the following calculation, the answers could be 51, 13 or 19:

Evaluate: 20 − 4 + 1 × 3

The correct answer is 19, which results from following the right procedure. This procedure, known as the order of precedence of operations, involves dealing with brackets (B) first and then of (O), division (D), multiplication (M), addition (A), subtraction (S), in that order. This is usually remembered as BODMAS.

In the above example, 20 − 4 + (1 × 3) = 20 − 4 + 3 = 20 − 1 = 19 (−4 + 3 = −1)

Example 1.1

Solve: a) 16 + 5 − 2 × 1.5

b) 20 − 2 + (2 × 3)

c) 25 + 5 − 3(1.5 × 4) − 3 × 2

Solution:

a) 16 + 5 − 2 × 1.5 = 16 + 5 − 3 = 21 − 3 = 18

b) 20 − 2 + (2 × 3) = 20 − 2 + 6 = 20 + 4 = 24 (−2 + 6 = + 4)

c) 25 + 5 − 3(1.5 × 4) − 3 × 2 = 25 + 5 − 3(6) − 6 = 25 + 5 − 18 − 6

= 30 − 18 − 6 = 6

1.3 Rounding

1.3.1 To the nearest whole number

The convention is to round 0.5 and above to the next highest whole number, and 0.499 (recurring) to the next lowest whole number. For example, 8.5 will become 9.0 when rounded to the nearest whole number. Similarly, 8.499 will become 8.0 when rounded to the nearest whole number.

1.3.2 Truncation

Truncation involves the omission of the unwanted digits at the end of a number. For example, 25.3458 truncated to four figures becomes 25.34.

1.3.3 Significant figures

3462, 346200 and 0.03462 all have four significant figures, not counting zeros at the beginning or end of the number. To write these numbers to 3 significant figures, the last figur...

Table of contents

• Cover Page
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Units, Symbols and Prefixes
• Preface
• 1 Introduction to Some Basic Techniques
• 2 Algebra 1
• 3 Algebra 2
• 4 Simultaneous and Quadratic Equations
• 5 Graphical Solutions
• 6 Geometry, Areas and Volumes
• 7 Trigonometry 1
• 8 Trigonometry 2
• 9 Logarithmic, Exponential and Hyperbolic Functions
• 10 Differentiation
• 11 Applications of Differentiation
• 12 Integration
• 13 Applications of integration
• 14 Properties of Sections
• 15 Matrices and Determinants
• 16 Vectors
• 17 Statistics
• 18 Computer Techniques
• End of Unit Assignment
• Appendix 1
• Appendix 2
• Appendix 3
• Index