Multi-variable calculus: a first step
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston
De Gruyter
[2020]
|
| Schriftenreihe: | De Gruyter textbook
|
| Schlagworte: | |
| Online-Zugang: | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110674149&searchTitles=true Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | XI, 323 Seiten Illustrationen, Diagramme (teilweise farbig) 24 cm, 564 g |
| ISBN: | 9783110674149 3110674149 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV046727532 | ||
| 003 | DE-604 | ||
| 005 | 20221115 | ||
| 007 | t | ||
| 008 | 200519s2020 gw a||| |||| 00||| eng d | ||
| 016 | 7 | |a 1195794843 |2 DE-101 | |
| 020 | |a 9783110674149 |c Broschur |9 978-3-11-067414-9 | ||
| 020 | |a 3110674149 |9 3-11-067414-9 | ||
| 035 | |a (OCoLC)1121493890 | ||
| 035 | |a (DE-599)DNB1195794843 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c XA-DE-BE | ||
| 049 | |a DE-634 |a DE-706 |a DE-83 |a DE-703 |a DE-11 | ||
| 082 | 0 | |a 515 |2 23/ger | |
| 084 | |a SK 490 |0 (DE-625)143242: |2 rvk | ||
| 084 | |a 510 |2 sdnb | ||
| 100 | 1 | |a Zou, Yunzhi |e Verfasser |0 (DE-588)1155862910 |4 aut | |
| 245 | 1 | 0 | |a Multi-variable calculus |b a first step |c Yunzhi Zou |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2020] | |
| 264 | 4 | |c © 2020 | |
| 300 | |a XI, 323 Seiten |b Illustrationen, Diagramme (teilweise farbig) |c 24 cm, 564 g | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a De Gruyter textbook | |
| 650 | 0 | 7 | |a Gewöhnliche Differentialgleichung |0 (DE-588)4020929-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Integralrechnung |0 (DE-588)4027232-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mehrere Variable |0 (DE-588)4277015-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Analysis |0 (DE-588)4001865-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Vektorrechnung |0 (DE-588)4062471-7 |2 gnd |9 rswk-swf |
| 653 | |a TB: Textbook | ||
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Analysis |0 (DE-588)4001865-9 |D s |
| 689 | 0 | 1 | |a Mehrere Variable |0 (DE-588)4277015-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Vektorrechnung |0 (DE-588)4062471-7 |D s |
| 689 | 1 | 1 | |a Integralrechnung |0 (DE-588)4027232-1 |D s |
| 689 | 1 | 2 | |a Gewöhnliche Differentialgleichung |0 (DE-588)4020929-5 |D s |
| 689 | 1 | |5 DE-604 | |
| 710 | 2 | |a Walter de Gruyter GmbH & Co. KG |0 (DE-588)10095502-2 |4 pbl | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, PDF |z 978-3-11-067437-8 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, EPUB |z 978-3-11-067443-9 |
| 856 | 4 | 2 | |m X:MVB |u http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110674149&searchTitles=true |
| 856 | 4 | 2 | |m B:DE-101 |q application/pdf |u https://d-nb.info/1195794843/04 |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032137643&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-032137643 | ||
