Are you looking for a text that explains the mathematical derivations for NMR and MRI theory? Struggling to comprehend the fundamental equations used in this vast topic? This book has been designed to help you.
Thoroughly reviewed and revised, this new edition begins by assessing the important areas of mathematics and 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 bridges a gap between high level and introductory titles used in NMR or MRI spectroscopy taking a very careful pedagogical approach to the mathematics behind NMR and MRI. Coverage is comprehensive – it leaves out very few steps – which distinguishes it from other books in the field.
The author, now retired, was 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 essential text is 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.
สารบัญ
- Complex Numbers
- Matrices
- Vectors
- Vector Calculus
- Introductory Tensor Analysis
- Probability and Statistics
- Waves
- Fourier Transforms
- Introductory Classical Mechanics
- Electric and Magnetic Fields
- The Magnetic Moment and the Bloch Equations
- Introductory Quantum Mechanics
- The Hamiltonians of NMR
- The Quantum Mechanics of Angular Momentum
- NMR Rotation Operators
- Density Operators and Matrices
- The Product Operator Formalism
- Coherence Transfer
- Relaxation and the NOE
- Dynamic NMR Spectroscopy
- Data Processing
- Magnetic Resonance Imaging
- Electronics
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