Mathematics for geographers and planners:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Clarendon Press
1980
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Contemporary problems in geography
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 408 S. Ill., graph. Darst. |
| ISBN: | 0198741146 0198741154 |
Internformat
MARC
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| 100 | 1 | |a Wilson, Alan G. |c Sir |d 1939- |e Verfasser |0 (DE-588)121868060 |4 aut | |
| 245 | 1 | 0 | |a Mathematics for geographers and planners |c A. G. Wilson and M. J. Kirkby |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Oxford |b Clarendon Press |c 1980 | |
| 300 | |a XV, 408 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Contemporary problems in geography | |
| 650 | 4 | |a Géographie mathématique | |
| 650 | 4 | |a Geografie | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Geography |x Mathematics | |
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
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| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Geografie |0 (DE-588)4020216-1 |D s |
| 689 | 1 | 1 | |a Mathematik |0 (DE-588)4037944-9 |D s |
| 689 | 1 | 2 | |a Grundlage |0 (DE-588)4158388-7 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Kirkby, Michael J. |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001292346&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1804116426587373568 |
|---|---|
| adam_text | Titel: Mathematics for geographers and planners
Autor: Wilson, Alan G
Jahr: 1980
Contents
PART
1
1.
MATHEMATICAL
ANALYSIS
IN
GEOGRAPHY
AND
PLANNING
3
1.1.
Why
mathematical
analysis
is
important
3
1.1.1.
The
context
3
1.1.2.
Levels
of
resolution
5
1.1.3.
General
aspects
of
geographical
methodology
7
1.2.
The
structure
of
the
mathematical
argument
10
1.3.
Some
examples
to
be
considered
in
more
detail
11
1.3.1.
Introduction
11
1.3.1.
Micro-location
theory
1:
land
use
and
rent
12
1.3.3.
Micro-location
theory
2:
plant
location
and
resource
use
12
1.3.4.
Location
theory
via
quadrat
analysis
13
1.3.5.
Meso-spatial
interaction
and
location
theory
13
1.3.6.
Interaction
and
nodal
structure
14
1.3.7.
Network
theory
1:
descriptive
concepts
14
1.3.8.
Network
theory
2:
shortest
paths
and
flow
loading
14
1.3.9.
A
note
on
the
concept
of‘equilibrium’and
‘maximization’
in
the
time
development
of
geographical
systems
14
1.3.10.
Diffusion
processes
15
1.3.11.
Growth
and
decline:
accounting
and
time
development
equations
15
1.3.12.
Process
studies:
flows
and
mass
or
energy
balance
relationships
16
1.3.13.
Miscellaneous
examples
16
2.
ELEMENTARY
ALGEBRA
AND
SYSTEM
DESCRIPTION
18
2.1.
Notation
and
the
basic
algebraic
operations
18
2.2.
Principles
of
system
description
21
2.2.1.
The
algebra
of
space
21
2.2.2.
Further
preliminaries
24
2.2.3.
Von
Thlinen’s
and
Alonso’s
problems
24
2.2.4.
The
Weberian
problem
25
2.2.5.
Quadrat
analysis
26
2.2.6.
Meso-spatial
interaction
and
location
theory
26
2.2.7.
Network
theory
27
X
Contents
2.2.8.
Diffusion
processes
30
2.2.9.
Accounting
and
time
development
31
2.2.10.
Process
studies
based
on
balance
relationships
32
2.3.
Relating
data
to
algebraic
variables
33
2.4.
Simple
equations
34
2.4.1.
Linear
equations
in
one
dependent
variable
34
2.4.2.
Quadratic
equations
37
2.4.3.
Cubic
and
higher
order
equations
39
2.4.4.
Checking
that
equations
make
sense
40
2.5.
Simultaneous
equations
-
more
than
one
dependent
variable
40
2.6.
Inequalities
43
2.7.
Some
simple
series
2.7.1.
The
arithmetric
progression
45
2.7.2.
The
geometric
progression
46
3.
FUNCTIONS,
GRAPHS,
CO-ORDINATE
GEOMETRY,
AND
MORE
EQUATIONS
54
3.1.