Datensatz im Suchindex
| _version_ | 1804181472310984704 |
|---|---|
| adam_text | CONTENTS
INTRODUCTION
*
IX
1
1.1
1.1.1
1.1.2
1.1.3
1.1.4
1.1.5
1.2
1.2.1
1.2.2
1.2.3
1.2.4
1.3
1.3.1
1.3.2
1.4
1.5
1.5.1
1.5.2
1.5.3
1.6
1.6.1
1.6.2
1.6.3
1.6.4
1.7
1.8
1.9
1.10
1.11
1.11.1
1.11.2
1.11.3
VECTORS
AND
THE
GEOMETRY
OF
SPACE
*
1
VECTORS
*
1
CONCEPTS
OF
VECTORS
*
1
LINEAR
OPERATIONS
INVOLVING
VECTORS
*
2
COORDINATE
SYSTEMS
IN
THREE-DIMENSIONAL
SPACE
*
3
REPRESENTING
VECTORS
USING
COORDINATES
*
5
LENGTHS,
DIRECTION
ANGLES
*
7
DOT
PRODUCT,
CROSS
PRODUCT,
AND
TRIPLE
PRODUCT
*
9
THE
DOT
PRODUCT
-----
9
PROJECTIONS
*
12
THE
CROSS
PRODUCT
*
13
SCALAR
TRIPLE
PRODUCT
-----
17
EQUATIONS
OF
LINES
AND
PLANES
*
18
LINES
-----
18
PLANES
-----
23
CURVES
AND
VECTOR-VALUED
FUNCTIONS
*
30
CALCULUS
OF
VECTOR-VALUED
FUNCTIONS
*
32
LIMITS,
DERIVATIVES,
AND
TANGENT
VECTORS
*
32
ANTIDERIVATIVES
AND
DEFINITE
INTEGRALS
*
35
LENGTH
OF
CURVES,
CURVATURES,
TNB
FRAME
-----
37
SURFACES
IN
SPACE
-----
42
GRAPH
OF
AN
EQUATION
F(X,Y,Z)
=
0
-----
42
CYLINDER
-----44
QUADRIC
SURFACES
-----
46
SURFACE
OF
REVOLUTION
*
46
PARAMETERIZED
SURFACES
*
49
INTERSECTING
SURFACES
AND
PROJECTION
CURVES
*
50
REGIONS
BOUNDED
BY
SURFACES
*
56
REVIEW
-----
57
EXERCISES
-----
59
VECTORS
*
59
LINES
AND
PLANES
IN
SPACE
*
60
CURVES
AND
SURFACES
IN
SPACE
*
61
2
2.1
2.1.1
2.1.2
FUNCTIONS
OF
MULTIPLE
VARIABLES
*
65
FUNCTIONS
OF
MULTIPLE
VARIABLES
*
65
DEFINITIONS
-----
65
GRAPHS
AND
LEVEL
CURVES
*
67
V!
*
CONTENTS
2.1.3
2.1.4
2.1.5
2.2
2.2.1
2.2.2
2.2.3
2.3
2.3.1
2.3.2
2.3.3
2.4
2.4.1
2.4.2
2.4.3
2.5
2.6
2.6.1
2.6.2
2.7
2.7.1
2.7.2
2.8
2.9
2.9.1
2.9.2
2.10
2.11
2.11.1
2.11.2
2.11.3
2.11.4
2.11.5
FUNCTIONS
OF
MORE
THAN
TWO
VARIABLES
*
69
LIMITS
-----
70
CONTINUITY
-----
75
PARTIAL
DERIVATIVES
*
76
DEFINITION
-----
76
INTERPRETATIONS
OF
PARTIAL
DERIVATIVES
*
80
PARTIAL
DERIVATIVES
OF
HIGHER
ORDER
*
82
TOTAL
DIFFERENTIAL
*
83
LINEARIZATION
AND
DIFFERENTIABILITY
*
83
THE
TOTAL
DIFFERENTIAL
*
89
THE
LINEAR/DIFFERENTIAL
APPROXIMATION
-----
90
THE
CHAIN
RULE
-----
92
THE
CHAIN
RULE
WITH
ONE
INDEPENDENT
VARIABLE
*
92
THE
CHAIN
RULE
WITH
MORE
THAN
ONE
INDEPENDENT
VARIABLE
*
94
PARTIAL
DERIVATIVES
FOR
ABSTRACT
FUNCTIONS
*
97
THE
TAYLOR
EXPANSION
-----
98
IMPLICIT
DIFFERENTIATION
-----
101
FUNCTIONS
IMPLICITLY
DEFINED
BY
A
SINGLE
EQUATION
*
101
FUNCTIONS
DEFINED
IMPLICITLY
BY
SYSTEMS
OF
EQUATIONS
*
103
TANGENT
LINES
AND
TANGENT
PLANES
*
106
TANGENT
LINES
AND
NORMAL
PLANES
TO
A
CURVE
*
106
TANGENT
PLANES
AND
NORMAL
LINES
TO
A
SURFACE
*
109
DIRECTIONAL
DERIVATIVES
AND
GRADIENT
VECTORS
*
113
MAXIMUM
AND
MINIMUM
VALUES
*
122
EXTREMA
OF
FUNCTIONS
OF
TWO
VARIABLES
*
122
LAGRANGE
MULTIPLIERS
*
130
REVIEW
-----
136
EXERCISES
-----
138
FUNCTIONS
OF
TWO
VARIABLES
*
138
