Atjaunināt sīkdatņu piekrišanu

E-grāmata: Mathematics For Physics: An Illustrated Handbook

4.33/5 (3 ratings by Goodreads)
(Crosscoin Ventures, Usa & Hennessey Wellness, Usa)
  • Formāts: 300 pages
  • Izdošanas datums: 27-Nov-2017
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • Valoda: eng
  • ISBN-13: 9789813233935
Citas grāmatas par šo tēmu:
  • Formāts - EPUB+DRM
  • Cena: 38,32 €*
  • * ši ir gala cena, t.i., netiek piemērotas nekādas papildus atlaides
  • Ielikt grozā
  • Pievienot vēlmju sarakstam
  • Šī e-grāmata paredzēta tikai personīgai lietošanai. E-grāmatas nav iespējams atgriezt un nauda par iegādātajām e-grāmatām netiek atmaksāta.
Mathematics For Physics: An Illustrated HandbookPalielināt
  • Formāts: 300 pages
  • Izdošanas datums: 27-Nov-2017
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • Valoda: eng
  • ISBN-13: 9789813233935
Citas grāmatas par šo tēmu:

DRM restrictions

  • Kopēšana (kopēt/ievietot):

    nav atļauts

  • Drukāšana:

    nav atļauts

  • Lietošana:

    Digitālo tiesību pārvaldība (Digital Rights Management (DRM))
    Izdevējs ir piegādājis šo grāmatu šifrētā veidā, kas nozīmē, ka jums ir jāinstalē bezmaksas programmatūra, lai to atbloķētu un lasītu. Lai lasītu šo e-grāmatu, jums ir jāizveido Adobe ID. Vairāk informācijas šeit. E-grāmatu var lasīt un lejupielādēt līdz 6 ierīcēm (vienam lietotājam ar vienu un to pašu Adobe ID).

    Nepieciešamā programmatūra
    Lai lasītu šo e-grāmatu mobilajā ierīcē (tālrunī vai planšetdatorā), jums būs jāinstalē šī bezmaksas lietotne: PocketBook Reader (iOS / Android)

    Lai lejupielādētu un lasītu šo e-grāmatu datorā vai Mac datorā, jums ir nepieciešamid Adobe Digital Editions (šī ir bezmaksas lietotne, kas īpaši izstrādāta e-grāmatām. Tā nav tas pats, kas Adobe Reader, kas, iespējams, jau ir jūsu datorā.)

    Jūs nevarat lasīt šo e-grāmatu, izmantojot Amazon Kindle.

