Calculus of several variables:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
Springer
1987
|
| Edition: | 3. ed. |
| Series: | Undergraduate texts in mathematics
|
| Subjects: | |
| Online Access: | Publisher description Table of contents only Inhaltsverzeichnis |
| Physical Description: | Getr. Zählung (XII, 503, [95] S.) zahlr. graph. Darst. |
| ISBN: | 0387964053 3540964053 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804116655623634944 |
|---|---|
| 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 VECTCFR 17
§5. PARAMETRIC LINES . . 32
§6. PLANES 36
§7. THE GROSS 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
HTTP://D-NB.INFO/870642979
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 A1
INDEX II
|
| 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 |
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| building | Verbundindex |
| bvnumber | BV002200286 |
| callnumber-first | Q - Science |
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| callnumber-raw | QA303 .L256 1987 |
| callnumber-search | QA303 .L256 1987 |
| callnumber-sort | QA 3303 L256 41987 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 400 |
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| ctrlnum | (OCoLC)263103727 (DE-599)BVBBV002200286 |
| dewey-full | 515/.84 515.8/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.84 515.8/4 |
| dewey-search | 515/.84 515.8/4 |
| dewey-sort | 3515 284 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV002200286 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:41:58Z |
| institution | BVB |
| isbn | 0387964053 3540964053 |
| language | English |
| lccn | 86017724 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001445340 |
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| physical | Getr. Zählung (XII, 503, [95] S.) zahlr. graph. Darst. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Springer |
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| series2 | Undergraduate texts in mathematics |
| spelling | Lang, Serge 1927-2005 Verfasser (DE-588)119305119 aut Calculus of several variables Serge Lang 3. ed. New York, NY [u.a.] Springer 1987 Getr. Zählung (XII, 503, [95] S.) zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Calculus Functions of several real variables Differentialrechnung (DE-588)4012252-9 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Infinitesimalrechnung (DE-588)4072798-1 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 gnd rswk-swf Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Analysis (DE-588)4001865-9 s Mehrere Variable (DE-588)4277015-4 s DE-604 Funktion Mathematik (DE-588)4071510-3 s Differentialrechnung (DE-588)4012252-9 s Infinitesimalrechnung (DE-588)4072798-1 s text/html http://www.loc.gov/catdir/enhancements/fy0814/86017724-d.html Publisher description text/html http://www.loc.gov/catdir/enhancements/fy0814/86017724-t.html Table of contents only DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001445340&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lang, Serge 1927-2005 Calculus of several variables Calculus Functions of several real variables Differentialrechnung (DE-588)4012252-9 gnd Analysis (DE-588)4001865-9 gnd Infinitesimalrechnung (DE-588)4072798-1 gnd Funktion Mathematik (DE-588)4071510-3 gnd Mehrere Variable (DE-588)4277015-4 gnd |
| subject_GND | (DE-588)4012252-9 (DE-588)4001865-9 (DE-588)4072798-1 (DE-588)4071510-3 (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 | Calculus Functions of several real variables Differentialrechnung (DE-588)4012252-9 gnd Analysis (DE-588)4001865-9 gnd Infinitesimalrechnung (DE-588)4072798-1 gnd Funktion Mathematik (DE-588)4071510-3 gnd Mehrere Variable (DE-588)4277015-4 gnd |
| topic_facet | Calculus Functions of several real variables Differentialrechnung Analysis Infinitesimalrechnung Funktion Mathematik Mehrere Variable |
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