Saturday, July 6, 2019

Understanding Engineering Mathematics (Free PDF)

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This book contains most of the material covered in a typical first year mathematics course in an engineering or science programme. It devotes Chapters 1–10 to consolidating the foundations of basic algebra, elementary functions and calculus. Chapters 11–17 cover the range of more advanced topics that are normally treated in the first year, such as vectors and matrices, differential equations, partial differentiation and transform methods.

With widening participation in higher education, broader school curricula and the wide range of engineering programmes available, the challenges for both teachers and learners in engineering mathematics are now considerable. As a result, a substantial part of many first year engineering programmes is dedicated to consolidation of the basic mathematics material covered at pre-university level. However, individual students have widely varying backgrounds in mathematics and it is difficult for a single mathematics course to address everyone’s needs. This book is designed to help with this by covering the basics in a way that enables students and teachers to quickly identify the strengths and weaknesses of individual students and ‘top up’ where necessary. The structure of the book is therefore somewhat different to the conventional textbook, and ‘To the student’ provides some suggestions on how to use it.

Throughout, emphasis is on the key mathematical techniques, covered largely in isolation from the applications to avoid cluttering up the explanations. When you teach someone to drive it is best to find a quiet road somewhere for them to learn the basic techniques before launching them out onto the High Street! In this book the mathematical techniques are motivated by explaining where you may need them, and each chapter has a short section giving typical applications. More motivational material will also be available on the book web-site. Rigorous proof for its own sake is avoided, but most things are explained sufficiently to give an understanding that the educated engineer should appreciate. Even though you may use mathematics as a tool, it usually helps to have an idea of how and why the tool works.

To the Student
1. Number and Arithmetic
2. Algebra
3. Functions and Series
4. Exponential and Logarithm Functions
5. Geometry of Lines, Triangles and Circles
6. Trigonometry
7. Coordinate Geometry
8. Techniques of Differentiation
9. Techniques of Integration
10. Applications of Differentiation and Integration
11. Vectors
12. Complex Numbers
13. Matrices and Determinants
14. Analysis for Engineers – Limits, Sequences, Iteration, Series and All That
15. Ordinary Differential Equations
16. Functions of More than One Variable – Partial Differentiation
17. An Appreciation of Transform Methods

Author Details
"Bill Cox"

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