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# Learn Maths A and Maths B with Mathematics for Technicians by Blair Alldis

## Mathematics for Technicians by Blair Alldis: A Comprehensive Guide for Engineering Students

If you are an engineering student who wants to master the basic mathematics required for your course, you might be interested in Mathematics for Technicians by Blair Alldis. This book is a thorough and practical guide that covers the learning outcomes for Maths A and Maths B, as well as providing additional theory and exercises on a CD. In this article, we will review what Mathematics for Technicians is, how to use it effectively, what are some key topics and concepts covered in it, and how to apply it to real-world engineering problems.

## What is Mathematics for Technicians?

Mathematics for Technicians is a textbook that provides a solid foundation in the essential mathematics needed for engineering courses across the board. It was written by Blair Alldis, a former head teacher of mathematics at Randwick College of TAFE, who has more than 35 years of experience in teaching mathematics, physics and chemistry in schools and TAFE. The book was first published in 2003 by McGraw-Hill Education, and has been revised and updated several times since then.

### The purpose and scope of the book

The main purpose of Mathematics for Technicians is to help engineering students develop their mathematical skills and confidence, as well as prepare them for further studies or employment in engineering fields. The book follows the requirements of the new Engineering Maths Training Package, which specifies the learning outcomes for Maths A (basic mathematics) and Maths B (applied mathematics). The book covers both Maths A and Maths B in a single volume, making it convenient and cost-effective for students.

### The structure and content of the book

The book is divided into four parts, each consisting of several chapters that cover different mathematical topics. The four parts are:

• Part 1: Basic Algebra (Chapters 1-5)

• Part 2: Trigonometry (Chapters 6-9)

• Part 3: Calculus (Chapters 10-14)

• Part 4: Statistics (Chapters 15-18)

Each chapter begins with an introduction that outlines the objectives, key terms, formulas and concepts of the topic. Then, it provides clear theoretical explanations with practical examples that illustrate how to apply the theory to engineering problems. Next, it offers a bank of exercises for each section that allow students to practice their skills and test their understanding. Finally, it ends with a summary that reviews the main points of the chapter.

### The features and benefits of the book

Mathematics for Technicians has several features that make it a valuable and user-friendly resource for engineering students. Some of these features are:

• A free CD that comes with each book. The CD contains extra exercises and some extended theory for extra clarification of some concepts. An icon appears in the text, providing a link to the CD content. Answers to all the exercises and self-test problems are included on the CD.

• A conversational and informal style of writing that engages the reader and makes the material easy to follow and understand.

• A focus on both class teaching and self-paced learning, allowing students to learn at their own speed and level of difficulty.

• A comprehensive coverage of the essential mathematics for engineering courses, as well as some advanced topics for further exploration.

• A variety of examples and applications from different engineering fields, such as mechanical, electrical, civil, chemical and biomedical engineering.

• A rigorous and logical approach to mathematical concepts and methods, with an emphasis on problem-solving and critical thinking skills.

## How to use Mathematics for Technicians effectively?

Mathematics for Technicians is designed to help engineering students achieve their learning outcomes and improve their mathematical abilities. However, to get the most out of the book, students need to use it effectively and efficiently. Here are some tips and strategies for using Mathematics for Technicians successfully:

### The prerequisites and learning outcomes for Maths A and Maths B

Before starting to use Mathematics for Technicians, students should have a basic knowledge of arithmetic, fractions, decimals, percentages, powers and roots. These topics are covered in Chapter 1 of the book, but students are advised to review them beforehand if they are not confident with them. Students should also be familiar with the use of a scientific calculator, as it is an essential tool for solving many engineering problems.

Students should also be aware of the learning outcomes for Maths A and Maths B, as they are the main goals of using Mathematics for Technicians. The learning outcomes for Maths A are:

• Perform calculations involving fractions, decimals, percentages, ratios and proportions.

• Manipulate algebraic expressions and solve linear equations.

• Use graphs to represent linear functions and interpret their features.

• Apply Pythagoras' theorem and trigonometry to right-angled triangles.

• Solve problems involving angles, polygons, circles and sectors.

The learning outcomes for Maths B are:

• Solve simultaneous linear equations using matrices and determinants.

• Use trigonometry to solve problems involving oblique triangles and vectors.

• Differentiate and integrate polynomial functions using basic rules.

• Solve simple differential equations using separation of variables.

