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Beginning with a review of the important areas of mathematics, this book then covers many of the underlying theoretical and practical aspects of NMR and MRI spectroscopy from a maths point of view. Competence in algebra and introductory calculus is needed but all other maths concepts are covered. It will bridge a gap between high level and introductory titles used in NMR or MRI spectroscopy. Uniquely, it takes a very careful and pedagogical approach to the mathematics behind NMR and MRI. It leaves out very few steps, which distinguishes it from other books in the field.


The author is an NMR laboratory manager and is sympathetic to the frustrations of trying to understand where some of the fundamental equations come from hence his desire to either explicitly derive all equations for the reader or direct them to derivations. This is an essential text aimed at graduate students who are beginning their careers in NMR or MRI spectroscopy and laboratory managers if they need an understanding of the theoretical foundations of the technique. Excellent for many aspects of NMR spectroscopy, including the treatment of product operator formalism and density matrix. -- Gianluigi Veglia * University of Minnesota * The tallest hurdle faced by practitioners of NMR and MRI, is an understanding of the high level mathematics needed to describe the techniques.There are many papers and books on magnetic resonance which present either over-simplistic explanations, in order to avoid the detailed mathematics, or provide very detailed descriptions without an adequate explanation of the mathematics employed. Essential Mathematics for NMR and MRI Spectroscopists is the first book to addresses these problems in a comprehensive manner. The only prerequisites for the reader are an undergraduate level of mathematics and a general familiarity of the fundamentals of NMR spectroscopy. With the end goal being a detailed understanding of NMR and MRI, the first third of the book introduces all of the necessary mathematics required to understand the chapters thereafter. Those with a good undergraduate foundation in mathematics will find most of this to be a useful review but will likely learn more. The concepts of complex numbers, vectors, matrices, linear algebra, calculus, probability and statistics are reviewed in detail. With very few exceptions, all derivations are explicit and easy to follow. Frequent reference is made to a very well written appendix providing details for identities, theorems and concepts used. After the mathematics is introduced, classical and quantum mechanics are described in sufficient detail to understand their relevance and application to the theory of NMR spectroscopy which is the subject of all but the last of the remaining chapters of the book. The last chapter is devoted to electronics - a subject of much relevance to NMR laboratory technical staff. Very detailed descriptions of the Bloch equations, angular momentum, Hamiltonian operators, density matrices, product operators, coherence transfer, relaxation, nuclear Overhauser effects and magnetic resonance imaging are given for which the reader will have a new appreciation and greater understanding from a mathematical perspective.
This well written book is a valuable resource for graduate students, post-doctoral fellows, university faculty members and NMR practitioners in search of a deeper understanding of magnetic resonance theory. It is ideally suited as a textbook for graduate level courses in NMR theory and must certainly be added as additional reading for any other course in NMR spectroscopy. Unlike many books on mathematics and physics, this book is relatively easy to read. The author has sprinkled the text generously with insightful (and often amusing) footnotes bringing a personal perspective to the material. -- Glenn A. Facey, NMR Facility Manager, University of Ottawa

Essential Mathematics for NMR and MRI Spectroscopists

Complex Numbers; Matrices; Vectors; Vector Calculus; Tensor Analysis; Probability and Statistics; Waves; Fourier Transforms; Classical Mechanics; Special Relativity; Electric and Magnetic Fields; The Magnetic Moment and the Bloch Equations; Quantum Mechanics; The Hamiltonians of NMR; The Quantum Mechanics of Angular Momentum; NMR Rotation Operators; Density Operators; The Product Operator Formalism; Relaxation and the NOE; Data Processing; Coherence Transfer; Electronics; Appendices