Calculus of several variables:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
New York ; Berlin ; Heidelberg ; London ; Paris ; Tokyo ; Hong K
Springer
1994
|
| Edition: | 3. ed., 3. corr. print. |
| Series: | Undergraduate texts in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 698 S. in getr. Zählung graph. Darst. |
| ISBN: | 3540964053 0387964053 |
Staff View
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| 245 | 1 | 0 | |a Calculus of several variables |c Serge Lang |
| 250 | |a 3. ed., 3. corr. print. | ||
| 264 | 1 | |a New York ; Berlin ; Heidelberg ; London ; Paris ; Tokyo ; Hong K |b Springer |c 1994 | |
| 300 | |a 698 S. in getr. Zählung |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1807502698414604288 |
|---|---|
| adam_text |
CONTENTS
PART
ONE
BASIC
MATERIAL
.
1
CHAPTER
I
VECTORS
.
3
§1.
DEFINITION
OF
POINTS
IN
SPACE
.
3
§2.
LOCATED
VECTORS
.
11
§3.
SCALAR
PRODUCT
.
14
§4.
THE
NORM
OF
A
VECTOR
.
17
§5.
PARAMETRIC
LINES
.
32
§6.
PLANES
.
36
§7.
THE
CROSS
PRODUCT
.
44
CHAPTER
II
DIFFERENTIATION
OF
VECTORS
.
49
§1.
DERIVATIVE
.
49
§2.
LENGTH
OF
CURVES
.
62
CHAPTER
III
FUNCTIONS
OF
SEVERAL
VARIABLES
.
66
§1.
GRAPHS
AND
LEVEL
CURVES
.
66
§2.
PARTIAL
DERIVATIVES
.
70
§3.
DIFFERENTIABILITY
AND
GRADIENT
.
77
§4.
REPEATED
PARTIAL
DERIVATIVES
.
82
X
CONTENTS
CHAPTER
IV
THE
CHAIN
RULE
AND
THE
GRADIENT
.
87
§1.
THE
CHAIN
RULE
.
87
§2.
TANGENT
PLANE
.
92
§3.
DIRECTIONAL
DERIVATIVE
.
99
§4.
FUNCTIONS
DEPENDING
ONLY
ON
THE
DISTANCE
FROM
THE
ORIGIN
.
103
§5.
THE
LAW
OF
CONSERVATION
OF
ENERGY
.
ILL
§6.
FURTHER
TECHNIQUE
IN
PARTIAL
DIFFERENTIATION
.
114
PART
TWO
MAXIMA,
MINIMA,
AND
TAYLOR
'S
FORMULA
.
121
CHAPTER
V
MAXIMUM
AND
MINIMUM
.
123
§1.
CRITICAL
POINTS
.
123
§2.
BOUNDARY
POINTS
.
126
§3.
LAGRANGE
MULTIPLIERS
.
135
CHAPTER
VI
HIGHER
DERIVATIVES
.
143
§1.
THE
FIRST
TWO
TERMS
IN
TAYLOR
'
S
FORMULA
.
143
§2.
THE
QUADRATIC
TERM
AT
CRITICAL
POINTS
.
149
§3.
ALGEBRAIC
STUDY
OF
A
QUADRATIC
FORM
.
155
§4.
PARTIAL
DIFFERENTIAL
OPERATORS
.
162
§5.
THE
GENERAL
EXPRESSION
FOR
TAYLOR
'
S
FORMULA
.
170
APPENDIX.
TAYLOR
'
S
FORMULA
IN
ONE
VARIABLE
.
176
NOTE.
CHAPTER
IX
ON
DOUBLE
INTEGRALS
IS
SELF
CONTAINED,
AND
COULD
BE
COVERED
HERE.
PART
THREE
CURVE
INTEGRALS
AND
DOUBLE
INTEGRALS
.
181
CHAPTER
VII
POTENTIAL
FUNCTIONS
.
183
§1.
EXISTENCE
AND
UNIQUENESS
OF
POTENTIAL
FUNCTIONS
.
184
§2.
