Vector calculus, linear algebra, and differential forms: a unified approach [1]
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Ithaca, NY
Matrix Ed.
2009
|
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 818 S. graph. Darst. |
| ISBN: | 9780971576650 |
Internformat
MARC
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| 020 | |a 9780971576650 |9 978-0-9715766-5-0 | ||
| 035 | |a (OCoLC)705673408 | ||
| 035 | |a (DE-599)BVBBV036570625 | ||
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| 100 | 1 | |a Hubbard, John H. |d 1946- |e Verfasser |0 (DE-588)113172346 |4 aut | |
| 245 | 1 | 0 | |a Vector calculus, linear algebra, and differential forms |b a unified approach |n [1] |c John Hamal Hubbard ; Barbara Burke Hubbard |
| 264 | 1 | |a Ithaca, NY |b Matrix Ed. |c 2009 | |
| 300 | |a XII, 818 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 700 | 1 | |a Hubbard, Barbara Burke |d 1948- |e Verfasser |0 (DE-588)115406174 |4 aut | |
| 773 | 0 | 8 | |w (DE-604)BV036570620 |g 1 |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020491748&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-020491748 | ||
Datensatz im Suchindex
| _version_ | 1804143152166076416 |
|---|---|
| adam_text | Contents
Preface
xi
Chapter
0
Preliminaries
0.0
Introduction
1
0.1
Reading mathematics
1
0.2
Quantifiers and negation
4
0.3
Set theory
6
0.4
Functions
9
0.5
Real numbers
17
0.6
Infinite sets
22
0.7
Complex numbers
25
Chapter
1
Vectors, matrices, and derivatives
1.0
Introduction
32
1.1
Introducing the actors: points and vectors
33
1.2
Introducing the actors: matrices
42
1.3
Matrix multiplication as a linear transformation
56
1.4
The geometry of Rn
67
1.5
Limits and continuity
84
1.6
Four big theorems
106
1.7
Derivatives in several variables as linear transformations
120
1.8
Rules for computing derivatives
140
1.9
The mean value theorem and criteria for differentiability
148
1.10
Review exercises for chapter
1 155
Chapter
2
Solving equations
2.0
Introduction
161
2.1
The main algorithm: row reduction
162
2.2
Solving equations with row reduction
168
2.3
Matrix inverses and elementary matrices
177
2.4
Linear combinations, span, and linear independence
182
2.5
Kernels, images, and the dimension formula
195
2.6
Abstract vector spaces
211
2.7
Eigenvectors and eigenvalues
222
2.8
Newton s method
232
2.9
Superconvergence
253
2.10
The inverse and implicit function theorems
259
2.11
Review exercises for chapter
2 278
Contents
v
Chapter
3
Manifolds, Taylor polynomials,
quadratic forms, and curvature
3.0
Introduction
284
3.1
Manifolds
285
3.2
Tangent spaces
306
3.3
Taylor polynomials in several variables
314
3.4
Rules for computing Taylor polynomials
326
3.5
Quadratic forms
334
3.6
Classifying critical points of functions
344
3.7
Constrained critical points and
Lagrange
multipliers
351
3.8
Geometry of curves and surfaces
371
3.9
Review exercises for chapter
3 389
Chapter
4
Integration
4.0
Introduction
393
4.1
Defining the integral
394
4.2
Probability and centers of gravity
409
4.3
What functions can be integrated?
