Modern Engineering Mathematics

Glyn James was most recently Emeritus Professor in Mathematics at Coventry University and was previously Dean of the School of Mathematical and Information Sciences at Coventry University. He had an active interest in mathematics education and was a past chairman of the Education Committee of the Institute of Mathematics and its Applications, and a member of the Royal Society Mathematics Education Subcommittee. In 1995 he was chairman of the Working Group that produced the report Mathematics Matters in Engineering on behalf of UK professional bodies in engineering and mathematics. He also co-edited five mathematics books and was a member of the advisory boards for three international journals. Sadly, Glyn James passed away in October 2019 during the production of this edition; his enthusiastic input was sorely missed, but this and its companion text Advanced Modern Engineering Mathematics remain a fitting legacy. Phil Dyke is Professor of Applied Mathematics at the University of Plymouth. He was a Head of School for 22 years, 18 of these as Head of Mathematics and Statistics. He has over 45 years' teaching and research experience in Higher Education, much of this teaching engineering students not only mathematics but also marine and coastal engineering. Apart from his contributions to both Modern Engineering Mathematics and Advanced Modern Engineering Mathematics he is the author of 11 other textbooks ranging in topic from advanced calculus, Laplace transforms and Fourier series to mechanics and marine physics. He is now semi-retired, but still teaches, is involved in research, and writes. He is a Fellow of the Institute of Mathematics and its Applications. Matthew Craven is a Lecturer in Applied Mathematics at the University of Plymouth. For fifteen years, he has taught foundation year courses, postgraduate courses and everything in between. He is also part of the author team for the 5th edition of the companion text, Advanced Modern Engineering Mathematics. He has research interests in computational simulation, real-world operational research, high performance computing and optimisation. Yinghui Wei is an Associate Professor of Statistics at the University of Plymouth. She has taught probability and statistics modules for mathematics programmes as well as for programmes in other subject areas, including engineering, business and medicine. She has broad research interests in statistical modelling, data analysis and evidence synthesis. John Searl was Director of the Edinburgh Centre for Mathematical Education at the University of Edinburgh before his retirement. As well as lecturing on mathematical education, he taught service courses for engineers and scientists. His most recent research concerned the development of learning environments that make for the effective learning of mathematics for 16 - 20 year olds. As an applied mathematician he worked collaboratively with (amongst others) engineers, physicists, biologists and pharmacologists, and he is keen to develop problem-solving skills of students and to provide them with opportunities to display their mathematical knowledge within a variety of practical contexts. The contexts develop the extended reasoning needed in all fields of engineering.

Preface xxii

About the authors xxv

Publishers acknowledgements xxvii

Chapter 1    Number, Algebra and Geometry

Chapter 2 Functions

Chapter 3    Complex Numbers

Chapter 4    Vector Algebra

Chapter 5    Matrix Algebra

Chapter 6    An Introduction to Discrete Mathematics

Chapter 7    Sequences, Series and Limits

Chapter 8    Differentiation and Integration

Chapter 9    Further Calculus

Chapter 10 Introduction to Ordinary Differential Equations

Chapter 11 Introduction to Laplace Transforms

Chapter 12 Introduction to Fourier Series

Chapter 13 Data Handling and Probability Theory

Appendix I Tables

Answers to Exercises

Index