Introduction
54
3.2.
Some
formal
definitions
and
general
notation
54
3.2.1.
Definition
of
a
function
54
3.2.2.
Notation
55
3.2.3.
Implicit
and
inverse
functions
gg
3.3.
Graphs
and
co-ordinate
geometry
57
3.3.1.
Graphs
57
3.3.2.
The
geometry
of
the
straight
line
gg
3.3.3.
The
intersection
of
two
straight
lines
g
j
3.3.4.
The
distance
between
two
points
g4
3.3.5.
Equations
of
particular
straight
lines
g4
3.3.6.
The
interpretation
of
linear
inequalities
gg
3.4.
The
standard
functions
gg
3.4.1.
Introduction
gg
3.4.2.
The
power
function
gg
3.4.3.
The
logarithmic
function
7
^
3.4.4.
The
exponential
function
74
3.4.5.
Trigonometric
functions
7g
3.4.6.
Inverse
trigonometric
functions
7g
3.5.
A
wider
range
of
functions
79
3.5.1.
Introduction
79
3.5.2.
Polynomial
and
rational
functions,
graphical
solution
of
equations
79
3.5.3.
The
hyperbolic
functions
81
3.5.4.
The
logistic
function,
and
a
note
on
asymptotes
83
3.5.5.
Miscellaneous
examples
84
3.6.
Series
expansion
of
functions
85
3.7.
Functions
of
more
than
one
independent
variable
87
3.7.1.
Notation
and
examples
87
3.7.2.
Higher
dimensional
co-ordinate
geometry
88
3.8.
More
examples
of
equations,
functions
and
associated
algebraic
manipulation
89
Contents
XI
3.8.1.
Introduction
89
3.8.2.
Infiltration
rates
90
3.8.3.
Scree
slopes
92
3.8.4.
Horton’s
network
laws
92
3.8.5.
A
simple
population
model
95
3.8.6.
von
ThUnen’s
rings
96
3.8.7.
Meso-spatial
interaction
and
location
models
98
3.8.8.
Diffusion
from
a
polluting
source
105
4.
MATRIX
ALGEBRA
110
4.1.
Definitions
110
4.2.
The
basic
operations
of
matrix
algebra
112
4.3.
Linear
simultaneous
equations
in
matrix
form
116
4.4.
Matrices
and
linear
transformations
120
4.4.1.
Rotations
120
4.4.2.
Linear
transformations
of
vectors
and
matrices
122
4.4.3.
Canonical
forms,
eigenvalues
and
eigenvectors
124
4.5.
Examples
of
the
use
of
matrices
124
4.5.1.
The
analysis
of
nodal
structure
124
4.5.2.
An
account-based
population
model
126
4.5.3.
The
input-output
model
129
5.
CALCULUS
136
5.1.
Introduction
136
5.2.
The
basic
concepts
of
differential
calculus
137
5.2.1.
The
gradient
as
a
limit
137
5.2.2.
Notation
and
main
concepts
138
5.2.3.
The
sign
of
the
derivative,
and
a
preliminary
note
on
a
maxima
and
minima
140
5.3.
Derivatives
of
standard
functions
140
5.4.
Rules
for
differentiating
non-standard
functions
142
5.4.1.
Introduction
142
5.4.2.
Scalar
multiples
142
5.4.3.
The
sum
of
two
functions
143
5.4.4.
Function
of
a
function
143
5.4.5.
Differentiation
of
a
product
144
5.4.6.
Differentiation
of
a
quotient
145
5.4.7.
Differentiation
of
a
parametrically
specified
function
146
5.4.8.
The
‘rules’
in
combination
146
5.4.9.
Differentiation
in
practice
147
5.5.
Second
and
higher
order
derivatives
147
5.6.
Maxima,
minima
and
points
of
inflexion
148
5.7.
The
basic
concepts
of
integral
calculus
151
5.7.1.
Integral
calculus
as
the
inverse
of
differential
calculus
151
5.7.2.
Integrals
as
areas
under
curves
151
5.7.3.