LOCAL
EXISTENCE
OF
POTENTIAL
FUNCTIONS
.
188
§3.
AN
IMPORTANT
SPECIAL
VECTOR
FIELD
.
194
§4.
DIFFERENTIATING
UNDER
THE
INTEGRAL
.
198
§5.
PROOF
OF
THE
LOCAL
EXISTENCE
THEOREM
.
201
CHAPTER
VIII
CURVE
INTEGRALS
.
206
§1.
DEFINITION
AND
EVALUATION
OF
CURVE
INTEGRALS
.
207
§2.
THE
REVERSE
PATH
.
217
CONTENTS
XI
§3.
CURVE
INTEGRALS
WHEN
THE
VECTOR
FIELD
HAS
A
POTENTIAL
FUNCTION
.
220
§4.
DEPENDENCE
OF
THE
INTEGRAL
ON
THE
PATH
.
228
CHAPTER
IX
DOUBLE
INTEGRALS
.
233
§1.
DOUBLE
INTEGRALS
.
233
§2.
REPEATED
INTEGRALS
.
242
§3.
POLAR
COORDINATES
.
252
CHAPTER
X
GREEN
'S
THEOREM
.
269
§1.
THE
STANDARD
VERSION
.
269
§2.
THE
DIVERGENCE
AND
THE
ROTATION
OF
A
VECTOR
FIELD
.
280
PART
FOUR
TRIPLE
AND
SURFACE
INTEGRALS
.
291
CHAPTER
XI
TRIPLE
INTEGRALS
.
293
§1.
TRIPLE
INTEGRALS
.
293
§2.
CYLINDRICAL
AND
SPHERICAL
COORDINATES
.
298
§3.
CENTER
OF
MASS
.
313
CHAPTER
XII
SURFACE
INTEGRALS
.
318
§1.
PARAMETRIZATION,
TANGENT
PLANE,
AND
NORMAL
VECTOR
.
318
§2.
SURFACE
AREA
.
325
§3.
SURFACE
INTEGRALS
.
333
§4.
CURL
AND
DIVERGENCE
OF
A
VECTOR
FIELD
.
342
§5.
DIVERGENCE
THEOREM
IN
3-SPACE
.
345
§6.
STOKES
'
THEOREM
.
355
PART
FIVE
MAPPINGS,
INVERSE
MAPPINGS,
AND
CHANGE
OF
VARIABLES
FORMULA
.
365
CHAPTER
XIII
MATRICES
.
367
§1.
MATRICES
.
367
§2.
MULTIPLICATION
OF
MATRICES
.
372
XII
CONTENTS
CHAPTER
XIV
LINEAR
MAPPINGS
.
385
§1.
MAPPINGS
.
385
§2.
LINEAR
MAPPINGS
.
392
§3.
GEOMETRIC
APPLICATIONS
.
398
§4.
COMPOSITION
AND
INVERSE
OF
MAPPINGS
.
404
CHAPTER
XV
DETERMINANTS
.
412
§1.
DETERMINANTS
OF
ORDER
2
.
412
§2.
DETERMINANTS
OF
ORDER
3
.
416
§3.
ADDITIONAL
PROPERTIES
OF
DETERMINANTS
.
420
§4.
INDEPENDENCE
OF
VECTORS
.
428
§5.
DETERMINANT
OF
A
PRODUCT
.
430
§6.
INVERSE
OF
A
MATRIX
.
431
CHAPTER
XVI
APPLICATIONS
TO
FUNCTIONS
OF
SEVERAL
VARIABLES
.
434
§1.
THE
JACOBIAN
MATRIX
.
434
§2.
DIFFERENTIABILITY
.
438
§3.
THE
CHAIN
RULE
.
440
§4.
INVERSE
MAPPINGS
.
443
§5.
IMPLICIT
FUNCTIONS
.
446
§6.
THE
HESSIAN
.
450
CHAPTER
XVII
THE
CHANGE
OF
VARIABLES
FORMULA
.
453
§1.
DETERMINANTS
AS
AREA
AND
VOLUME
.
453
§2.
