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.
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