Mathematics for biological scientists:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
Garland Science
2010
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 452 S. Ill., graph. Darst. cm |
| ISBN: | 9780815341369 |
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MARC
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| 100 | 1 | |a Aitken, Mike |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematics for biological scientists |c Mike Aitken ; Bill Broadhurst ; Steve Hladky |
| 264 | 1 | |a New York, NY [u.a.] |b Garland Science |c 2010 | |
| 300 | |a XIX, 452 S. |b Ill., graph. Darst. |c cm | ||
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| 700 | 1 | |a Hladky, Stephen |e Verfasser |4 aut | |
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Record in the Search Index
| _version_ | 1804138695089979393 |
|---|---|
| adam_text | Contents
Preface
Introduction
0.1
Arithmetic with integers
The origins of number notation
Addition, subtraction, and negative numbers
Multiplication
0.2
Division, reciprocals, fractions, and
rational numbers
0.3
Decimal numbers
0.4
Real numbers
The importance of rational numbers
0.5
Forbidden operations using real numbers:
complex numbers
0.6
Summary
Chapter
1
Quantities and Units
1.1
Symbols, operations, relations, and the basic
language of mathematics
1.2
Physical quantities and physical value
equations
1.3
Physical quantities, numerical values,
and units
1.4
Conversion of units
1.5
SI units
Amount versus mass
1.6
Concentration
Units for concentrations
Molarity
Molality
Molarity versus molality
Mass concentration
Concentrations expressed as percentages
Conversion between molarity and
g
I 1
Conversion between molarity and molality
1.7
Dilutions and doses
1.8
Numerical value equations
1.9
Scalar and vector physical quantities
27
Presenting Your Work
28
XIII
xiii
End
of Chapter Questions
30
xiii
xiv
Chapter
2
Numbers and Equations
33
XV
2.1
Arithmetic with fractions
33
The fundamental fraction is the
xvi
reciprocal of an integer
34
xvii
The reciprocal of a product is the
product of the reciprocals
34
xvii
Factorization and the reduced form of
xviii
a fraction
34
Addition and subtraction
34
xviii
Multiplication
35
xix
Reciprocal of a fraction
35
Division
36
1
2.2
Addition of many terms
36
2.3
Powers and roots
38
2
Finding the nth root of a number
40
Raising a number to any fractional power
42
4
2.4
Order of precedence or sequence
of operations
42
5
2.5
Ratios and percentages
44
6
2.6
Scientific notation and significant figures
46
9
Truncation and rounding
47
13
Arithmetic in scientific notation
47
14
2.7
Solving equations
48
15
Some basics
48
15
Basic manipulations on equations
50
16
Solving first-order equations
52
17
Quadratic equations
53
18
2.8
Simultaneous equations
56
18
Simultaneous linear equations
57
19
Simultaneous nonlinear equations
59
20
Binding of small molecules to large ones
59
20
Presenting Your Work
62
23
End
of Chapter Questions
65
CONTENTS
Chapter
3
Tables, Graphs,
and Functions
3.1
Tables
3.2
Graphs
3.3
Functions
3.4
Inverse functions
3.5
Powers and roots revisited: an example
of inverse functions
3.6
Exponentials and logs
3.7
Log plots and log paper
3.8
What use are logarithms?
Plotting the logarithm of the number
of cells displays whether cells are growing
in an exponential phase
Plotting the logarithm of the plasma
concentration of a drag shows whether the
concentration is decreasing exponentially
with time
Logarithms are used to display data that
are spread over a large range of values
pH
Bels
and decibels
Presenting Your Work
End of Chapter Questions
Chapter
4
Shapes, Waves, and
Trigonometry
4.1
Circles and angles
4.2
Straight lines, angles, and a
parallelogram
4.3
Area and volume
4.4
Pythagoras theorem
4.5
Basic trigonometric functions: sine
and cosine
Sine and cosine rales for triangles
4.6
Sinusoidal oscillations
Amplitude, frequency, and phase of
a sinusoidal oscillation
Damped oscillations
4.7
Waves
Presenting Your Work
End of Chapter Questions
5.3
The slope of a curve
120
67
5.4
Differentiating simple expressions
122
67
5.5
Differentiating a sum of two functions
124
69
5.6
Higher derivatives
126
72
5.7
Maximum and minimum points
128
74
5.8
Points of inflexion
132
5.9
Sketching graphs
134
76
5.10
Tangents
137
76
5.11
Linear approximations
138
81
5.12
Handling experimental errors
139
82
Presenting Your Work
141
End of Chapter Questions
144
83
Chapter
6
Integration
147
6.1
Undoing the effects of differentiation
149
83
6.2
Integrating simple expressions
153
84
6.3
Definite and indefinite integrals
157
85
6.4
The area under a curve
159
86
6.5
Cumulative change
163
89
6.6
Composite, zero, and negative areas
165
92
6.7
The mean value of a function
169
Presenting Your Work
173
End of Chapter Questions
176
93
94
Chapter
7
Calculus: Expanding
the Toolkit
179
97
7.1
Sinusoidal functions
180
98
101
102
106
106
107
108
110
113
114
Chapter
5
Differentiation
115
5.1
The slope of a straight line
117
5.2
Average and instantaneous rates of change
118
7.2
Differentiating a pair of nested
functions
183
7.3
Differentiating a product of two
functions
187
7.4
Differentiating a ratio of two functions
188
7.5
Analyzing asymptotes
191
7.6
Changing the variable of an integral
193
7.7
Using a table of standard integrals
198
7.8
Simple harmonic motion
201
Presenting Your Work
205
End of Chapter Questions
206
Chapter
8
The Calculus of Growth
and Decay Processes
209
8.1
Integrating a reciprocal function
210
8.2
Calculus with logarithms
215
CONTENTS
XI
8.3
