Basic Engineering Mathematics 5th Edition introduces and then consolidates basic mathematical principles and promotes awareness of mathematical concepts for students needing a broad base for further vocational studies.

In this fifth edition, new material has been added to many of the chapters, particularly some of the earlier chapters, together with extra practice problems interspersed throughout the text. The extent of this fifth edition is such that four chapters from the previous edition have been removed and placed on the easily available website.

Contents

1. Basic arithmetic

• Introduction
• Revision of addition and subtraction
• Revision of multiplication and division
• Highest common factors and lowest common multiples
• Order of precedence and brackets

2. Fractions

• Introduction
• Multiplication and division of fractions
• Order of precedence with fractions

Revision Test 1

3. Decimals

• Introduction
• Converting decimals to fractions and vice-versa
• Significant figures and decimal places
• Adding and subtracting decimal numbers
• Multiplying and dividing decimal numbers

4. Using a calculator

• Introduction
• Adding, subtracting, multiplying and dividing
• Further calculator functions
• Evaluation of formulae

5. Percentages

• Introduction
• Percentage calculations
• Further percentage calculations
• More percentage calculations

Revision Test 2

6. Ratio and proportion

• Introduction
• Ratios
• Direct proportion
• Inverse proportion

7. Powers, roots, and laws of indices

• Introduction
• Powers and roots
• Laws of indies

8. Units, prefixes, and engineering notation

• Introduction
• SI units
• Common prefixes
• Standard form
• Engineering notation

Revision Test 3

9. Basic algebra

• Introduction
• Basic operations
• Laws of indices

10. Further algebra

• Introduction
• Brackets
• Factorization
• Laws of precedence

11. Solving simple equations

• Introduction
• Solving equations
• Practical problems involving simple equations

Revision Test 4

• Transposing formulae
• Introduction
• Transposing formulae
• Further transposing of formulae
• More difficult transposing of formulae

13. Solving simultaneous equations

• Introduction
• Solving simultaneous equations in two unknowns
• Further solving of simultaneous equations
• Solving more difficult simultaneous equations
• Practical problems involving simultaneous equations
• Solving simultaneous equations in three unknowns

Revision Test 5

• Introduction
• A solution of quadratic equations by factorization
• The solution of quadratic equations by ‘completing the square’
• A solution of quadratic equations by formula
• Practical problems involving quadratic equations
• A solution of linear and quadratic equations simultaneously

15. Logarithms

• Introduction to logarithms
• Laws of logarithms
• Indicial equations
• Graphs of logarithmic functions

16. Exponential functions

• Introduction to exponential functions
• The power series for e
• Graphs of exponential functions
• Napierian logarithms
• Laws of growth and decay

Revision Test 6

17. Straight line graphs

• Introduction to graphs
• Axes, scales, and co-ordinates
• Straight-line graphs
• Gradients, intercepts, and equations of graphs
• Practical problems involving straight line graphs

18. Graphs reducing non-linear laws to linear form

• Introduction
• Determination of law
• Revision of laws of logarithms
• Determination of law involving logarithms

19. Graphical solution of equations

• Simultaneous equations
• Linear and quadratic equations simultaneously
• Cubic equations

Revision Test 7

20. Angles and triangles

• Introduction
• Angular measurement
• Triangles
• Congruent triangles
• Similar triangles
• Construction of triangles

21. Introduction to trigonometry

• Introduction
• The theorem of Pythagoras
• Sines, cosines, and tangents
• Evaluating trigonometric ratios of acute angles
• Solving right-angled triangles
• Angles of elevation and depression

Revision Test 8

22 Trigonometric waveforms

• Graphs of trigonometric functions
• Angles of any magnitude
• The production of sine and cosine waves
• The terminology involved with sine and cosine waves
• Sinusoidal form: Asin(ωt ±α)

23. Non-right-angled triangles and some practical applications

• The sine and cosine rules
• Area of any triangle
• Worked problems on the solution of triangles and their areas
• Further worked problems on the solution of triangles and their areas
• Practical situations involving trigonometry
• Further practical situations involving trigonometry

24. Cartesian and polar coordinates

• Introduction
• Changing from Cartesian to polar coordinates
• Changing from polar to Cartesian coordinates
• Use of Pol/Rec functions on calculators

Basic Engineering Mathematics 5th Edition provides a lead into Engineering Mathematics 6th Edition. Each topic considered in the text is presented in the way that assumes in the reader little previous knowledge of that topic. Each chapter begins with a brief outline of essential theory, definitions, formulae, laws, and procedures; however, these are kept to a minimum as problem-solving is extensively used to establish and exemplify the theory.

It is intended that readers will gain real understanding through seeing problems solved and then solving similar problems themselves.

This textbook contains some 750 worked problems, followed by over 1550 further problems (all with answers at the end of the book) contained within some 161 Practice Exercises; each Practice Exercise follows on directly from the relevant section of work. In addition, 376 line diagrams enhance an understanding of the theory. Where at all possible, the problems mirror potential practical situations found in engineering and science.

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