PARTIAL
DERIVATIVES
AND
DIFFERENTIABILITY
*
139
CHAIN
RULESAND
IMPLICIT
DIFFERENTIATION
-----
140
TANGENT
LINES/PLANES,
DIRECTIONAL
DERIVATIVES
*
141
MAXIMUM/MINIMUM
PROBLEMS
*
142
3
3.1
3.2
3.3
3.4
3.5
3.5.1
3.5.2
MULTIPLE
INTEGRALS
*
145
DEFINITION
AND
PROPERTIES
*
145
DOUBLE
INTEGRALS
IN
RECTANGULAR
COORDINATES
*
150
DOUBLE
INTEGRAL
IN
POLAR
COORDINATES
*
157
CHANGE
OF
VARIABLES
FORMULA
FOR
DOUBLE
INTEGRALS
*
161
TRIPLE
INTEGRALS
*
165
TRIPLE
INTEGRALS
IN
RECTANGULAR
COORDINATES
-----
165
CYLINDRICAL
AND
SPHERICAL
COORDINATES
*
175
CONTENTS
*
VII
3.6
3.7
3.7.1
3.7.2
3.8
3.9
3.9.1
3.9.2
3.9.3
CHANGE
OF
VARIABLES
IN
TRIPLE
INTEGRALS
*
179
OTHER
APPLICATIONS
OF
MULTIPLE
INTEGRALS
*
181
SURFACE
AREA
*
181
CENTER
OF
MASS,
MOMENT
OF
INERTIA
*
187
REVIEW
-----
188
EXERCISES
*
191
DOUBLE
INTEGRALS
*
191
TRIPLE
INTEGRALS
*
192
OTHER
APPLICATIONS
OF
MULTIPLE
INTEGRALS
*
193
4
4.1
4.1.1
4.1.2
4.1.3
4.2
4.2.1
4.2.2
4.3
4.4
4.4.1
4.4.2
4.4.3
4.4.4
4.4.5
4.5
4.5.1
4.5.2
4.5.3
4.6
4.7
4.8
4.8.1
4.8.2
4.9
4.9.1
4.9.2
4.10
4.10.1
4.10.2
4.11
LINE
AND
SURFACE
INTEGRALS
*
195
LINE
INTEGRAL
WITH
RESPECT
TO
ARC
LENGTH
*
195
DEFINITION
AND
PROPERTIES
*
196
EVALUATING
A
LINE
INTEGRAL,
$
C
F(X,Y)DS,
IN
R
2
*
197
LINE
INTEGRALS
J
C
F(X,Y,Z)DS
IN
R
3
*
199
LINE
INTEGRAL
OF
A
VECTOR
FIELD
*
201
VECTOR
FIELDS
*
201
THE
LINE
INTEGRAL
OF
A
VECTOR
FIELD
ALONG
A
CURVE
C
*
202
THE
FUNDAMENTAL
THEOREM
OF
LINE
INTEGRALS
*
208
GREEN
*
S
THEOREM:
CIRCULATION-CURL
FORM
*
216
POSITIVE
ORIENTED
SIMPLE
CURVE
AND
SIMPLY
CONNECTED
REGION
*
216
CIRCULATION
AROUND
A
CLOSED
CURVE
*
217
CIRCULATION
DENSITY
*
217
GREEN
*
S
THEOREM:
CIRCULATION-CURL
FORM
*
219
APPLICATIONS
OF
GREEN
*
S
THEOREM
IN
CIRCULATION-CURL
FORM
*
222
GREEN
*
S
THEOREM:
FLUX-DIVERGENCE
FORM
*
231
FLUX
-----
231
FLUX
DENSITY
-
DIVERGENCE
*
232
THE
DIVERGENCE-FLUX
FORM
OF
GREEN
*
S
THEOREM
*
233
SOURCE-FREE
VECTOR
FIELDS
*
235
SURFACE
INTEGRAL
WITH
RESPECT
TO
SURFACE
AREA
*
237
SURFACE
INTEGRALS
OF
VECTOR
FIELDS
*
241
ORIENTABLE
SURFACES
*
241
FLUX
INTEGRAL
JJ
S
(F
-
N)DS
-----
242
DIVERGENCE
THEOREM
*
248
DIVERGENCE
OF
A
THREE-DIMENSIONAL
VECTOR
FIELD
*
248
DIVERGENCE
THEOREM
*
250
STOKES
THEOREM
*
256
THE
CURL
OF
A
THREE-DIMENSIONAL
VECTOR
FIELD
*
256
STOKES
THEOREM
*
258
REVIEW
*
265
VIII
CONTENTS
FURTHER
READING
*
319
4.12
4.12.1
4.12.2
EXERCISES
*
268
LINE
INTEGRALS
*
268
SURFACE
INTEGRALS
*
269
5
5.1
5.2
5.2.1
5.2.2
5.2.3
5.2.4
5.2.5
5.3
5.3.1
5.3.2
5.3.3
5.4
5.4.1
5.4.2
5.5
5.6
5.6.1
5.6.2
5.6.3
INTRODUCTION
TO
ORDINARY
DIFFERENTIAL
EQUATIONS
*
273
INTRODUCTION
*
273
FIRST-ORDER
ODES
*
275
GENERAL
AND
PARTICULAR
SOLUTIONS
AND
DIRECTION
FIELDS
*
275
SEPARABLE
DIFFERENTIAL
EQUATIONS
*
277
SUBSTITUTION
METHODS
*
279
EXACT
DIFFERENTIAL
EQUATIONS
*
281
FIRST-ORDER
LINEAR
DIFFERENTIAL
EQUATIONS
*
283
SECOND-ORDER
ODES
*
287
REDUCIBLE
SECOND-ORDER
EQUATIONS
