Mathematical techniques for biology and medicine:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, Mass.
MIT Pr.
1977
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 1. Aufl. u.d.T.: Simon, William: Mathematical techniques for physiology and medicine |
| Beschreibung: | XII, 291 S. graph. Darst. |
| ISBN: | 0262690578 |
Internformat
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| 500 | |a 1. Aufl. u.d.T.: Simon, William: Mathematical techniques for physiology and medicine | ||
| 650 | 4 | |a Biomathématiques | |
| 650 | 4 | |a Médecine - Mathématiques | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Medizin | |
| 650 | 4 | |a Biomathematics | |
| 650 | 4 | |a Biometry | |
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Medicine | |
| 650 | 4 | |a Medicine |x Mathematics | |
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Datensatz im Suchindex
| _version_ | 1804121854228561920 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
PREFACE TO PAPERBACK EDITION IX
PREFACE X
I. REVIEW OF DIFFERENTIAL CALCULUS
1. DIMENSIONS 1
2. THE CONCEPT OF A FUNCTIONAL RELATIONSHIP 3
3. THE DERIVATIVE 6
4. THE FUNCTION THAT IS ITS OWN DERIVATIVE 12
5. DIFFERENTIAL EQUATIONS 16
PROBLEMS 19
11. HOW DIFFERENTIAL EQUATIONS ARISE
1. THE ONE-COMPARTMENT DILUTION PROCESS 23
2. ONE-COMPARTMENT METABOLIC TURNOVER 28
3. RADIOACTIVE DECAY 29
4. X-RAY ABSORPTION 29
5. ONE COMPARTMENT WITH CONSTANT INJECTION 30
6. THE TWO-COMPARTMENT SERIES DILUTION 32
7. DIMENSIONLESS VARIABLES 33
8. MOTHER-DAUGHTER RADIOACTIVE DECAY 37
9. A CIRCULAR REACTION 37
PROBLEMS 39
III. GUESSING THE SOLUTION OF A DIFFERENTIAL EQUATION
1. INTRODUCTION: QUADRATIC EQUATIONS 41
2. MORE ABOUT EXPONENTIAL FUNCTIONS 42
IMAGE 2
3. SECOND DERIVATIVES 43
4. SOLUTIONS OF SIMPLE DIFFERENTIAL EQUATIONS 44
5. LINEAR AND NONLINEAR EQUATIONS 44
6. HOMOGENEOUS AND INHOMOGENEOUS EQUATIONS 46
7. THE FORMS OF SOLUTIONS 47
8. THE TWO-COMPARTMENT SERIES DILUTION 49
9. ONE COMPARTMENT WITH A LONG INPUT 51
10. DIFFUSION BETWEEN COMPARTMENTS 52
11. A SIMPLE KINETIC REACTION 56
PROBLEMS 57
IV. THE LAPLACE TRANSFORM
1. INTRODUCTION: ANTIDERIVATIVES 61
2. AREA UNDER A CURVE 62
3. THE SPLIT INTEGRAL THEOREM 65
4. SIMULTANEOUS LINEAR EQUATIONS 67
5. TRANSFORMING THE DIFFERENTIAL EQUATION 69
6. ONE COMPARTMENT WITH NONZERO INITIAL CONCENTRATION 71
7. THE SECOND COMPARTMENT OF THE TWO-COMPARTMENT SERIES DILUTION 72 8.
DIFFUSION BETWEEN COMPARTMENTS 73
9. FINDING NEW TRANSFORMS 75
10. THREE SPECIAL CASES 77
11. THE PARTIAL FRACTION EXPANSION 78
12. THE CONVOLUTION INTEGRAL 79
PROBLEMS 82
V. COMPARTMENTAL PROBLEMS
1. INTRODUCTION 84
2. THE ONE-COMPARTMENT MIXED CASE 85
3. THE TWO-COMPARTMENT PROBLEM 88
4. A SIMPLE THREE-COMPARTMENT PROBLEM 95
5. THE UNIT IMPULSE RESPONSE 97
6. THE CONVOLUTION THEOREM 99
7. NUMERICAL SOLUTIONS FROM THE UNIT IMPULSE RESPONSE 107
8. WORKING BACKWARD 108
PROBLEMS 109
VI. NUMERICAL METHODS
1. EULER S METHOD 113
2. VERIFYING THE RESULT 114
3. NUMERICAL SOLUTION OF A CIRCULAR REACTION WITH CHANGING RATE CONSTANT
117 4. RESTRICTED VALUE PROBLEMS 120
5. NUMERICAL SOLUTION OF HIGHER-ORDER EQUATIONS 122
PROBLEMS 124
IMAGE 3
VII. REGULATION AND OSCILLATION
1. THE SINE AND COSINE FUNCTIONS 127
2. PROPERTIES OF CONTROL SYSTEMS 132
3. A SIMPLE REGULATOR 133
4. THE OUTPUT RATE ERROR RESPONSE 137
5. THE EFFECT OF TIME DELAY IN THE FEEDBACK LOOP 140
6. POOLING DELAY VERSUS PURE TIME DELAY 143
7. A THREE-COMPARTMENT SYSTEM 151
8. CONTROL OF BIOSYNTHESIS 155
9. OTHER OSCILLATORS 158
PROBLEMS 160
VIII. DIFFUSION
1. INTRODUCTION: INFINITE SERIES 161
2. FOURIER SERIES 162
3. THE THERMAL DIFFUSION EQUATION 167
4. CHEMICAL DIFFUSION 172
5. SEMI-INFINITE SECTION WITH MIXED LOSS 176
6. FINITE SECTION WITH MIXED LOSS 177
7. THRESHOLD-DEPENDENT LOSS 178
8. SEMI-INFINITE SECTION WITH INTERNAL GENERATION 180
9. FINITE SECTION WITH INTERNAL GENERATION 181
10. SPHERICAL DIFFUSION 182
