Algebra and analysis for engineers and scientists:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2007
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 484 S. graph. Darst. |
| ISBN: | 9780817647063 0817647066 |
Staff View
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Record in the Search Index
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| adam_text | ANTHONY N. MICHEL CHARLES J. HERGET ALGEBRA AND ANALYSIS FOR ENGINEERS
AND SCIENTISTS BIRKHAUSER BOSTON * BASEL * BERLIN CONTENTS PREFACE IX
CHAPTER 1: FUNDAMENTAL CONCEPTS 1 1.1 SETS 1 1.2 FUNCTIONS 12 1.3
RELATIONS AND EQUIVALENCE RELATIONS 25 1.4 OPERATIONS ON SETS 26 1.5
MATHEMATICAL SYSTEMS CONSIDERED IN THIS BOOK 30 1.6 REFERENCES AND NOTES
31 REFERENCES 32 CHAPTER 2: ALGEBRAIC STRUCTURES 33 2.1 SOME BASIC
STRUCTURES OF ALGEBRA 34 A. SEMIGROUPS AND GROUPS 36 B. RINGS AND FIELDS
46 C. MODULES, VECTOR SPACES, AND ALGEBRAS * 53 D. OVERVIEW 61 2.2
HOMOMORPHISMS 62 2.3 APPLICATION TO POLYNOMIALS 69 2.4 REFERENCES AND
NOTES 74 REFERENCES 74 VI CONTENTS CHAPTER 3: VECTOR SPACES AND LINEAR
TRANSFORMATIONS 75 3.1 LINEAR SPACES 75 3.2 LINEAR SUBSPACES AND DIRECT
SUMS 81 3.3 LINEAR INDEPENDENCE, BASES, AND DIMENSION 85 3.4 LINEAR
TRANSFORMATIONS 95 3.5 LINEAR FUNCTIONALS 109 3.6 BILINEAR FUNCTIONALS
113 3.7 PROJECTIONS 119 3.8 NOTES AND REFERENCES 123 REFERENCES 123
CHAPTER 4: FINITE-DIMENSIONAL VECTOR SPACES AND MATRICES 124 4.1
COORDINATE REPRESENTATION OF VECTORS 124 4.2 MATRICES 129 A.
REPRESENTATION OF LINEAR TRANSFORMATIONS BY MATRICES 129 B. RANK OF A
MATRIX 134 C. PROPERTIES OF MATRICES 136 4.3 EQUIVALENCE AND SIMILARITY
148 4.4 DETERMINANTS OF MATRICES 155 4.5 EIGENVALUES AND EIGENVECTORS
163 4.6 SOME CANONICAL FORMS OF MATRICES 169 4.7 MINIMAL POLYNOMIALS,
NILPOTENT OPERATORS AND THE JORDAN CANONICAL FORM 178 A. MINIMAL
POLYNOMIALS 178 B. NILPOTENT OPERATORS 185 C. THE JORDAN CANONICAL FORM
190 4.8 BILINEAR FUNCTIONALS AND CONGRUENCE 194 4.9 EUCLIDEAN VECTOR
SPACES 202 A. EUCLIDEAN SPACES: DEFINITION AND PROPERTIES 202 B.