An
interpretation
of
the
integral
notation
154
5.7.4.
Integration
of
standard
functions
154
.
Contents
xii
5.8.
Some
methods
for
integrating
non-standard
functions
155
5.8.1.
Integration
by
substitution
155
5.8.2.
Integration
by
parts
156
5.9.
Calculus
of
functions
of
several
variables
157
5.9.1.
Partial
differentiation
157
5.9.2.
Estimation
of
a‘best
fitting’straight
line
159
5.9.3.
Weber’s
problem
162
5.9.4.
Multiple
integration
164
5.10.
Series
expansions
and
the
mean
value
theorem
164
5.10.1.
Taylor’s
theorem
164
5.10.2.
Maclaurin’s
theorem
165
5.10.3.
Series
expansion
by
the
differentiation
and
integration
of
known
series
166
5.10.4.
The
mean
value
theorem
166
5.10.5.
A
word
of
caution
on
series
expansions
169
5.11.
Some
examples
169
5.11.1.
Introduction
169
5.11.2.
Population
models
169
5.11.3.
The
intervening
opportunities’
model
171
5.11.4.
Error
propagation
in
photogrammetry
172
5.11.5.
Consumers’surplus
173
5.11.6.
Total
population
given
a
density
distribution
176
5.11.7.
A
continuous
space
model
of
spatial
interaction
178
PART
2
6.
DIFFERENTIAL
AND
DIFFERENCE
EQUATIONS
187
6.1.
Definitions
187
6.2.
Ordinary
differential
equations
187
6.2.1.
Introduction
187
6.2.2.
Solution
by
inspection
188
6.2.3.
First-order
linear
differential
equations
189
6.2.4.
Particular
solutions
191
6.3.
Ordinary
linear
differential
equations
193
6.3.1.
Introduction
193
6.3.2.
Constant
coefficients:
F(x)
=
0
193
6.3.3.
Constant
coefficients:
F(x)
4
=
0
195
6.3.4.
Non-constant
coefficients;
solution
in
series
196
6.3.5.
Iterative
solutions
198
6.4.
Finite
differences
200
6.4.1.
Introduction
200
6.4.2.
Differentiation
and
integration
using
finite
differences
202
6.5.
Difference
equations
205
6.5.1.
Relation
to
differential
equations
205
6.5.2.
Linear
difference
equations
with
constant
coefficients
206
6.6.
Some
examples
of
ordinary
differential
and
difference
equations
209
6.6.1.
Hillslope
profile
development
with
a
steadily
down-cutting
river
209
Contents
xiii
6.6.2.
Freezing
of
water
in
a
lake
or
in
a
uniform
soil
from
above
210
6.6.3.
Length
probabilities
for
a
queue
in
a
steady
state
212
6.7.
Partial
differential
equations
214
6.7.1.
Some
contexts
and
examples
214
6.7.2.
The
continuity
equation
in
one-dimension
215
6.7.3.
Hillslope
profile
development
216
6.7.4.
Saturated
water
flow
218
6.7.5.
Unsaturated
infiltration
of
soil
water
219
6.7.6.
Glacier
flow
220
6.7.7.
Heat
conduction
in
the
ground
221
6.7.8.
Diffusion
processes
222
6.7.9.
Types
of
solution
of
the
continuity
equation
223
6.7.10.
Steady
state
solutions
224
6.7.11.
Separation
of
variables
225
6.7.12.
Laplace
transform
solutions
227
6.7.13.
Kinematic
wave
solutions
228
d
2
z
Kdz
6.7.14.
Some
examples
of
solutions
for-=-
232
ax
at
THE
MATHEMATICS
OF
PROBABILITY
AND
STATISTICS
244
7.1.
Introduction
244
7.2.
Basic
definitions
244
7.2.1.
Randomness
and
probability
244
7.2.2.
Adding
probabilities:
exclusive
and
exhaustive
events
246
7.2.3.
Multiplying
probabilities:
conditional
probability
and
independence
247
7.3.
Examples
of
simple
probabilities
248
7.3.1.
