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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, MAPLE and R further support students. The full text downloaded to your computer With eBooks you can: search for key concepts, words and phrases make highlights and notes as you study share your notes with friends eBooks are downloaded to your computer and accessible either offline through the Bookshelf (available as a free download), available online and also via the iPad and Android apps. Upon purchase, you'll gain instant access to this eBook. Time limit The eBooks products do not have an expiry date. You will continue to access your digital ebook products whilst you have your Bookshelf installed.

Advanced Modern Engineering Maths

• Half Title Page


• Title Page


• Copyright Page


• Contents


• Preface


• About the Authors


• Publisher?s Acknowledgements


• Chapter 1 Matrix Analysis


• 1.1 Introduction


• 1.2 Review of matrix algebra


• 1.2.1 Definitions


• 1.2.2 Basic operations on matrices


• 1.2.3 Determinants


• 1.2.4 Adjoint and inverse matrices


• 1.2.5 Linear equations


• 1.2.6 Rank of a matrix


• 1.3 Vector spaces


• 1.3.1 Linear independence


• 1.3.2 Transformations between bases


• 1.3.3 Exercises (1?4)


• 1.4 The eigenvalue problem


• 1.4.1 The characteristic equation


• 1.4.2 Eigenvalues and eigenvectors


• 1.4.3 Exercises (5?6)


• 1.4.4 Repeated eigenvalues


• 1.4.5 Exercises (7?9)


• 1.4.6 Some useful properties of eigenvalues


• 1.4.7 Symmetric matrices


• 1.4.8 Exercises (10?13)


• 1.5 Numerical methods


• 1.5.1 The power method


• 1.5.2 Exercises (14?18)


• 1.6 Reduction to canonical form


• 1.6.1 Reduction to diagonal form


• 1.6.2 The Jordan canonical form


• 1.6.3 Exercises (19?26)


• 1.6.4 Quadratic forms


• 1.6.5 Exercises (27?33)


• 1.7 Functions of a matrix


• 1.7.1 Exercises (34? 41)


• 1.8 Singular value decomposition


• 1.8.1 Singular values


• 1.8.2 Singular value decomposition (SVD)


• 1.8.3 Pseudo inverse


• 1.8.4 Exercises (42?49)


• 1.9 State-space representation


• 1.9.1 State-space representation


• 1.9.2 Multi-input?multi-output (MIMO) systems


• 1.9.3 Exercises


• 1.10 Solution of the state equation


• 1.10.1 Direct