*
287
SECOND-ORDER
LINEAR
DIFFERENTIAL
EQUATIONS
*
291
VARIATION
OF
PARAMETERS
*
307
OTHER
WAYS
OF
SOLVING
DIFFERENTIAL
EQUATIONS
*
308
POWER
SERIES
METHOD
*
309
NUMERICAL
APPROXIMATION:
EULER
*
S
METHOD
*
310
REVIEW
*
313
EXERCISES
*
315
INTRODUCTION
TO
DIFFERENTIAL
EQUATIONS
*
315
FIRST-ORDER
DIFFERENTIAL
EQUATIONS
*
315
SECOND-ORDER
DIFFERENTIAL
EQUATIONS
*
316
INDEX
*
321
|
| adam_txt |
CONTENTS
INTRODUCTION
*
IX
1
1.1
1.1.1
1.1.2
1.1.3
1.1.4
1.1.5
1.2
1.2.1
1.2.2
1.2.3
1.2.4
1.3
1.3.1
1.3.2
1.4
1.5
1.5.1
1.5.2
1.5.3
1.6
1.6.1
1.6.2
1.6.3
1.6.4
1.7
1.8
1.9
1.10
1.11
1.11.1
1.11.2
1.11.3
VECTORS
AND
THE
GEOMETRY
OF
SPACE
*
1
VECTORS
*
1
CONCEPTS
OF
VECTORS
*
1
LINEAR
OPERATIONS
INVOLVING
VECTORS
*
2
COORDINATE
SYSTEMS
IN
THREE-DIMENSIONAL
SPACE
*
3
REPRESENTING
VECTORS
USING
COORDINATES
*
5
LENGTHS,
DIRECTION
ANGLES
*
7
DOT
PRODUCT,
CROSS
PRODUCT,
AND
TRIPLE
PRODUCT
*
9
THE
DOT
PRODUCT
-----
9
PROJECTIONS
*
12
THE
CROSS
PRODUCT
*
13
SCALAR
TRIPLE
PRODUCT
-----
17
EQUATIONS
OF
LINES
AND
PLANES
*
18
LINES
-----
18
PLANES
-----
23
CURVES
AND
VECTOR-VALUED
FUNCTIONS
*
30
CALCULUS
OF
VECTOR-VALUED
FUNCTIONS
*
32
LIMITS,
DERIVATIVES,
AND
TANGENT
VECTORS
*
32
ANTIDERIVATIVES
AND
DEFINITE
INTEGRALS
*
35
LENGTH
OF
CURVES,
CURVATURES,
TNB
FRAME
-----
37
SURFACES
IN
SPACE
-----
42
GRAPH
OF
AN
EQUATION
F(X,Y,Z)
=
0
-----
42
CYLINDER
-----44
QUADRIC
SURFACES
-----
46
SURFACE
OF
REVOLUTION
*
46
PARAMETERIZED
SURFACES
*
49
INTERSECTING
SURFACES
AND
PROJECTION
CURVES
*
50
REGIONS
BOUNDED
BY
SURFACES
*
56
REVIEW
-----
57
EXERCISES
-----
59
VECTORS
*
59
LINES
AND
PLANES
IN
SPACE
*
60
CURVES
AND
SURFACES
IN
SPACE
*
61
2
2.1
2.1.1
2.1.2
FUNCTIONS
OF
MULTIPLE
VARIABLES
*
65
FUNCTIONS
OF
MULTIPLE
VARIABLES
*
65
DEFINITIONS
-----
65
GRAPHS
AND
LEVEL
CURVES
*
67
V!
*
CONTENTS
2.1.3
2.1.4
2.1.5
2.2
2.2.1
2.2.2
2.2.3
2.3
2.3.1
2.3.2
2.3.3
2.4
2.4.1
2.4.2
2.4.3
2.5
2.6
2.6.1
2.6.2
2.7
2.7.1
2.7.2
2.8
2.9
2.9.1
2.9.2
2.10
2.11
2.11.1
2.11.2
2.11.3
2.11.4
2.11.5
FUNCTIONS
OF
MORE
THAN
TWO
VARIABLES
*
69
LIMITS
-----
70
CONTINUITY
-----
75
PARTIAL
DERIVATIVES
*
76
DEFINITION
-----
76
INTERPRETATIONS
OF
PARTIAL
DERIVATIVES
*
80
PARTIAL
DERIVATIVES
OF
HIGHER
ORDER
*
82
TOTAL
DIFFERENTIAL
*
83
LINEARIZATION
AND
DIFFERENTIABILITY
*
83
THE
TOTAL
DIFFERENTIAL
*
89
THE
LINEAR/DIFFERENTIAL
APPROXIMATION
-----
90
THE
CHAIN
RULE
-----
92
THE
CHAIN
RULE
WITH
ONE
INDEPENDENT
VARIABLE
*
92
THE
CHAIN
RULE
WITH
MORE
THAN
ONE
INDEPENDENT
VARIABLE
*
94
PARTIAL
DERIVATIVES
FOR
ABSTRACT
FUNCTIONS
*
97
THE
TAYLOR
EXPANSION
-----
98
IMPLICIT
DIFFERENTIATION
-----
101
FUNCTIONS
IMPLICITLY
DEFINED
BY
A
SINGLE
EQUATION
*
101
FUNCTIONS
DEFINED
IMPLICITLY
BY
SYSTEMS
OF
EQUATIONS
*
103
TANGENT
LINES
AND
TANGENT
PLANES
*
106
TANGENT
LINES
AND
NORMAL
PLANES
TO
A
CURVE
*
106
TANGENT
PLANES
AND
NORMAL
LINES
TO
A
SURFACE
*
109
DIRECTIONAL
