Students today enter engineering courses with a wide range of mathematical skills, due to the many different pre-university qualifications studied. Bill Cox's aim is for students to gain a thorough understanding of the maths they are studying, by first strengthening their background in the essentials of each topic. His approach allows a unique self-paced study style, in which students Review their strengths and weaknesses through self-administered diagnostic tests, then focus on Revision where they need it, to finally Reinforce the skills required. Understanding Engineering Mathematics is structured around a highly successful 'transition' maths course at Aston University which has demonstrated a clear improvement in students' achievement in mathematics, and has been commended by QAA Subject Review and engineering accreditation reports. A core undergraduate text with a unique interactive style that enables students to diagnose their strengths and weaknesses and focus their efforts where needed Ideal for self-paced self-study and tutorial work, building from an initially supportive approach to the development of independent learning skills Lots of targeted examples and exercises
Studying engineering, whether it is mechanical, electrical or civil relies heavily on an understanding of mathematics. This new textbook clearly demonstrates the relevance of mathematical principles and shows how to apply them to solve real-life engineering problems. It deliberately starts at an elementary level so that students who are starting from a low knowledge base will be able to quickly get up to the level required. Students who have not studied mathematics for some time will find this an excellent refresher. Each chapter starts with the basics before gently increasing in complexity. A full outline of essential definitions, formulae, laws and procedures are introduced before real world situations, practicals and problem solving demonstrate how the theory is applied. Focusing on learning through practice, it contains examples, supported by 1,600 worked problems and 3,000 further problems contained within exercises throughout the text. In addition, 34 revision tests are included at regular intervals. An interactive companion website is also provided containing 2,750 further problems with worked solutions and instructor materials
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. As the book progresses through the more advanced first year material there is an increasing expectation on the student to learn independently and ‘fill in the gaps’ for themselves – possibly with the teacher’s help. This is designed to help the student to develop a mature, self-disciplined approach as they move from the supportive environment of pre-university to the more independent university environment. In addition the book web-site (www.bh.com/companions/0750650982) will provide a developing resource to supplement the book and to focus on specific engineering disciplines where appropriate. In the years that this book has been in development I have benefited from advice and help from too many people to list. The following deserve special mention however. Dave Hatter for having faith in the original idea and combining drink and incisive comment well mixed in the local pub. Peter Jack for many useful discussions and for the best part of the S(ketch) GRAPH acronym (I just supplied the humps and hollows). Val Tyas for typing ix P r e f a c e much of the manuscript, exploring the limits of RSI in the process, and coping cheerfully with my continual changes. The late Lynn Burton for initial work on the manuscript and diagrams. She was still fiddling with the diagrams only weeks before she succumbed to cancer after a long and spirited fight. I am especially indebted to her for her friendship and inspiration – she would chuckle at that. I also benefited from an anonymous reviewer who went far beyond the call of duty in providing meticulous, invaluable comment – It’s clear that (s)he is a good teacher. Of course, any remaining errors are my responsibility. The team at Butterworth-Heinemann did a wonderful job in dealing with a complicated manuscript – sense of humour essential! Last but not least I must mention the hundreds of students who have kept me in line over the years. I have tried to write the book that would help most of them. I hope they, and their successors, will be pleased with it. Bill Cox, June 2001
Mathematics is, by its very nature, an abstract discipline. However, many students learn best by thinking in terms of tangible constructs. Enhancing Mathematics Understanding through Visualization: The Role of Dynamical Software brings these conflicting viewpoints together by offering visual representations as a method of mathematics instruction. The book explores the role of technology in providing access to multiple representations of concepts, using software applications to create a rich environment in which a students understanding of mathematical concepts can flourish. Both students and instructors of mathematics at the university level will use this book to implement various novel techniques for the delivery of mathematical concepts in their classrooms. This book is part of the Research Essential collection.
Mathematical Understanding of Chemical Engineering Systems is a collection of articles that covers the mathematical model involved in the practice of chemical engineering. The materials of the book are organized thematically into section. The text first covers the historical development of chemical engineering, and then proceeds to tackling a much more technical and specialized topics in the subsequent sections. The second section talks about the physical separation process, while the third section deals with stirred tank stability and control. Next, the book tackles polymerization and particle problems. Section 6 discusses empty tubular and fixed-bed catalytic reactors, while Section 7 details fluid-bed reactors and coal combustion. In the last two sections, the text presents mathematical and miscellaneous papers. The book will be most useful to researchers and practitioners of chemical engineering. Mathematicians and chemists will also benefit from the text.