423
4.4
Measure zero
430
4.5
Fubini s theorem and iterated integrals
438
4.6
Numerical methods of integration
450
4.7
Other pavings
461
4.8
Determinants
463
4.9
Volumes and determinants
478
4.10
The change of variables formula
485
4.11
Lebesgue integrals
497
4.12
Review exercises for chapter
4 516
Chapter
5
Volumes of manifolds
5.0
Introduction
520
5.1
Parallelograms and their volumes
521
5.2
Parametrizations
524
5.3
Computing volumes of manifolds
532
5.4
Integration and curvature
544
5.5
Fractals and fractional dimension
554
5.6
Review exercises for chapter
5 556
Chapter
6
Forms and vector calculus
6.0
Introduction
558
6.1
Forms on W1
559
6.2
Integrating form fields over parametrized domains
572
6.3
Orientation of manifolds
576
6.4
Integrating forms over oriented manifolds
584
vi
Contents
6.5
Forms in the language of vector calculus
594
6.6
Boundary orientation
606
6.7
The exterior derivative
620
6.8 Grad,
curl,
div,
and all that
627
6.9
The generalized Stokes s theorem
635
6.10
The integral theorems of vector calculus
643
6.11
Electromagnetism
654
6.12
Potentials
667
6.13
Review exercises for chapter
6 678
Appendix: Analysis
A.O Introduction
683
A.I Arithmetic of real numbers
683
A.
2
Cubic and quartic equations
687
A.3 Two results in topology: nested compact sets
and Heine-Borel
692
A.4 Proof of the chain rule
693
A.
5
Proof of Kantorovich s theorem
696
A.
6
Proof of lemma
2.9.5
(superconvergence)
702
A.7 Proof of differentiability of the inverse function
704
A.8 Proof of the implicit function theorem
708
A.9 Proving the equality of crossed
partials
711
A.
10
Functions with many vanishing partial derivatives
712
A.
11
Proving rules for Taylor polynomials; big
О
and little
о
715
A.
12
Taylor s theorem with remainder
720
A.
13
Proving theorem
3.5.3
(completing squares)
725
A.
14
Classifying constrained critical points
726
A.
15
Geometry of curves and surfaces: proofs
730
A.
16
Stirling s formula and proof of the central limit theorem
735
A.
17
Proving Fubini s theorem
740
A.
18
Justifying the use of other pavings
742
A.
19
Results concerning the determinant
745
A.
20
Change of variables formula: a rigorous proof
750
A.21 Justifying volume
0 756
A.22 Lebesgue measure and proofs for Lebesgue integrals
758
A.23 Justifying the change of parametrization
776
A.
24
Computing the exterior derivative
781
A.25 Thepuliback
785
A.26 Proving Stokes s theorem
790
Bibliography
804
Photo credits
805
Index
807
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T22:43:07Z |
| institution | BVB |
| isbn | 9780971576650 |
| language | English |
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| physical | XII, 818 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Matrix Ed. |
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| spelling | Hubbard, John H. 1946- Verfasser (DE-588)113172346 aut Vector calculus, linear algebra, and differential forms a unified approach [1] John Hamal Hubbard ; Barbara Burke Hubbard Ithaca, NY Matrix Ed. 2009 XII, 818 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hubbard, Barbara Burke 1948- Verfasser (DE-588)115406174 aut (DE-604)BV036570620 1 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020491748&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hubbard, John H. 1946- Hubbard, Barbara Burke 1948- Vector calculus, linear algebra, and differential forms a unified approach |
| title | Vector calculus, linear algebra, and differential forms a unified approach |
| title_auth | Vector calculus, linear algebra, and differential forms a unified approach |
| title_exact_search | Vector calculus, linear algebra, and differential forms a unified approach |
| title_full | Vector calculus, linear algebra, and differential forms a unified approach [1] John Hamal Hubbard ; Barbara Burke Hubbard |
| title_fullStr | Vector calculus, linear algebra, and differential forms a unified approach [1] John Hamal Hubbard ; Barbara Burke Hubbard |
| title_full_unstemmed | Vector calculus, linear algebra, and differential forms a unified approach [1] John Hamal Hubbard ; Barbara Burke Hubbard |
| title_short | Vector calculus, linear algebra, and differential forms |
| title_sort | vector calculus linear algebra and differential forms a unified approach |
| title_sub | a unified approach |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020491748&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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