Coin
tossing
248
7.3.2.
Examples
of
real-world
data:
the
relation
to
statistics
250
7.4.
Compound
probabilities;
the
binomial
distribution
255
7.4.1.
Probability
distributions
255
7.4.2.
The
binomial
distribution
256
7.4.3.
Stirling’s
formula
258
7.5.
Moments
of
distributions
259
7.5.1.
Definitions
259
7.5.2.
Moments
of
the
binomial
distribution
260
7.6.
Limiting
cases
of
the
binomial
distribution
261
7.6.1.
Introduction
261
7.6.2.
The
Poisson
distribution
261
7.6.3.
The
normal
distribution
263
7.6.4.
The
central
limit
theorem
263
STOCHASTIC
PROCESSES
268
8.1.
Random
walks
268
8.1.1.
Introduction
268
8.1.2.
The
binomial
process
268
xiv
Contents
8.1.3.
The
ballot
theorem
26
8.1.4.
Returns
to
zero
27
8.1.5.
Examples
of
random
walks
21
.
8.1.6.
Stream
networks
as
random
walks
27
8.1.7.
Gambler’s
ruin
:
absorbing
and
reflecting
barriers
27 ,
8.1.8.
The
effect
of
base
level:
a
geortiorphological
example
27S
8.2.
Markov
chains
28C
8.2.1.
Definition
280
8.2.2.
Change
in
probabilities
over
time
281
8.2.3.
Distribution
after
long
times
282
8.2.4.
Other
types
of
chain
284
8.3.
Poisson
processes.
284
8.3.1.
Derivation
284
8.3.2.
Spacing
of
occurrences
285
8.3.3.
Nearest
neighbour
statistics
286
8.3.4.
Other
examples
of
Poisson
processes
288
8.4.
Branching
processes
288
8.4.1.
Introduction
288
8.4.2.
Generating
function
for
number
in
each
generation
288
8.4.3.
Extinction
probabilities
290
8.5.
Other
stochastic
processes
291
8.5.1.
Types
of
stochastic
process
291
8.5.2.
Birth
and
death
processes
292
9.
MAXIMIZATION
AND
MINIMIZATION
METHODS
297
9.1.
Introduction
297
9.2.
Constrained
maximization
298
9.2.1.
The
Lagrangian
method
298
9.2.2.
Example
1:
utility
maximizing
and
profit
maximizing
303
9.2.3.
Example
2:
entropy
maximizing
models
306
9.2.4.
A
note
on
maximum
likelihood
methods
311
9.3.
The
‘calculus
of
variations’
method
for
finding
optimum
paths
311
9.3.1.
The
problem
and
the
method
311
9.3.2.
Minimum
distance
and
time
paths
313
9.4.
Algorithmic
mathematics
317
9.4.1.
Introduction
317
9.4.2.
The
shortest
path
through
a
network
317
9.4.3.
Linear
programming
321
10.
CATASTROPHE
THEORY
AND
BIFURCATION:
NEW
METHODS
FOR
DYNAMIC
MODELLING
329
10.1.
Introduction
329
10.2.
System
description
329
10.3.
Catastrophe
theory
334
10.3.1.
Introduction
334
10.3.2.
The
fold
catastrophe
334
10.3.3.
The
cusp
catastrophe
335
Contents
xv
10.3.4.
The
deeper
theorems
of
catastrophe
theory
338
10.3.5.
Example
1:
retail
centres
of
varying
size
340
10.3.6.
Example
2:
modal
choice
and
the
cusp
catastrophe
343
10.3.7.
Example
3:
location
theory
and
a
non-canonical
cusp
344
10.3.8.
Other
geographical
applications
349
10.4.
A
framework
for
the
development
of
dynamic
models
350
10.5.
Differential
equations
and
bifurcation
350
10.5.1.
Dynamical
systems
as
differential
equations
350
10.5.2.
Typical
forms
of
solution
of
dynamic
differential
equations
351
10.5.3.
Example
1:
growth
equations
354
10-5.4.
Example
2:
the
Lotka-Volterra
prey-predator
equations
356
10.5.5.
