Essential mathematics for NMR and MRI spectroscopists:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Royal Society of Chemistry
[2017]
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xvi, 867 Seiten Illustrationen, Diagramme |
| ISBN: | 9781782627975 |
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MARC
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| 100 | 1 | |a Brown, Keith C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Essential mathematics for NMR and MRI spectroscopists |c Keith C. Brown |
| 264 | 1 | |a Cambridge |b Royal Society of Chemistry |c [2017] | |
| 300 | |a xvi, 867 Seiten |b Illustrationen, Diagramme | ||
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Record in the Search Index
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| adam_text |
Contents
1 Complex Numbers 1
1 1 The History of Numbers 1
1 2 Why Complex Numbers? 2
1 3 Properties of Complex Numbers 5
Further Reading 11
2 Matrices 12
2 1 Matrix Algebra 12
2 2 Determinants 19
2 3 Solving Matrix Equations 27
2 4 Transforms 40
2 5 Exponentials of Matrices 47
Further Reading 50
3 Vectors 51
31A Preliminary Definition of Vectors 51
3 2 Euclidean Vector Algebra and Inner Product Spaces 55
3 3 Vector Multiplication 60
3 4 Matrix Notation 78
3 5 Vector Transformations 86
3 6 Dirac Notation and Operator Matrices 95
Essential Mathematics for NMR and MRI Spectroscopists
By Keith C Brown
© Keith C Brown 2017
Published by the Royal Society of Chemistry, www rsc org
lx
3 7 Hilbert Space
3 8 Merging Vector Spaces
Further Reading
111
112
118
4 Vector Calculus 119
4 1 Vector Differentiation 119
4 2 Vector Integration 128
4 3 Curvilinear Coordinates and Grad, Div and Curl 149
4 4 Green’s Theorem, Gauss’s Theorem and Stokes’ Theorem 157
4 5 Vector Rotation in a Rotating Frame of Reference 173
Further Reading 176
5 Introductory Tensor Analysis 177
5 1 Dyadic Algebra 177
5 2 The Gradient of a Vector 185
5 3 Transformations 186
54A Tensor Definition 188
5 5 Isotropic Tensors 190
5 6 Symmetric, Antisymmetric and Irreducible Tensors 194
Further Reading 196
6 Probability and Statistics 197
6 1 Simple Probability and Statistics 197
6 2 Permutations and Combinations 200
6 3 Stirling’s Approximation 204
6 4 Probability Distributions 205
6 5 The Boltzmann Distribution 207
6 6 Random Processes and the Autocorrelation Function 217
Further Reading 219
Contents
xi
7 Waves 220
7 1 Characteristics of Waves 220
7 2 The Classical Wave Equation 223
7 3 Superposition of Waves 231
7 4 Standing Waves 232
Further Reading 234
8 The Fourier Transform 235
8 1 Fourier Series 235
8 2 Properties of the Time-Domain Functions 243
8 3 The Fourier Integral 248
8 4 Properties of Fourier Transforms 250
8 5 Some Important Fourier Pairs 253
8 6 Convolution 268
8 7 Impulse Sampling and the Nyquist
Frequency 274
8 8 The Discrete Fourier Transform 279
8 9 Real and Complex DFTs 287
8 10 The Fast Fourier Transform 294
Further Reading 304
9 Introductory Classical Mechanics 305
9 1 Newton’s Laws 305
9 2 Energy 310
9 3 Generalised Coordinates 312
9 4 The Lagrangian 313
9 5 The Hamiltonian 318
9 6 Classical Angular Momentum 319
Further Reading 326
10 Special Relativity 327
10 1 The Lorentz Transformation Equations 327
10 2 Kinematic Consequences of the Lorentz
Transformations 336
10 3 Space-time 339
10 4 Minkowski Diagrams 344
Further Reading 348
11 Electric and Magnetic Fields 349
11 1 Coulomb’s Law and the Electric Field 349
11 2 Field Flux and Gauss’s Law 352
11 3 The Magnetic Field 359
11 4 Maxwell’s Laws 377