11. CYLINDRICAL DIFFUSION AND THE KROGH EQUATION 185
12. TIME-DEPENDENT DIFFUSION 188
PROBLEMS 192
IX. THE THEORY OF BLOOD FLOW MEASUREMENT
1. TIME AVERAGES AND STATIONARY SYSTEMS 194
2. INDICATOR DILUTION 196
3. CONSTANT INJECTION 197
4. IMPULSE INJECTION 199
5. VASCULAR VOLUME 200
6. PARALLEL COMPARTMENTS 202
7. THE PEEL-BACK METHOD 205
8. THE FICK METHOD 207
PROBLEMS 208
X. CURVE FITTING
1. PARTIAL DERIVATIVES 211
2. MAXIMIZATION AND MINIMIZATION 212
3. DIFFERENTIALS IN MORE THAN ONE VARIABLE 214
4. THE SOLUTION OF NONLINEAR EQUATIONS 216
5. THE METHOD OF LEAST SQUARES 218
IMAGE 4
6. EXPONENTIAL FITTING 223
7. THE FLAW IN PRONY S METHOD 226
8. THE MODIFIED PRONY METHOD 227
9. INVERTED EXPONENTIALS 229
10. THE GENERAL METHOD FOR NONLINEAR LEAST-SQUARES FITTING 231
XI. TRACER EXPERIMENTS
1. INTRODUCTION: QUANTIFICATION OF RADIOACTIVITY 238
2. FLUX THROUGH CELL MEMBRANES 239
3. EFFLUX MEASUREMENTS 240
4. INFLUX MEASUREMENTS 243
5. SURVIVAL TIME MEASUREMENTS 244
6. PRECURSOR PRODUCT RELATIONSHIPS 245
APPENDIX 1. THE RULES OF DIFFERENTIATION 251
APPENDIX II. TABLE OF LAPLACE TRANSFORMS 258
APPENDIX III. DERIVATIVES OF SINE AND COSINE FUNCTIONS 260
APPENDIX IV. SOLUTIONS TO SELECTED PROBLEMS 261
APPENDIX V. ADDITIONAL PROBLEMS 272
APPENDIX VI. SOLUTIONS TO ADDITIONAL PROBLEMS - 277
REFERENCES 283
SUBJECT INDEX 287
|
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| dewey-search | 510/.2461 |
| dewey-sort | 3510 42461 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2024-07-09T17:04:36Z |
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| isbn | 0262690578 |
| language | English |
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| spelling | Simon, William Verfasser aut Mathematical techniques for biology and medicine Cambridge, Mass. MIT Pr. 1977 XII, 291 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier 1. Aufl. u.d.T.: Simon, William: Mathematical techniques for physiology and medicine Biomathématiques Médecine - Mathématiques Mathematik Medizin Biomathematics Biometry Mathematics Medicine Medicine Mathematics Physiology Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Medizin (DE-588)4038243-6 gnd rswk-swf Biomathematik (DE-588)4139408-2 gnd rswk-swf Medizin (DE-588)4038243-6 s Mathematische Methode (DE-588)4155620-3 s DE-604 Biomathematik (DE-588)4139408-2 s SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004925728&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Simon, William Mathematical techniques for biology and medicine Biomathématiques Médecine - Mathématiques Mathematik Medizin Biomathematics Biometry Mathematics Medicine Medicine Mathematics Physiology Mathematische Methode (DE-588)4155620-3 gnd Medizin (DE-588)4038243-6 gnd Biomathematik (DE-588)4139408-2 gnd |
| subject_GND | (DE-588)4155620-3 (DE-588)4038243-6 (DE-588)4139408-2 |
| title | Mathematical techniques for biology and medicine |
| title_auth | Mathematical techniques for biology and medicine |
| title_exact_search | Mathematical techniques for biology and medicine |
| title_full | Mathematical techniques for biology and medicine |
| title_fullStr | Mathematical techniques for biology and medicine |
| title_full_unstemmed | Mathematical techniques for biology and medicine |
| title_short | Mathematical techniques for biology and medicine |
| title_sort | mathematical techniques for biology and medicine |
| topic | Biomathématiques Médecine - Mathématiques Mathematik Medizin Biomathematics Biometry Mathematics Medicine Medicine Mathematics Physiology Mathematische Methode (DE-588)4155620-3 gnd Medizin (DE-588)4038243-6 gnd Biomathematik (DE-588)4139408-2 gnd |
| topic_facet | Biomathématiques Médecine - Mathématiques Mathematik Medizin Biomathematics Biometry Mathematics Medicine Medicine Mathematics Physiology Mathematische Methode Biomathematik |
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