DERIVATIVES
AND
GRADIENT
VECTORS
*
113
MAXIMUM
AND
MINIMUM
VALUES
*
122
EXTREMA
OF
FUNCTIONS
OF
TWO
VARIABLES
*
122
LAGRANGE
MULTIPLIERS
*
130
REVIEW
-----
136
EXERCISES
-----
138
FUNCTIONS
OF
TWO
VARIABLES
*
138
PARTIAL
DERIVATIVES
AND
DIFFERENTIABILITY
*
139
CHAIN
RULESAND
IMPLICIT
DIFFERENTIATION
-----
140
TANGENT
LINES/PLANES,
DIRECTIONAL
DERIVATIVES
*
141
MAXIMUM/MINIMUM
PROBLEMS
*
142
3
3.1
3.2
3.3
3.4
3.5
3.5.1
3.5.2
MULTIPLE
INTEGRALS
*
145
DEFINITION
AND
PROPERTIES
*
145
DOUBLE
INTEGRALS
IN
RECTANGULAR
COORDINATES
*
150
DOUBLE
INTEGRAL
IN
POLAR
COORDINATES
*
157
CHANGE
OF
VARIABLES
FORMULA
FOR
DOUBLE
INTEGRALS
*
161
TRIPLE
INTEGRALS
*
165
TRIPLE
INTEGRALS
IN
RECTANGULAR
COORDINATES
-----
165
CYLINDRICAL
AND
SPHERICAL
COORDINATES
*
175
CONTENTS
*
VII
3.6
3.7
3.7.1
3.7.2
3.8
3.9
3.9.1
3.9.2
3.9.3
CHANGE
OF
VARIABLES
IN
TRIPLE
INTEGRALS
*
179
OTHER
APPLICATIONS
OF
MULTIPLE
INTEGRALS
*
181
SURFACE
AREA
*
181
CENTER
OF
MASS,
MOMENT
OF
INERTIA
*
187
REVIEW
-----
188
EXERCISES
*
191
DOUBLE
INTEGRALS
*
191
TRIPLE
INTEGRALS
*
192
OTHER
APPLICATIONS
OF
MULTIPLE
INTEGRALS
*
193
4
4.1
4.1.1
4.1.2
4.1.3
4.2
4.2.1
4.2.2
4.3
4.4
4.4.1
4.4.2
4.4.3
4.4.4
4.4.5
4.5
4.5.1
4.5.2
4.5.3
4.6
4.7
4.8
4.8.1
4.8.2
4.9
4.9.1
4.9.2
4.10
4.10.1
4.10.2
4.11
LINE
AND
SURFACE
INTEGRALS
*
195
LINE
INTEGRAL
WITH
RESPECT
TO
ARC
LENGTH
*
195
DEFINITION
AND
PROPERTIES
*
196
EVALUATING
A
LINE
INTEGRAL,
$
C
F(X,Y)DS,
IN
R
2
*
197
LINE
INTEGRALS
J
C
F(X,Y,Z)DS
IN
R
3
*
199
LINE
INTEGRAL
OF
A
VECTOR
FIELD
*
201
VECTOR
FIELDS
*
201
THE
LINE
INTEGRAL
OF
A
VECTOR
FIELD
ALONG
A
CURVE
C
*
202
THE
FUNDAMENTAL
THEOREM
OF
LINE
INTEGRALS
*
208
GREEN
*
S
THEOREM:
CIRCULATION-CURL
FORM
*
216
POSITIVE
ORIENTED
SIMPLE
CURVE
AND
SIMPLY
CONNECTED
REGION
*
216
CIRCULATION
AROUND
A
CLOSED
CURVE
*
217
CIRCULATION
DENSITY
*
217
GREEN
*
S
THEOREM:
CIRCULATION-CURL
FORM
*
219
APPLICATIONS
OF
GREEN
*
S
THEOREM
IN
CIRCULATION-CURL
FORM
*
222
GREEN
*
S
THEOREM:
FLUX-DIVERGENCE
FORM
*
231
FLUX
-----
231
FLUX
DENSITY
-
DIVERGENCE
*
232
THE
DIVERGENCE-FLUX
FORM
OF
GREEN
*
S
THEOREM
*
233
SOURCE-FREE
VECTOR
FIELDS
*
235
SURFACE
INTEGRAL
WITH
RESPECT
TO
SURFACE
AREA
*
237
SURFACE
INTEGRALS
OF
VECTOR
FIELDS
*
241
ORIENTABLE
SURFACES
*
241
FLUX
INTEGRAL
JJ
S
(F
-
N)DS
-----
242
DIVERGENCE
THEOREM
*
248
DIVERGENCE
OF
A
THREE-DIMENSIONAL
VECTOR
FIELD
*
248
DIVERGENCE
THEOREM
*
250
STOKES
THEOREM
*
256
THE
CURL
OF
A
THREE-DIMENSIONAL
VECTOR
FIELD
*
256
STOKES
THEOREM
*
258
REVIEW
*
265
VIII
CONTENTS
FURTHER
READING
*
319
4.12
4.12.1
4.12.2
EXERCISES
*
268
LINE
INTEGRALS
*
268
SURFACE
INTEGRALS
*
269
5
5.1
5.2
5.2.1
5.2.2
5.2.3
5.2.4
5.2.5
5.3
5.3.1
5.3.2
5.3.3
5.4
5.4.1
5.4.2
5.5
5.6
5.6.1
5.6.2
5.6.3
INTRODUCTION
TO
ORDINARY
DIFFERENTIAL
EQUATIONS
*
273
INTRODUCTION
*
273
FIRST-ORDER
ODES
*
275
GENERAL
AND
PARTICULAR
SOLUTIONS
AND
DIRECTION