11 5 Special Relativity and Magnetism 382
11 6 Electric Dipoles 393
11 7 Magnetic Dipoles 399
Further Reading 411
12 The Magnetic Moment and the Bloch
Equations 412
12 1 The Bloch Equations 412
12 2 The Vector Model of NMR Spectroscopy 427
Further Reading 433
13 Introductory Quantum Mechanics 435
13 1 Historical 435
13 2 The Basics of Quantum Mechanics 444
13 3 The Postulates of Quantum Mechanics 446
13 4 Vector Notation 451
13 5 The Uncertainty Principle 452
Further Reading 459
14 The Hamiltonians of NMR 460
14 1 The NMR Hamiltonian
14 2 The Zeeman Field Hamiltonian
460
461
Contents
xiii
14 3 The Chemical Shift Hamiltonian 463
14 4 The Dipolar Coupling Hamiltonian 465
■^jjf '■ 14 5 The Indirect (Scalar) Coupling Hamiltonian 465
W' 14 6 The RF-Field Hamiltonian 466
* Further Reading 468
: 15 The Quantum Mechanics of Angular
,i1 Momentum 469
? 15 1 A Brief History 469
•f 15 2 General Angular Momentum 470
15 3 Angular Momentum Operators in Spherical
Coordinates 481
15 4 Angular Momentum Operator Matrices 483
;|j:'; 15 5 Expectation Values 488
~ 15 6 Time Evolution 490
Further Reading 498
J§ i 16 NMR Rotation Operators 499
16 1 Rotation in Euclidean Space 499
16 2 The Euler Rotation Matrix 502
* X 16 3 Angular Momentum Rotation Operators 506
1 * 'W:, Further Reading 509
# 17 Density Operators and Matrices 510
i 17 1 The Density Matrix 510
17 2 Pure and Mixed States 514
It £ 17 3 The Time Evolution of the Density Matrix 518
17 4 Multiple-Spin Density Matrices 527
t 17 5 Spin-One 543
17 6 Density Matrices and Perturbation Calculations 549
17 7 Strong Coupling 553
t Further Reading 560
xiv Contents
18 The Product Operator Formalism 561
18 1 The Density Operator Method Revisited 561
18 2 The Product Operator Method 563
18 3 Multiple Quantum Coherence 568
18 4 Product Operator Rotations 570
18 5 Pulse Sequence Analysis 573
18 6 Three Spins and Higher 580
18 7 The Product Operator Tree 588
18 8 Single Transition Product Operators 592
Further Reading 597
19 Coherence Transfer 598
19 1 Phase Cycling 598
19 2 Coherence Order 603
19 3 Coherence Transfer Pathways 612
19 4 Phase Cycling Revisited 617
19 5 Pulsed Field Gradients 626
Further Reading 635
20 Relaxation and the NOE 636
20 1 Spin Temperature 636
20 2 Longitudinal 7\ Relaxation 638
20 3 Transverse T2 Relaxation 640
20 4 How Does Relaxation Work? 643
20 5 The Nuclear Overhauser Enhancement 661
Further Reading 668
21 Data Processing 670
21 1 Fourier Transform Spectroscopy 670
21 2 The 2D Fourier Transform 679
21 3 Window Functions 682
21 4 Zero Filling 685
21 5 Digital Filtering 689
21 6 Oversampling 691
Contents xv
! i W:l 21 7 21 8 21 9 Phase Correction Linear Prediction Baseline Correction Further Reading 692 695 698 700
22 Magnetic Resonance Imaging 701
■4s«-' - 22 1 Selective Pulses 701
22 2 Gradients 702
!: 22 3 Putting It All Together 711
1 ■ 22 4 The Discrete Fourier Transform 715
jEy- 22 5 Tlt T2 and Spin Density Weighting 718
T 22 6 Pulse Sequences 723
i ; Further Reading 728
: 23 Electronics 729
jfe; 23 1 The Modern NMR Spectrometer 729
Ife fr 23 2 DC Electronics 731
Ipf 23 3 AC Electronics 747
\ 23 4 AC Circuits 756
Jk- ' #1 #: 23 5 Antenna Theory 772
23 6 Analogue-to-Digital Conversion 782
fe jt Further Reading 785
J| ; ' rils, ■ Appendix A Identities, Proofs and Miscellany 786
A 1 Euler’s Formula 786
A 2 The Binomial Expansion 788
A 3 Trigonometric Identities 791
A 4 Direction Cosines 797
A 5 The Area of a Parallelogram 799
A 6 The Area of a Trapezoid 800
A 7 The Number ‘e’ 801
A 8 Alternate Coordinate Systems 803