ORTHOGONAL BASES 209 4.10 LINEAR TRANSFORMATIONS ON EUCLIDEAN
VECTORSPACES 216 A. ORTHOGONAL TRANSFORMATIONS 216 B. ADJOINT
TRANSFORMATIONS 218 C. SELF-ADJOINT TRANSFORMATIONS 221 D. SOME EXAMPLES
227 E. FURTHER PROPERTIES OF ORTHOGONAL TRANSFORMATIONS 231 CONTENTS
4.11 APPLICATIONS TO ORDINARY DIFFERENTIAL EQUATIONS 238 A.
INITIAL-VALUE PROBLEM: DEFINITION 238 B. INITIAL-VALUE PROBLEM: LINEAR
SYSTEMS 244 4.12 NOTES AND REFERENCES 261 REFERENCES 262 CHAPTER 5:
METRIC SPACES 263 5.1 DEFINITION OF METRIC SPACES 264 5.2 SOME
INEQUALITIES 268 5.3 EXAMPLES OF IMPORTANT METRIC SPACES 271 5.4 OPEN
AND CLOSED SETS 275 5.5 COMPLETE METRIC SPACES 286 5.6 COMPACTNESS 298
5.7 CONTINUOUS FUNCTIONS 307 5.8 SOME IMPORTANT RESULTS IN APPLICATIONS
314 5.9 EQUIVALENT AND HOMEOMORPHIC METRIC SPACES. TOPOLOGICAL SPACES
317 5.10 APPLICATIONS 323 A. APPLICATIONS OF THE CONTRACTION MAPPING
PRINCIPLE 323 B. FURTHER APPLICATIONS TO ORDINARY DIFFERENTIAL EQUATIONS
329 5.11 REFERENCES AND NOTES 341 REFERENCES 341 CHAPTER 6: NORMED
SPACES AND INNER PRODUCT SPACES 343 6.1 NORMED LINEAR SPACES 344 6.2
LINEAR SUBSPACES 348 6.3 INFINITE SERIES 350 6.4 CONVEX SETS 351 6.5
LINEAR FUNCTIONALS 355 6.6 FINITE-DIMENSIONAL SPACES 360 ** 6.7
GEOMETRIC ASPECTS OF LINEAR FUNCTIONALS 363 6.8 EXTENSION OF LINEAR
FUNCTIONALS 367 6.9 DUAL SPACE AND SECOND DUAL SPACE 370 6.10 WEAK
CONVERGENCE 372 6.11 INNER PRODUCT SPACES 375 6.12 ORTHOGONAL
COMPLEMENTS 381 VIII CONTENTS 6.13 FOURIER SERIES 387 6.14 THE RIESZ
REPRESENTATION THEOREM 393 6.15 SOME APPLICATIONS 394 A. APPROXIMATION
OF ELEMENTS IN HILBERT SPACE (NORMAL EQUATIONS) 395 B. RANDOM VARIABLES
397 C. ESTIMATION OF RANDOM VARIABLES 398 6.16 NOTES AND REFERENCES 404
REFERENCES 404 CHAPTER 7: LINEAR OPERATORS 406 7.1 BOUNDED LINEAR
TRANSFORMATIONS 407 7.2 INVERSES 415 7.3 CONJUGATE AND ADJOINT OPERATORS
419 7.4 HERMITIAN OPERATORS 427 7.5 OTHER LINEAR OPERATORS: NORMAL
OPERATORS, PROJECTIONS, UNITARY OPERATORS, AND ISOMETRIC OPERATORS 431
7.6 THE SPECTRUM OF AN OPERATOR 439 7.7 COMPLETELY CONTINUOUS OPERATORS
447 7.8 THE SPECTRAL THEOREM FOR COMPLETELY CONTINUOUS NORMAL OPERATORS
454 7.9 DIFFERENTIATION OF OPERATORS 458 7.10 SOME APPLICATIONS 465 A.
APPLICATIONS TO INTEGRAL EQUATIONS 465 B. AN EXAMPLE FROM OPTIMAL
CONTROL 468 C. MINIMIZATION OF FUNCTIONALS: METHOD OF STEEPEST DESCENT
471 7.11 REFERENCES AND NOTES 473 REFERENCES 473 INDEX 475
|
| adam_txt |
ANTHONY N. MICHEL CHARLES J. HERGET ALGEBRA AND ANALYSIS FOR ENGINEERS
AND SCIENTISTS BIRKHAUSER BOSTON * BASEL * BERLIN CONTENTS PREFACE IX
CHAPTER 1: FUNDAMENTAL CONCEPTS 1 1.1 SETS 1 1.2 FUNCTIONS 12 1.3
RELATIONS AND EQUIVALENCE RELATIONS 25 1.4 OPERATIONS ON SETS 26 1.5
MATHEMATICAL SYSTEMS CONSIDERED IN THIS BOOK 30 1.6 REFERENCES AND NOTES
31 REFERENCES 32 CHAPTER 2: ALGEBRAIC STRUCTURES 33 2.1 SOME BASIC
STRUCTURES OF ALGEBRA 34 A. SEMIGROUPS AND GROUPS 36 B. RINGS AND FIELDS
46 C. MODULES, VECTOR SPACES, AND ALGEBRAS *" 53 D. OVERVIEW 61 2.2
HOMOMORPHISMS 62 2.3 APPLICATION TO POLYNOMIALS 69 2.4 REFERENCES AND
NOTES 74 REFERENCES 74 VI CONTENTS CHAPTER 3: VECTOR SPACES AND LINEAR
TRANSFORMATIONS 75 3.1 LINEAR SPACES 75 3.2 LINEAR SUBSPACES AND DIRECT
SUMS 81 3.3 LINEAR INDEPENDENCE, BASES, AND DIMENSION 85 3.4 LINEAR
TRANSFORMATIONS 95 3.5 LINEAR FUNCTIONALS 109 3.6 BILINEAR FUNCTIONALS
113 3.7 PROJECTIONS 119 3.8 NOTES AND REFERENCES 123 REFERENCES 123
CHAPTER 4: FINITE-DIMENSIONAL VECTOR SPACES AND MATRICES 124 4.1
COORDINATE REPRESENTATION OF VECTORS 124 4.2 MATRICES 129 A.