• Use statistics to describe data sets, calculate probabilities and perform hypothesis testing.

Students should aim to achieve these learning outcomes by the end of using Mathematics for Technicians, as they will prepare them for further studies or employment in engineering fields.

### The tips and strategies for self-paced learning and revision

Mathematics for Technicians is suitable for both class teaching and self-paced learning, depending on the preferences and needs of the students. However, self-paced learning requires more discipline and motivation from the students, as they have to set their own goals and pace. Here are some tips and strategies for self-paced learning and revision using Mathematics for Technicians:

• Plan a realistic schedule that allows enough time for studying each chapter, doing the exercises, reviewing the summary and taking the self-test. Try to stick to the schedule as much as possible, but be flexible if necessary.

• Read each chapter carefully and try to understand the theory before attempting the examples. Use the CD or online resources if you need more clarification or help with some concepts.

• Do the exercises after each section to practice your skills and check your understanding. Compare your answers with those on the CD or online. If you get stuck or make a mistake, try to find out why and how to fix it.

• Review the summary at the end of each chapter to refresh your memory of the main points. Try to recall or write down the key terms, formulas and concepts without looking at the book.

• Take the self-test at the end of each chapter to assess your progress and identify your strengths and weaknesses. Use the CD or online resources to check your answers and explanations. If you score below 80%, you may need to revise some parts of the chapter again.

• Repeat this process for each chapter until you finish the book. Then, review the whole book again before taking a final test or exam.

## What are some key topics and concepts covered in Mathematics for Technicians?

Mathematics for Technicians covers a wide range of topics and concepts that are essential for engineering students. Some of these topics and concepts are:

### Algebra and equations

Algebra is the branch of mathematics that deals with symbols and rules for manipulating them. Equations are statements that express the equality of two algebraic expressions. In Mathematics for Technicians, students will learn how to:

• Perform calculations involving fractions, decimals, percentages, ratios and proportions.

• Manipulate algebraic expressions using the laws of indices, surds, logarithms and exponentials.

• Solve linear equations, quadratic equations, simultaneous equations and inequalities.

• Use graphs to represent linear functions and interpret their features, such as slope, intercepts and roots.

• Use matrices and determinants to solve systems of linear equations.

These skills are important for engineering students because they enable them to model and solve various engineering problems using algebraic methods.

### Trigonometry and vectors

Trigonometry is the branch of mathematics that deals with the relationships between angles and sides of triangles. Vectors are quantities that have both magnitude and direction. In Mathematics for Technicians, students will learn how to:

• Use Pythagoras' theorem and trigonometric ratios to solve problems involving right-angled triangles.

• Use the sine rule, the cosine rule and the area rule to solve problems involving oblique triangles.

• Use radians and degrees to measure angles and convert between them.

• Use trigonometric identities and formulas to simplify and manipulate trigonometric expressions.

• Add, subtract, multiply and divide vectors using graphical and algebraic methods.

• Use vectors to represent forces, velocities, displacements and other physical quantities.

These skills are important for engineering students because they enable them to analyze and design various engineering systems using trigonometry and vector methods.

### Calculus and differential equations

Calculus is the branch of mathematics that deals with rates of change and areas under curves. Differential equations are equations that involve derivatives of unknown functions. In Mathematics for Technicians, students will learn how to:

• Differentiate polynomial functions using basic rules, such as the power rule, the product rule, the quotient rule and the chain rule.

• Integrate polynomial functions using basic rules, such as the reverse power rule, the sum rule, the difference rule and the substitution rule.

• Use differentiation and integration to determine the rate of change, turning points, maximum, minimum and optimum values of functions.

• Solve simple differential equations using separation of variables.

• Use calculus to model and solve various engineering problems involving motion, growth, decay, optimization and more.

These skills are important for engineering students because they enable them to understand and apply the principles of calculus and differential equations to various engineering problems.

### Statistics and probability

Statistics is the branch of mathematics that deals with collecting, organizing, analyzing and interpreting data. Probability is the branch of mathematics that deals with measuring the likelihood of events. In Mathematics for Technicians, students will learn how to:

• Use statistics to describe data sets using measures of central tendency (mean, median, mode) and measures of dispersion (range, standard deviation).

• Use graphs and charts to display data visually using histograms, frequency polygons, box plots and more.

• Use probability to calculate the chances of events occurring using rules of addition, multiplication and conditional probability.