A 9 The Fundamental Theorem of Calculus 811
A 10 Some Commonly Used Derivatives and Their
Properties 815
A 11 Partial Derivatives 816
A 12 Parametric Equations 817
A 13 Some Commonly Used Integrals and Their
Properties 819
A 14 Integration by Substitution 819
A 15 Integration by Parts 820
A 16 The Trapezoid Rule for Estimating Definite
Integrals 821
A 17 Solving Differential Equations 823
A 18 Commutator Algebra 827
A 19 L’Hopital’s Rule 829
A 20 Even and Odd Functions 831
A 21 Group Theory 834
Appendix B A Bruker to Varian Translation Table 839
Subject Index |
| any_adam_object | 1 |
| author | Brown, Keith C. |
| author_facet | Brown, Keith C. |
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| author_sort | Brown, Keith C. |
| author_variant | k c b kc kcb |
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| bvnumber | BV044010269 |
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| classification_tum | CHE 244 |
| ctrlnum | (OCoLC)971262389 (DE-599)BSZ481764240 |
| discipline | Chemie / Pharmazie Chemie Medizin |
| format | Book |
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| id | DE-604.BV044010269 |
| illustrated | Illustrated |
| indexdate | 2025-01-10T19:04:54Z |
| institution | BVB |
| isbn | 9781782627975 |
| language | English |
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| physical | xvi, 867 Seiten Illustrationen, Diagramme |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | Royal Society of Chemistry |
| record_format | marc |
| spelling | Brown, Keith C. Verfasser aut Essential mathematics for NMR and MRI spectroscopists Keith C. Brown Cambridge Royal Society of Chemistry [2017] xvi, 867 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Mathematische Methode (DE-588)4155620-3 gnd rswk-swf NMR-Spektroskopie (DE-588)4075421-2 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Kernspintomografie (DE-588)4120806-7 gnd rswk-swf Kernspintomografie (DE-588)4120806-7 s Mathematische Methode (DE-588)4155620-3 s NMR-Spektroskopie (DE-588)4075421-2 s DE-604 Mathematik (DE-588)4037944-9 s HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029417994&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brown, Keith C. Essential mathematics for NMR and MRI spectroscopists Mathematische Methode (DE-588)4155620-3 gnd NMR-Spektroskopie (DE-588)4075421-2 gnd Mathematik (DE-588)4037944-9 gnd Kernspintomografie (DE-588)4120806-7 gnd |
| subject_GND | (DE-588)4155620-3 (DE-588)4075421-2 (DE-588)4037944-9 (DE-588)4120806-7 |
| title | Essential mathematics for NMR and MRI spectroscopists |
| title_auth | Essential mathematics for NMR and MRI spectroscopists |
| title_exact_search | Essential mathematics for NMR and MRI spectroscopists |
| title_full | Essential mathematics for NMR and MRI spectroscopists Keith C. Brown |
| title_fullStr | Essential mathematics for NMR and MRI spectroscopists Keith C. Brown |
| title_full_unstemmed | Essential mathematics for NMR and MRI spectroscopists Keith C. Brown |
| title_short | Essential mathematics for NMR and MRI spectroscopists |
| title_sort | essential mathematics for nmr and mri spectroscopists |
| topic | Mathematische Methode (DE-588)4155620-3 gnd NMR-Spektroskopie (DE-588)4075421-2 gnd Mathematik (DE-588)4037944-9 gnd Kernspintomografie (DE-588)4120806-7 gnd |
| topic_facet | Mathematische Methode NMR-Spektroskopie Mathematik Kernspintomografie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029417994&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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