REPRESENTATION OF LINEAR TRANSFORMATIONS BY MATRICES 129 B. RANK OF A
MATRIX 134 C. PROPERTIES OF MATRICES 136 4.3 EQUIVALENCE AND SIMILARITY
148 4.4 DETERMINANTS OF MATRICES 155 4.5 EIGENVALUES AND EIGENVECTORS
163 4.6 SOME CANONICAL FORMS OF MATRICES 169 4.7 MINIMAL POLYNOMIALS,
NILPOTENT OPERATORS AND THE JORDAN CANONICAL FORM 178 A. MINIMAL
POLYNOMIALS 178 B. NILPOTENT OPERATORS 185 C. THE JORDAN CANONICAL FORM
190 4.8 BILINEAR FUNCTIONALS AND CONGRUENCE 194 4.9 EUCLIDEAN VECTOR
SPACES 202 A. EUCLIDEAN SPACES: DEFINITION AND PROPERTIES 202 B.
ORTHOGONAL BASES 209 4.10 LINEAR TRANSFORMATIONS ON EUCLIDEAN
VECTORSPACES 216 A. ORTHOGONAL TRANSFORMATIONS 216 B. ADJOINT
TRANSFORMATIONS 218 C. SELF-ADJOINT TRANSFORMATIONS 221 D. SOME EXAMPLES
227 E. FURTHER PROPERTIES OF ORTHOGONAL TRANSFORMATIONS 231 CONTENTS
4.11 APPLICATIONS TO ORDINARY DIFFERENTIAL EQUATIONS 238 A.
INITIAL-VALUE PROBLEM: DEFINITION 238 B. INITIAL-VALUE PROBLEM: LINEAR
SYSTEMS 244 4.12 NOTES AND REFERENCES 261 REFERENCES 262 CHAPTER 5:
METRIC SPACES 263 5.1 DEFINITION OF METRIC SPACES 264 5.2 SOME
INEQUALITIES 268 5.3 EXAMPLES OF IMPORTANT METRIC SPACES 271 5.4 OPEN
AND CLOSED SETS 275 5.5 COMPLETE METRIC SPACES 286 5.6 COMPACTNESS 298
5.7 CONTINUOUS FUNCTIONS 307 5.8 SOME IMPORTANT RESULTS IN APPLICATIONS
314 5.9 EQUIVALENT AND HOMEOMORPHIC METRIC SPACES. TOPOLOGICAL SPACES
317 5.10 APPLICATIONS 323 A. APPLICATIONS OF THE CONTRACTION MAPPING
PRINCIPLE 323 B. FURTHER APPLICATIONS TO ORDINARY DIFFERENTIAL EQUATIONS
329 5.11 REFERENCES AND NOTES 341 REFERENCES 341 CHAPTER 6: NORMED
SPACES AND INNER PRODUCT SPACES 343 6.1 NORMED LINEAR SPACES 344 6.2
LINEAR SUBSPACES 348 6.3 INFINITE SERIES 350 6.4 CONVEX SETS 351 6.5
LINEAR FUNCTIONALS 355 6.6 FINITE-DIMENSIONAL SPACES 360 ** 6.7
GEOMETRIC ASPECTS OF LINEAR FUNCTIONALS 363 6.8 EXTENSION OF LINEAR
FUNCTIONALS 367 6.9 DUAL SPACE AND SECOND DUAL SPACE 370 6.10 WEAK
CONVERGENCE 372 6.11 INNER PRODUCT SPACES 375 6.12 ORTHOGONAL
COMPLEMENTS 381 VIII CONTENTS 6.13 FOURIER SERIES 387 6.14 THE RIESZ
REPRESENTATION THEOREM 393 6.15 SOME APPLICATIONS 394 A. APPROXIMATION
OF ELEMENTS IN HILBERT SPACE (NORMAL EQUATIONS) 395 B. RANDOM VARIABLES
397 C. ESTIMATION OF RANDOM VARIABLES 398 6.16 NOTES AND REFERENCES 404
REFERENCES 404 CHAPTER 7: LINEAR OPERATORS 406 7.1 BOUNDED LINEAR
TRANSFORMATIONS 407 7.2 INVERSES 415 7.3 CONJUGATE AND ADJOINT OPERATORS
419 7.4 HERMITIAN OPERATORS 427 7.5 OTHER LINEAR OPERATORS: NORMAL
OPERATORS, PROJECTIONS, UNITARY OPERATORS, AND ISOMETRIC OPERATORS 431
7.6 THE SPECTRUM OF AN OPERATOR 439 7.7 COMPLETELY CONTINUOUS OPERATORS
447 7.8 THE SPECTRAL THEOREM FOR COMPLETELY CONTINUOUS NORMAL OPERATORS
454 7.9 DIFFERENTIATION OF OPERATORS 458 7.10 SOME APPLICATIONS 465 A.
APPLICATIONS TO INTEGRAL EQUATIONS 465 B. AN EXAMPLE FROM OPTIMAL