• Use probability distributions to model random phenomena using binomial distribution, normal distribution and more.

## How to apply Mathematics for Technicians to real-world engineering problems?

Mathematics for Technicians is not only a theoretical book, but also a practical one. It shows how to apply the mathematical concepts and methods learned in the book to real-world engineering problems. Some of these problems are:

### The examples and applications from various engineering fields

The book provides numerous examples and applications from different engineering fields, such as mechanical, electrical, civil, chemical and biomedical engineering. These examples and applications illustrate how to use mathematics to model, analyze and design various engineering systems and processes. For instance, some of the examples and applications are:

• Using algebra and equations to calculate the power output of a wind turbine.

• Using trigonometry and vectors to determine the resultant force and direction of a crane.

• Using calculus and differential equations to model the motion of a car on a curved road.

• Using statistics and probability to perform quality control and hypothesis testing for a manufacturing process.

These examples and applications help students to see the relevance and usefulness of mathematics for engineering practice.

### The exercises and problems for practice and assessment

The book also provides a large number of exercises and problems for students to practice their skills and assess their progress. The exercises are divided into two types: review exercises and application exercises. The review exercises are designed to reinforce the theory and concepts learned in each chapter. The application exercises are designed to apply the theory and concepts to real-world engineering problems. The exercises are graded according to their level of difficulty: easy, moderate or hard. The answers to all the exercises are provided on the CD or online.

### The solutions and explanations on the CD and online

The book comes with a free CD that contains extra exercises, extended theory, solutions and explanations for all the exercises and self-test problems in the book. The CD also contains links to online resources that provide additional support and guidance for students. These resources include:

• Tutorials that explain how to use MINITAB, R and JMP software for statistical analysis.

• Videos that demonstrate how to solve some of the application exercises using mathematical software.

• Quizzes that test students' knowledge and understanding of each chapter.

• Case studies that present real-world engineering scenarios that require mathematical solutions.

These resources help students to enhance their learning experience and outcomes using Mathematics for Technicians.

## Conclusion

In conclusion, Mathematics for Technicians by Blair Alldis is a comprehensive and practical guide for engineering students who want to master the basic mathematics required for their course. The book covers the learning outcomes for Maths A and Maths B, as well as providing additional theory and exercises on a CD. The book also shows how to apply mathematics to real-world engineering problems using examples, applications, exercises and online resources. Mathematics for Technicians is an ideal textbook for undergraduate or graduate level engineering students who want to improve their mathematical skills and confidence.

### A summary of the main points and benefits of Mathematics for Technicians

To summarize, here are some of the main points and benefits of Mathematics for Technicians:

• It provides a thorough grounding in the essential mathematics needed for engineering courses across the board.

### FAQs

Question

Who is the author of Mathematics for Technicians?

The author of Mathematics for Technicians is Blair Alldis, a former head teacher of mathematics at Randwick College of TAFE, who has more than 35 years of experience in teaching mathematics, physics and chemistry in schools and TAFE.

What are the prerequisites for using Mathematics for Technicians?

The prerequisites for using Mathematics for Technicians are a basic knowledge of arithmetic, fractions, decimals, percentages, powers and roots, and a familiarity with the use of a scientific calculator.

What are the learning outcomes for Maths A and Maths B?

The learning outcomes for Maths A and Maths B are the essential mathematical skills and knowledge required for engineering courses across the board. They are specified by the new Engineering Maths Training Package.

What are the features and benefits of Mathematics for Technicians?

Some of the features and benefits of Mathematics for Technicians are: a free CD that contains extra exercises and some extended theory; a conversational and informal style of writing; a focus on both class teaching and self-paced learning; a comprehensive coverage of the essential mathematics for engineering courses; a variety of examples and applications from different engineering fields; a rigorous and logical approach to mathematical concepts and methods; and online resources that provide additional support and guidance.

How to use Mathematics for Technicians effectively?

Some tips and strategies for using Mathematics for Technicians effectively are: plan a realistic schedule that allows enough time for studying each chapter, doing the exercises, reviewing the summary and taking the self-test; read each chapter carefully and try to understand the theory before attempting the examples; do the exercises after each section to practice your skills and check your understanding; review the summary at the end of each chapter to refresh your memory of the main points; take the self-test at the end of each chapter to assess your progress and identify your strengths and weaknesses; repeat this process for each chapter until you finish the book; review the whole book again before taking a final test or exam.

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