Example
3:
competition
for
fixed
resources
358
10.6.
Applications
in
planning
360
PROBLEM
SOLVING
METHODS
363
11.1.
Introduction:
types
of
problem
solving
363
11.2.
Model
building
methods:
a
summary
364
11.3.
Concluding
comments
365
REFERENCES
367
ANSWERS
TO
EXERCISES
375
INDEX
399
|
| any_adam_object | 1 |
| author | Wilson, Alan G. Sir 1939- Kirkby, Michael J. |
| author_GND | (DE-588)121868060 |
| author_facet | Wilson, Alan G. Sir 1939- Kirkby, Michael J. |
| author_role | aut aut |
| author_sort | Wilson, Alan G. Sir 1939- |
| author_variant | a g w ag agw m j k mj mjk |
| building | Verbundindex |
| bvnumber | BV001981420 |
| callnumber-first | G - Geography, Anthropology, Recreation |
| callnumber-label | G70 |
| callnumber-raw | G70.23 |
| callnumber-search | G70.23 |
| callnumber-sort | G 270.23 |
| callnumber-subject | G - General Geography |
| classification_rvk | QH 110 RB 10103 |
| ctrlnum | (OCoLC)6461647 (DE-599)BVBBV001981420 |
| dewey-full | 510/.2491 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510/.2491 |
| dewey-search | 510/.2491 |
| dewey-sort | 3510 42491 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften Geographie |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV001981420 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:38:19Z |
| institution | BVB |
| isbn | 0198741146 0198741154 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001292346 |
| oclc_num | 6461647 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-384 DE-739 DE-824 DE-19 DE-BY-UBM DE-83 |
| owner_facet | DE-91 DE-BY-TUM DE-384 DE-739 DE-824 DE-19 DE-BY-UBM DE-83 |
| physical | XV, 408 S. Ill., graph. Darst. |
| psigel | TUB-nveb |
| publishDate | 1980 |
| publishDateSearch | 1980 |
| publishDateSort | 1980 |
| publisher | Clarendon Press |
| record_format | marc |
| series2 | Contemporary problems in geography |
| spelling | Wilson, Alan G. Sir 1939- Verfasser (DE-588)121868060 aut Mathematics for geographers and planners A. G. Wilson and M. J. Kirkby 2. ed. Oxford Clarendon Press 1980 XV, 408 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Contemporary problems in geography Géographie mathématique Geografie Mathematik Geography Mathematics Mathematik (DE-588)4037944-9 gnd rswk-swf Grundlage (DE-588)4158388-7 gnd rswk-swf Geografie (DE-588)4020216-1 gnd rswk-swf Geografie (DE-588)4020216-1 s Mathematik (DE-588)4037944-9 s DE-604 Grundlage (DE-588)4158388-7 s Kirkby, Michael J. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001292346&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wilson, Alan G. Sir 1939- Kirkby, Michael J. Mathematics for geographers and planners Géographie mathématique Geografie Mathematik Geography Mathematics Mathematik (DE-588)4037944-9 gnd Grundlage (DE-588)4158388-7 gnd Geografie (DE-588)4020216-1 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4158388-7 (DE-588)4020216-1 |
| title | Mathematics for geographers and planners |
| title_auth | Mathematics for geographers and planners |
| title_exact_search | Mathematics for geographers and planners |
| title_full | Mathematics for geographers and planners A. G. Wilson and M. J. Kirkby |
| title_fullStr | Mathematics for geographers and planners A. G. Wilson and M. J. Kirkby |
| title_full_unstemmed | Mathematics for geographers and planners A. G. Wilson and M. J. Kirkby |
| title_short | Mathematics for geographers and planners |
| title_sort | mathematics for geographers and planners |
| topic | Géographie mathématique Geografie Mathematik Geography Mathematics Mathematik (DE-588)4037944-9 gnd Grundlage (DE-588)4158388-7 gnd Geografie (DE-588)4020216-1 gnd |
| topic_facet | Géographie mathématique Geografie Mathematik Geography Mathematics Grundlage |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001292346&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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