FIELDS
*
275
SEPARABLE
DIFFERENTIAL
EQUATIONS
*
277
SUBSTITUTION
METHODS
*
279
EXACT
DIFFERENTIAL
EQUATIONS
*
281
FIRST-ORDER
LINEAR
DIFFERENTIAL
EQUATIONS
*
283
SECOND-ORDER
ODES
*
287
REDUCIBLE
SECOND-ORDER
EQUATIONS
*
287
SECOND-ORDER
LINEAR
DIFFERENTIAL
EQUATIONS
*
291
VARIATION
OF
PARAMETERS
*
307
OTHER
WAYS
OF
SOLVING
DIFFERENTIAL
EQUATIONS
*
308
POWER
SERIES
METHOD
*
309
NUMERICAL
APPROXIMATION:
EULER
*
S
METHOD
*
310
REVIEW
*
313
EXERCISES
*
315
INTRODUCTION
TO
DIFFERENTIAL
EQUATIONS
*
315
FIRST-ORDER
DIFFERENTIAL
EQUATIONS
*
315
SECOND-ORDER
DIFFERENTIAL
EQUATIONS
*
316
INDEX
*
321 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Zou, Yunzhi |
| author_GND | (DE-588)1155862910 |
| author_facet | Zou, Yunzhi |
| author_role | aut |
| author_sort | Zou, Yunzhi |
| author_variant | y z yz |
| building | Verbundindex |
| bvnumber | BV046727532 |
| classification_rvk | SK 490 |
| ctrlnum | (OCoLC)1121493890 (DE-599)DNB1195794843 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02510nam a2200589 c 4500</leader><controlfield tag="001">BV046727532</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20221115 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">200519s2020 gw a||| |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">1195794843</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783110674149</subfield><subfield code="c">Broschur</subfield><subfield code="9">978-3-11-067414-9</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3110674149</subfield><subfield code="9">3-11-067414-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1121493890</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DNB1195794843</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">XA-DE-BE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-634</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515</subfield><subfield code="2">23/ger</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 490</subfield><subfield code="0">(DE-625)143242:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">510</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Zou, Yunzhi</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1155862910</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Multi-variable calculus</subfield><subfield code="b">a first step</subfield><subfield code="c">Yunzhi Zou</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin ; Boston</subfield><subfield code="b">De Gruyter</subfield><subfield code="c">[2020]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2020</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XI, 323 Seiten</subfield><subfield code="b">Illustrationen, Diagramme (teilweise farbig)</subfield><subfield code="c">24 cm, 564 g</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">De Gruyter textbook</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Gewöhnliche