CONTROL 468 C. MINIMIZATION OF FUNCTIONALS: METHOD OF STEEPEST DESCENT
471 7.11 REFERENCES AND NOTES 473 REFERENCES 473 INDEX 475 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.15 |
| dewey-search | 512.15 |
| dewey-sort | 3512.15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| id | DE-604.BV023194230 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:05:49Z |
| indexdate | 2024-07-09T21:12:46Z |
| institution | BVB |
| isbn | 9780817647063 0817647066 |
| language | English |
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| physical | XIV, 484 S. graph. Darst. |
| publishDate | 2007 |
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| publisher | Birkhäuser |
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| spelling | Michel, Anthony N. 1935- Verfasser (DE-588)11087076X aut Mathematical foundations in engineering and science Algebra and analysis for engineers and scientists Anthony N. Michel ; Charles J. Herget Boston [u.a.] Birkhäuser 2007 XIV, 484 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Algebra Textbooks Mathematical analysis Textbooks Analysis (DE-588)4001865-9 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Algebra (DE-588)4001156-2 s DE-604 Analysis (DE-588)4001865-9 s Herget, Charles J. Verfasser aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016380569&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Michel, Anthony N. 1935- Herget, Charles J. Algebra and analysis for engineers and scientists Algebra Textbooks Mathematical analysis Textbooks Analysis (DE-588)4001865-9 gnd Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4001865-9 (DE-588)4001156-2 (DE-588)4123623-3 |
| title | Algebra and analysis for engineers and scientists |
| title_alt | Mathematical foundations in engineering and science |
| title_auth | Algebra and analysis for engineers and scientists |
| title_exact_search | Algebra and analysis for engineers and scientists |
| title_exact_search_txtP | Algebra and analysis for engineers and scientists |
| title_full | Algebra and analysis for engineers and scientists Anthony N. Michel ; Charles J. Herget |
| title_fullStr | Algebra and analysis for engineers and scientists Anthony N. Michel ; Charles J. Herget |
| title_full_unstemmed | Algebra and analysis for engineers and scientists Anthony N. Michel ; Charles J. Herget |
| title_short | Algebra and analysis for engineers and scientists |
| title_sort | algebra and analysis for engineers and scientists |
| topic | Algebra Textbooks Mathematical analysis Textbooks Analysis (DE-588)4001865-9 gnd Algebra (DE-588)4001156-2 gnd |
| topic_facet | Algebra Textbooks Mathematical analysis Textbooks Analysis Algebra Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016380569&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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