Building on the foundations laid in the companion text Modern Engineering Mathematics, this book gives an extensive treatment of some of the advanced areas of mathematics that have applications in various fields of engineering, particularly as tools for computer-based system modelling, analysis and design. The philosophy of learning by doing helps students develop the ability to use mathematics with understanding to solve engineering problems. A wealth of engineering examples and the integration of MATLAB and MAPLE further support students.
Engineers require a solid knowledge of the relationship between engineering applications and underlying mathematical theory. However, most books do not present sufficient theory, or they do not fully explain its importance and relevance in understanding those applications. Advanced Engineering Mathematics with Modeling Applications employs a balanced approach to address this informational void, providing a solid comprehension of mathematical theory that will enhance understanding of applications – and vice versa. With a focus on modeling, this book illustrates why mathematical methods work, when they apply, and what their limitations are. Designed specifically for use in graduate-level courses, this book: Emphasizes mathematical modeling, dimensional analysis, scaling, and their application to macroscale and nanoscale problems Explores eigenvalue problems for discrete and continuous systems and many applications Develops and applies approximate methods, such as Rayleigh-Ritz and finite element methods Presents applications that use contemporary research in areas such as nanotechnology Apply the Same Theory to Vastly Different Physical Problems Presenting mathematical theory at an understandable level, this text explores topics from real and functional analysis, such as vector spaces, inner products, norms, and linear operators, to formulate mathematical models of engineering problems for both discrete and continuous systems. The author presents theorems and proofs, but without the full detail found in mathematical books, so that development of the theory does not obscure its application to engineering problems. He applies principles and theorems of linear algebra to derive solutions, including proofs of theorems when they are instructive. Tying mathematical theory to applications, this book provides engineering students with a strong foundation in mathematical terminology and methods.
Introductory mathematics written specifically for students new to engineering Now in its sixth edition, Basic Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams. John Bird's approach is based on worked examples and interactive problems. This makes it ideal for students from a wide range of academic backgrounds as the student can work through the material at their own pace. Mathematical theories are explained in a straightforward manner, being supported by practical engineering examples and applications in order to ensure that readers can relate theory to practice. The extensive and thorough topic coverage makes this an ideal text for introductory level engineering courses. This title is supported by a companion website with resources for both students and lecturers, including lists of essential formulae, multiple choice tests, full solutions for all 1,600 further questions contained within the practice exercises, and biographical information on the 25 famous mathematicians and engineers referenced throughout the book. The companion website for this title can be accessed from www.routledge.com/cw/bird
Biomedical Applications of Control Engineering is a lucidly written textbook for graduate control engineering and biomedical engineering students as well as for medical practitioners who want to get acquainted with quantitative methods. It is based on decades of experience both in control engineering and clinical practice. The book begins by reviewing basic concepts of system theory and the modeling process. It then goes on to discuss control engineering application areas like: Different models for the human operator,dosage and timing optimization in oral drug administration, measuring symptoms of and optimal dopaminergic therapy in Parkinson’s disease, measurement and control of blood glucose levels both naturally and by means of external controllers in diabetes, and control of depth of anaesthesia using inhalational anaesthetic agents like sevoflurane using both fuzzy and state feedback controllers. All chapters include three types of exercises constructed to: Review the concepts discussed in the chapter, allow the reader to apply the newly acquired techniques and subject related facts on simple problems, and indicate directions for open ended theses projects. Appendices on Optimal Control and Fuzzy Control meant as refreshers on those control engineering techniques used throughout the book are also included.
Publisher: Macmillan International Higher Education
This text teaches maths in a step-by-step fashion – ideal for students on first-year engineering and pre-degree courses. - Hundreds of examples and exercises, the majority set in an applied engineering context so that you immediately see the purpose of what you are learning - Introductory chapter revises indices, fractions, decimals, percentages and ratios - Fully worked solutions to every problem on the companion website at www.palgrave.com/engineering/singh plus searchable glossary, e-index, extra exercises, extra content and more!