This unique book complements traditional textbooks by providing a visual yet rigorous survey of the mathematics used in theoretical physics beyond that typically covered in undergraduate math and physics courses. The exposition is pedagogical but compact, and the emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions, alternative notations and jargon, and relevant facts and theorems. Special attention is given to detailed figures and geometric viewpoints, some of which would seem to be novel to the literature. Certain topics which are well covered in textbooks, such as historical motivations, proofs and derivations, and tools for practical calculations, are avoided. The primary physical models targeted are general relativity, spinors, and gauge theories, with notable chapters on Riemannian geometry, Clifford algebras, and fiber bundles.
Preface v
Notation ix
1 Mathematical structures 1(4)
1.1 Classifying mathematical concepts
1(1)
1.2 Defining mathematical structures and mappings
2(3)
2 Abstract algebra 5(22)
2.1 Generalizing numbers
5(3)
2.1.1 Groups
6(2)
2.1.2 Rings
8(1)
2.2 Generalizing vectors
8(9)
2.2.1 Inner products of vectors
10(1)
2.2.2 Norms of vectors
11(1)
2.2.3 Multilinear forms on vectors
12(2)
2.2.4 Orthogonality of vectors
14(1)
2.2.5 Algebras: multiplication of vectors
15(1)
2.2.6 Division algebras
16(1)
2.3 Combining algebraic objects
17(5)
2.3.1 The direct product and direct sum
18(1)
2.3.2 The free product
19(1)
2.3.3 The tensor product
20(2)
2.4 Dividing algebraic objects
22(3)
2.4.1 Quotient groups
22(1)
2.4.2 Semidirect products
23(1)
2.4.3 Quotient rings
24(1)
2.4.4 Related constructions and facts
25(1)
2.5 Summary
25(2)
3 Vector algebras 27(24)
3.1 Constructing algebras from a vector space
27(11)
3.1.1 The tensor algebra
27(1)
3.1.2 The exterior algebra
28(2)
3.1.3 Combinatorial notations
30(2)
3.1.4 The Hodge star
32(2)
3.1.5 Graded algebras
34(1)
3.1.6 Clifford algebras
34(2)
3.1.7 Geometric algebra
36(2)
3.2 Tensor algebras on the dual space
38(6)
3.2.1 The structure of the dual space
38(2)
3.2.2 Tensors
40(1)
3.2.3 Tensors as multilinear mappings
40(1)
3.2.4 Abstract index notation
41(2)
3.2.5 Tensors as multi-dimensional arrays
43(1)
3.3 Exterior forms
44(7)
3.3.1 Exterior forms as multilinear mappings
44(1)
3.3.2 Exterior forms as completely anti-symmetric tensors
45(1)
3.3.3 Exterior forms as anti-symmetric arrays
46(1)
3.3.4 The Clifford algebra of the dual space
46(1)
3.3.5 Algebra-valued exterior forms
47(2)
3.3.6 Related constructions and facts
49(2)
4 Topological spaces 51(16)
4.1 Generalizing surfaces
51(4)
4.1.1 Spaces
52(1)
4.1.2 Generalizing dimension
52(1)
4.1.3 Generalizing tangent vectors
53(1)
4.1.4 Existence and uniqueness of additional structure
53(1)
4.1.5 Summary
54(1)
4.2 Generalizing shapes
55(5)
4.2.1 Defining spaces
56(1)
4.2.2 Mapping spaces
57(3)
4.3 Constructing spaces
60(7)
4.3.1 Cell complexes
60(1)
4.3.2 Projective spaces
61(1)
4.3.3 Combining spaces
62(2)
4.3.4 Classifying spaces
64(3)
5 Algebraic topology 67(16)
5.1 Constructing surfaces within a space
68(3)
5.1.1 Simplices
68(1)
5.1.2 Triangulations
69(1)
5.1.3 Orientability
70(1)
5.1.4 Chain complexes
71(1)
5.2 Counting holes that aren't boundaries
71(5)
5.2.1 The homology groups
71(2)
5.2.2 Examples
73(2)
5.2.3 Calculating homology groups
75(1)
5.2.4 Related constructions and facts
75(1)
5.3 Counting the ways a sphere maps to a space
76(7)
5.3.1 The fundamental group
77(2)
5.3.2 The higher homotopy groups
79(1)
5.3.3 Calculating the fundamental group
80(1)
5.3.4 Calculating the higher homotopy groups
80(1)
5.3.5 Related constructions and facts
80(3)
6 Manifolds 83(28)
6.1 Defining coordinates and tangents
84(8)
6.1.1 Coordinates
84(1)
6.1.2 Tangent vectors and differential forms
85(4)
6.1.3 Frames
89(2)
6.1.4 Tangent vectors in terms of frames
91(1)
6.2 Mapping manifolds
92(4)
6.2.1 Diffeomorphisms
92(1)
6.2.2 The differential and pullback
92(2)
6.2.3 Immersions and embeddings
94(1)
6.2.4 Critical points
95(1)
6.3 Derivatives on manifolds
96(11)
6.3.1 Derivations
96(1)
6.3.2 The Lie derivative of a vector field
97(2)
6.3.3 The Lie derivative of an exterior form
99(2)
6.3.4 The exterior derivative of a 1-form
101(3)
6.3.5 The exterior derivative of a k-form
104(2)