Differentialgleichung</subfield><subfield code="0">(DE-588)4020929-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Integralrechnung</subfield><subfield code="0">(DE-588)4027232-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mehrere Variable</subfield><subfield code="0">(DE-588)4277015-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Analysis</subfield><subfield code="0">(DE-588)4001865-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Vektorrechnung</subfield><subfield code="0">(DE-588)4062471-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">TB: Textbook</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4123623-3</subfield><subfield code="a">Lehrbuch</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Analysis</subfield><subfield code="0">(DE-588)4001865-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Mehrere Variable</subfield><subfield code="0">(DE-588)4277015-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Vektorrechnung</subfield><subfield code="0">(DE-588)4062471-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Integralrechnung</subfield><subfield code="0">(DE-588)4027232-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="2"><subfield code="a">Gewöhnliche Differentialgleichung</subfield><subfield code="0">(DE-588)4020929-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="710" ind1="2" ind2=" "><subfield code="a">Walter de Gruyter GmbH & Co. KG</subfield><subfield code="0">(DE-588)10095502-2</subfield><subfield code="4">pbl</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe, PDF</subfield><subfield code="z">978-3-11-067437-8</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe, EPUB</subfield><subfield code="z">978-3-11-067443-9</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">X:MVB</subfield><subfield code="u">http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110674149&searchTitles=true</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">B:DE-101</subfield><subfield code="q">application/pdf</subfield><subfield code="u">https://d-nb.info/1195794843/04</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">DNB Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032137643&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-032137643</subfield></datafield></record></collection> |
| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV046727532 |
| illustrated | Illustrated |
| index_date | 2024-07-03T14:35:41Z |
| indexdate | 2024-07-10T08:52:12Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110674149 3110674149 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032137643 |
| oclc_num | 1121493890 |
| open_access_boolean | |
| owner | DE-634 DE-706 DE-83 DE-703 DE-11 |
| owner_facet | DE-634 DE-706 DE-83 DE-703 DE-11 |