Calculus with exponential functions
8.4
Decay processes
8.5
Growth processes
Presenting Your Work
End of Chapter Questions
Chapter
9
Descriptive Statistics
and Data Display
9.1
Measurement scales
Nominal scales
Ordinal scales
Interval (and ratio) scales
Continuous and discrete data
9.2
Summarizing a data set
Pie charts and column graphs
Histograms
Lies, damn lies, and graphs
9.3
Numerical summary of a data set
Interval data: sample mean, variance,
and standard deviation
Ordinal or interval data: median, range,
and interquartile range
All data: the mode
9.4
Exploratory summaries of a data set
Population parameters
The standard error and accuracy of estimation
Difference between standard error
and standard deviation
Distribution shape and transformations
9.5
Describing more than one data set
Covariance and correlation
Covariance and the variance sum law
Presenting Your Work
End of Chapter Questions
Chapter
10
Probability
10.1
Probability
An example of probability in biology
Types of event
Probability diagrams
Combining probability: A and
В
Combining probability: A or
В
10.2
Conditional probability
Bayes
equation
10.3
Probability distributions
Discrete probability systems and
probability mass functions
220
Random variables
296
224
Continuous random variables and
228
probability density functions
298
Uniformly distributed continuous
233
random variables
300
235
Cumulative probability functions
302
10.4
Describing sampling distributions
306
Mean, standard deviation, and variance
307
237
10.5
The normal distribution
311
238
Presenting Your Work
315
239
End of Chapter Questions
318
239
239
240
Chapter
11
Statistical Inference
321
241
11.1
Inferential statistics
322
243
11.2
Interval estimates and confidence
244
intervals
324
Confidence intervals when the variance
is known
325
247
Interpreting confidence intervals
327
247
Confidence intervals for proportions
329
11.3
Hypothesis testing
332
250
11.4
Hypothesis testing using test statistics
337
252
Hypothesis tests for a normally
252
distributed value, with known variance
339
255
Combining hypothesis tests and
confidence intervals
340
Hypothesis tests when the population
259
variance is estimated (t tests)
342
Hypothesis tests and confidence intervals
¿fy J
for the mean of a single sample
343
264
Hypothesis tests for differences between
264
two means
345
269
The paired (related samples)
t
test
346
272
The independent (or unrelated samples)
274
ŕ
test
348
One-tailed and two-tailed tests
351
11.5
HvDotnesis tests for categorical data
353
277
278
280
282
283
284
286
290
294
295
Pearson s chi-square test for goodness-
of-fit for categorical data
354
Pearson s chi-square test for
contingency (relationship between
categorical measures)
356
11.6
Assumptions and validity conditions
359
Random sampling
360
Independent measurements
361
Normally distributed data
362
Assumptions of chi-square procedures
363
Presenting Your Work
365
End of Chapter Questions
368
xii CONTENTS
Chapter
12 Biological
Modeling
375
12.1
Fitting a model to experimental data:
linear models
376
12.2
Fitting nonlinear models
382
12.3
Differential equations: modeling
changing systems
387
Classifying differential equations
388
Solving differential equations
390
Separation of variables
391
12.4
Using differential equations I:
population growth and decline
393
Logistic growth
396
12.5
Using differential equations II:
biochemical reactions
401
Multi-stage processes and
steady-state models
403
Presenting Your Work
408
End of Chanter Questions
411
Answers to End of Chapter Questions
414
Appendices
Appendix
1
Summary of the Basic
Operations of Arithmetic and Algebra
433
Appendix
2
Four-figure Log Table
436
Appendix
3
Basic Trigonometric Functions
438
Appendix
4
The Standard Normal Distribution
439
Appendix
5
The
t
Distribution
441
Appendix
6
The
χ2
Distribution
442
Index
443
|
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| institution | BVB |
| isbn | 9780815341369 |
| language | English |
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| spelling | Aitken, Mike Verfasser aut Mathematics for biological scientists Mike Aitken ; Bill Broadhurst ; Steve Hladky New York, NY [u.a.] Garland Science 2010 XIX, 452 S. Ill., graph. Darst. cm txt rdacontent n rdamedia nc rdacarrier Biomathematics Biomathematics Textbooks Biomathematik (DE-588)4139408-2 gnd rswk-swf Biomathematik (DE-588)4139408-2 s b DE-604 Broadhurst, Bill Verfasser aut Hladky, Stephen Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017172007&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Aitken, Mike Broadhurst, Bill Hladky, Stephen Mathematics for biological scientists Biomathematics Biomathematics Textbooks Biomathematik (DE-588)4139408-2 gnd |
| subject_GND | (DE-588)4139408-2 |
| title | Mathematics for biological scientists |
| title_auth | Mathematics for biological scientists |
| title_exact_search | Mathematics for biological scientists |
| title_full | Mathematics for biological scientists Mike Aitken ; Bill Broadhurst ; Steve Hladky |
| title_fullStr | Mathematics for biological scientists Mike Aitken ; Bill Broadhurst ; Steve Hladky |
| title_full_unstemmed | Mathematics for biological scientists Mike Aitken ; Bill Broadhurst ; Steve Hladky |
| title_short | Mathematics for biological scientists |
| title_sort | mathematics for biological scientists |
| topic | Biomathematics Biomathematics Textbooks Biomathematik (DE-588)4139408-2 gnd |
| topic_facet | Biomathematics Biomathematics Textbooks Biomathematik |
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