DILATIONS
.
463
§3.
CHANGE
OF
VARIABLES
FORMULA
IN
TWO
DIMENSIONS
.
469
§4.
APPLICATION
OF
GREEN
'
S
FORMULA
TO
THE
CHANGE
OF
VARIABLES
FORMULA
.
474
§5.
CHANGE
OF
VARIABLES
FORMULA
IN
THREE
DIMENSIONS
.
478
§6.
VECTOR
FIELDS
ON
THE
SPHERE
.
483
APPENDIX
FOURIER
SERIES
.
487
§1.
GENERAL
SCALAR
PRODUCTS
.
487
§2.
COMPUTATION
OF
FOURIER
SERIES
.
494
ANSWERS
.
AL
INDEX
.
IL |
| any_adam_object | 1 |
| author | Lang, Serge 1927-2005 |
| author_GND | (DE-588)119305119 |
| author_facet | Lang, Serge 1927-2005 |
| author_role | aut |
| author_sort | Lang, Serge 1927-2005 |
| author_variant | s l sl |
| building | Verbundindex |
| bvnumber | BV010371580 |
| classification_rvk | SK 400 |
| classification_tum | MAT 263f |
| ctrlnum | (OCoLC)263576933 (DE-599)BVBBV010371580 |
| discipline | Mathematik |
| edition | 3. ed., 3. corr. print. |
| format | Book |
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| id | DE-604.BV010371580 |
| illustrated | Illustrated |
| indexdate | 2024-08-16T00:41:39Z |
| institution | BVB |
| isbn | 3540964053 0387964053 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006905010 |
| oclc_num | 263576933 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-11 DE-188 DE-91G DE-BY-TUM |
| owner_facet | DE-91 DE-BY-TUM DE-11 DE-188 DE-91G DE-BY-TUM |
| physical | 698 S. in getr. Zählung graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| series2 | Undergraduate texts in mathematics |
| spelling | Lang, Serge 1927-2005 Verfasser (DE-588)119305119 aut Calculus of several variables Serge Lang 3. ed., 3. corr. print. New York ; Berlin ; Heidelberg ; London ; Paris ; Tokyo ; Hong K Springer 1994 698 S. in getr. Zählung graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Infinitesimalrechnung (DE-588)4072798-1 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Differentialrechnung (DE-588)4012252-9 gnd rswk-swf Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Infinitesimalrechnung (DE-588)4072798-1 s Mehrere Variable (DE-588)4277015-4 s DE-604 Analysis (DE-588)4001865-9 s Differentialrechnung (DE-588)4012252-9 s 1\p DE-604 Funktion Mathematik (DE-588)4071510-3 s 2\p DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006905010&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lang, Serge 1927-2005 Calculus of several variables Infinitesimalrechnung (DE-588)4072798-1 gnd Funktion Mathematik (DE-588)4071510-3 gnd Analysis (DE-588)4001865-9 gnd Differentialrechnung (DE-588)4012252-9 gnd Mehrere Variable (DE-588)4277015-4 gnd |
| subject_GND | (DE-588)4072798-1 (DE-588)4071510-3 (DE-588)4001865-9 (DE-588)4012252-9 (DE-588)4277015-4 |
| title | Calculus of several variables |
| title_auth | Calculus of several variables |
| title_exact_search | Calculus of several variables |
| title_full | Calculus of several variables Serge Lang |
| title_fullStr | Calculus of several variables Serge Lang |
| title_full_unstemmed | Calculus of several variables Serge Lang |
| title_short | Calculus of several variables |
| title_sort | calculus of several variables |
| topic | Infinitesimalrechnung (DE-588)4072798-1 gnd Funktion Mathematik (DE-588)4071510-3 gnd Analysis (DE-588)4001865-9 gnd Differentialrechnung (DE-588)4012252-9 gnd Mehrere Variable (DE-588)4277015-4 gnd |
| topic_facet | Infinitesimalrechnung Funktion Mathematik Analysis Differentialrechnung Mehrere Variable |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006905010&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT langserge calculusofseveralvariables |