| physical | XI, 323 Seiten Illustrationen, Diagramme (teilweise farbig) 24 cm, 564 g |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter textbook |
| spelling | Zou, Yunzhi Verfasser (DE-588)1155862910 aut Multi-variable calculus a first step Yunzhi Zou Berlin ; Boston De Gruyter [2020] © 2020 XI, 323 Seiten Illustrationen, Diagramme (teilweise farbig) 24 cm, 564 g txt rdacontent n rdamedia nc rdacarrier De Gruyter textbook Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Integralrechnung (DE-588)4027232-1 gnd rswk-swf Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Vektorrechnung (DE-588)4062471-7 gnd rswk-swf TB: Textbook (DE-588)4123623-3 Lehrbuch gnd-content Analysis (DE-588)4001865-9 s Mehrere Variable (DE-588)4277015-4 s DE-604 Vektorrechnung (DE-588)4062471-7 s Integralrechnung (DE-588)4027232-1 s Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-067437-8 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-067443-9 X:MVB http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110674149&searchTitles=true B:DE-101 application/pdf https://d-nb.info/1195794843/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032137643&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zou, Yunzhi Multi-variable calculus a first step Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Integralrechnung (DE-588)4027232-1 gnd Mehrere Variable (DE-588)4277015-4 gnd Analysis (DE-588)4001865-9 gnd Vektorrechnung (DE-588)4062471-7 gnd |
| subject_GND | (DE-588)4020929-5 (DE-588)4027232-1 (DE-588)4277015-4 (DE-588)4001865-9 (DE-588)4062471-7 (DE-588)4123623-3 |
| title | Multi-variable calculus a first step |
| title_auth | Multi-variable calculus a first step |
| title_exact_search | Multi-variable calculus a first step |
| title_exact_search_txtP | Multi-variable calculus a first step |
| title_full | Multi-variable calculus a first step Yunzhi Zou |
| title_fullStr | Multi-variable calculus a first step Yunzhi Zou |
| title_full_unstemmed | Multi-variable calculus a first step Yunzhi Zou |
| title_short | Multi-variable calculus |
| title_sort | multi variable calculus a first step |
| title_sub | a first step |
| topic | Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Integralrechnung (DE-588)4027232-1 gnd Mehrere Variable (DE-588)4277015-4 gnd Analysis (DE-588)4001865-9 gnd Vektorrechnung (DE-588)4062471-7 gnd |
| topic_facet | Gewöhnliche Differentialgleichung Integralrechnung Mehrere Variable Analysis Vektorrechnung Lehrbuch |
| url | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110674149&searchTitles=true https://d-nb.info/1195794843/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032137643&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT zouyunzhi multivariablecalculusafirststep AT walterdegruytergmbhcokg multivariablecalculusafirststep |
Es ist kein Print-Exemplar vorhanden.
Inhaltsverzeichnis