6.3.6 Relationships between derivations
106(1)
6.4 Homology on manifolds
107(4)
6.4.1 The Poincare lemma
107(1)
6.4.2 de Rham cohomology
108(1)
6.4.3 Poincare duality
109(2)
7 Lie groups 111(30)
7.1 Combining algebra and geometry
111(2)
7.1.1 Spaces with multiplication of points
111(1)
7.1.2 Vector spaces with topology
112(1)
7.2 Lie groups and Lie algebras
113(6)
7.2.1 The Lie algebra of a Lie group
114(1)
7.2.2 The Lie groups of a Lie algebra
115(1)
7.2.3 Relationships between Lie groups and Lie algebras
116(1)
7.2.4 The universal cover of a Lie group
117(2)
7.3 Matrix groups
119(8)
7.3.1 Lie algebras of matrix groups
119(1)
7.3.2 Linear algebra
120(2)
7.3.3 Matrix groups with real entries
122(1)
7.3.4 Other matrix groups
123(1)
7.3.5 Manifold properties of matrix groups
124(2)
7.3.6 Matrix group terminology in physics
126(1)
7.4 Representations
127(8)
7.4.1 Group actions
128(2)
7.4.2 Group and algebra representations
130(1)
7.4.3 Lie group and Lie algebra representations
131(1)
7.4.4 Combining and decomposing representations
132(2)
7.4.5 Other representations
134(1)
7.5 Classification of Lie groups
135(6)
7.5.1 Compact Lie groups
136(2)
7.5.2 Simple Lie algebras
138(2)
7.5.3 Classifying representations
140(1)
8 Clifford groups 141(20)
8.1 Classification of Clifford algebras
141(8)
8.1.1 Isomorphisms
141(2)
8.1.2 Representations and spinors
143(2)
8.1.3 Pauli and Dirac matrices
145(3)
8.1.4 Chiral decomposition
148(1)
8.2 Clifford groups and representations
149(12)
8.2.1 Reflections
149(1)
8.2.2 Rotations
150(2)
8.2.3 Lie group properties
152(1)
8.2.4 Lorentz transformations
153(3)
8.2.5 Representations in spacetime
156(3)
8.2.6 Spacetime and spinors in geometric algebra
159(2)
9 Riemannian manifolds 161(56)
9.1 Introducing parallel transport of vectors
161(14)
9.1.1 Change of frame
161(1)
9.1.2 The parallel transporter
162(1)
9.1.3 The covariant derivative
163(2)
9.1.4 The connection
165(1)
9.1.5 The covariant derivative in terms of the connection
166(3)
9.1.6 The parallel transporter in terms of the connection
169(1)
9.1.7 Geodesics and normal coordinates
170(2)
9.1.8 Summary
172(3)
9.2 Manifolds with connection
175(19)
9.2.1 The covariant derivative on the tensor algebra
175(2)
9.2.2 The exterior covariant derivative of vector-valued forms
177(2)
9.2.3 The exterior covariant derivative of algebra-valued forms
179(2)
9.2.4 Torsion
181(3)
9.2.5 Curvature
184(3)
9.2.6 First Bianchi identity
187(3)
9.2.7 Second Bianchi identity
190(3)
9.2.8 The holonomy group
193(1)
9.3 Introducing lengths and angles
194(23)
9.3.1 The Riemannian metric
194(2)
9.3.2 The Levi-Civita connection
196(2)
9.3.3 Independent quantities and dependencies
198(1)
9.3.4 The divergence and conserved quantities
199(4)
9.3.5 Ricci and sectional curvature
203(3)
9.3.6 Curvature and geodesics
206(3)
9.3.7 Jacobi fields and volumes
209(3)
9.3.8 Summary
212(3)
9.3.9 Related constructions and facts
215(2)
10 Fiber bundles 217(48)
10.1 Gauge theory
217(5)
10.1.1 Matter fields and gauges
217(1)
10.1.2 The gauge potential and field strength
218(1)
10.1.3 Spinor fields
219(3)
10.2 Defining bundles
222(7)
10.2.1 Fiber bundles
222(3)
10.2.2 G-bundles
225(1)
10.2.3 Principal bundles
226(3)
10.3 Generalizing tangent spaces
229(17)
10.3.1 Associated bundles
229(1)
10.3.2 Vector bundles
230(3)
10.3.3 Frame bundles
233(4)
10.3.4 Gauge transformations on frame bundles
237(4)
10.3.5 Smooth bundles and jets
241(1)
10.3.6 Vertical tangents and horizontal equivariant forms
242(4)
10.4 Generalizing connections
246(13)
10.4.1 Connections on bundles
246(1)
10.4.2 Parallel transport on the frame bundle
247(3)
10.4.3 The exterior covariant derivative on bundles
250(1)
10.4.4 Curvature on principal bundles
251(1)
10.4.5 The tangent bundle and solder form
252(4)
10.4.6 Torsion on the tangent frame bundle
256(1)
10.4.7 Spinor bundles
257(2)
10.5 Characterizing bundles
259(6)
10.5.1 Universal bundles
259(3)
10.5.2 Characteristic classes
262(1)
10.5.3 Related constructions and facts
263(2)
Appendix A Categories and functors 265(4)
A.1 Generalizing sets and mappings
265(1)
A.2 Mapping mappings
266(3)
Bibliography 269(2)
Index 271
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
Permanent link: https://www.kriso.lv/db/97898132339356e.html
Keywords: