Muutke küpsiste eelistusi

E-raamat: Linear Algebra and Analytic Geometry for Physical Sciences

,
Teised raamatud teemal:
  • Formaat - EPUB+DRM
  • Hind: 67,91 €*
  • * hind on lõplik, st. muud allahindlused enam ei rakendu
  • Lisa ostukorvi
  • Lisa soovinimekirja
  • See e-raamat on mõeldud ainult isiklikuks kasutamiseks. E-raamatuid ei saa tagastada.
Linear Algebra and Analytic Geometry for Physical SciencesSuurem pilt
Teised raamatud teemal:

DRM piirangud

  • Kopeerimine (copy/paste):

    ei ole lubatud

  • Printimine:

    ei ole lubatud

  • Kasutamine:

    Digitaalõiguste kaitse (DRM)
    Kirjastus on väljastanud selle e-raamatu krüpteeritud kujul, mis tähendab, et selle lugemiseks peate installeerima spetsiaalse tarkvara. Samuti peate looma endale  Adobe ID Rohkem infot siin. E-raamatut saab lugeda 1 kasutaja ning alla laadida kuni 6'de seadmesse (kõik autoriseeritud sama Adobe ID-ga).

    Vajalik tarkvara
    Mobiilsetes seadmetes (telefon või tahvelarvuti) lugemiseks peate installeerima selle tasuta rakenduse: PocketBook Reader (iOS / Android)

    PC või Mac seadmes lugemiseks peate installima Adobe Digital Editionsi (Seeon tasuta rakendus spetsiaalselt e-raamatute lugemiseks. Seda ei tohi segamini ajada Adober Reader'iga, mis tõenäoliselt on juba teie arvutisse installeeritud )

    Seda e-raamatut ei saa lugeda Amazon Kindle's. 

A self-contained introduction to finite dimensional vector spaces, matrices, systems of linear equations, spectral analysis on euclidean and hermitian spaces, affine euclidean geometry, quadratic forms and conic sections. 
The mathematical formalism is motivated and introduced by problems from physics, notably mechanics (including celestial) and electro-magnetism, with more than two hundreds examples and solved exercises.
Topics include: The group of orthogonal transformations on euclidean spaces, in particular rotations, with Euler angles and angular velocity. The rigid body with its inertia matrix. The unitary group. Lie algebras and exponential map. The Dirac’s bra-ket formalism. Spectral theory for self-adjoint endomorphisms on euclidean and hermitian spaces. The Minkowski spacetime from special relativity and the Maxwell equations. Conic sections with the use of eccentricity and Keplerian motions. 
An appendix collects basic algebraic notions like group, ring and field; and complex numbers and integers modulo a prime number.
The book will be useful to students taking a physics or engineer degree for a basic education as well as for students who wish to be competent in the subject and who may want to pursue a post-graduate qualification.

Arvustused

There are over 230 exercises integrated into the text, most with several parts and explained in detail. These exercises also serve as examples. The book contains about 20 figures and several additional examples. This text will interest both beginning and advanced undergraduates studying physics. Summing Up: Recommended. Undergraduates through faculty and professionals. (D. P. Turner, Choice, Vol. 56 (04), December, 2018)

1 Vectors and Coordinate Systems 1(16)
1.1 Applied Vectors
1(4)
1.2 Coordinate Systems
5(4)
1.3 More Vector Operations
9(6)
1.4 Divergence, Rotor, Gradient and Laplacian
15(2)
2 Vector Spaces 17(18)
2.1 Definition and Basic Properties
17(4)
2.2 Vector Subspaces
21(3)
2.3 Linear Combinations
24(4)
2.4 Bases of a Vector Space
28(5)
2.5 The Dimension of a Vector Space
33(2)
3 Euclidean Vector Spaces 35(12)
3.1 Scalar Product, Norm
35(4)
3.2 Orthogonality
39(2)
3.3 Orthonormal Basis
41(4)
3.4 Hermitian Products
45(2)
4 Matrices 47(22)
4.1 Basic Notions
47(6)
4.2 The Rank of a Matrix
53(5)
4.3 Reduced Matrices
58(2)
4.4 Reduction of Matrices
60(6)
4.5 The Trace of a Matrix
66(3)
5 The Determinant 69(10)
5.1 A Multilinear Alternating Mapping
69(5)
5.2 Computing Determinants via a Reduction Procedure
74(3)
5.3 Invertible Matrices
77(2)
6 Systems of Linear Equations 79(18)
6.1 Basic Notions
79(2)
6.2 The Space of Solutions for Reduced Systems
81(3)
6.3 The Space of Solutions for a General Linear System
84(10)
6.4 Homogeneous Linear Systems
94(3)
7 Linear Transformations 97(28)
7.1 Linear Transformations and Matrices
97(7)
7.2 Basic Notions on Maps
104(1)
7.3 Kernel and Image of a Linear Map
104(3)
7.4 Isomorphisms
107(1)
7.5 Computing the Kernel of a Linear Map
108(3)
7.6 Computing the Image of a Linear Map
111(3)
7.7 Injectivity and Surjectivity Criteria
114(2)
7.8 Composition of Linear Maps
116(2)
7.9 Change of Basis in a Vector Space
118(7)
8 Dual Spaces 125(6)
8.1 The Dual of a Vector Space
125(3)
8.2 The Dirac's Bra-Ket Formalism
128(3)
9 Endomorphisms and Diagonalization 131(20)
9.1 Endomorphisms
131(2)
9.2 Eigenvalues and Eigenvectors
133(5)
9.3 The Characteristic Polynomial of an Endomorphism
138(5)
9.4 Diagonalisation of an Endomorphism
143(4)
9.5 The Jordan Normal Form
147(4)
10 Spectral Theorems on Euclidean Spaces 151(22)
10.1 Orthogonal Matrices and Isometries
151(5)
10.2 Self-adjoint Endomorphisms
156(2)
10.3 Orthogonal Projections
158(5)
10.4 The Diagonalization of Self-adjoint Endomorphisms
163(4)
10.5 The Diagonalization of Symmetric Matrices
167(6)
11 Rotations 173(24)
11.1 Skew-Adjoint Endomorphisms
173(5)
11.2 The Exponential of a Matrix
178(2)
11.3 Rotations in Two Dimensions
180(2)
11.4 Rotations in Three Dimensions
182(6)
11.5 The Lie Algebra
188(3)
11.6 The Angular Velocity
191(3)
11.7 Rigid Bodies and Inertia Matrix
194(3)
12 Spectral Theorems on Hermitian Spaces 197(16)
12.1 The Adjoint Endomorphism
197(6)
12.2 Spectral Theory for Normal Endomorphisms
203(4)
12.3 The Unitary Group
207(6)
13 Quadratic Forms 213(22)
13.1 Quadratic Forms on Real Vector Spaces
213(9)
13.2 Quadratic Forms on Complex Vector Spaces
222(2)
13.3 The Minkowski Spacetime
224(5)
13.4 Electro-Magnetism
229(6)
14 Affine Linear Geometry 235(34)
14.1 Affine Spaces
235(4)
14.2 Lines and Planes
239(6)
14.3 General Linear Affine Varieties and Parallelism
245(4)
14.4 The Cartesian Form of Linear Affine Varieties
249(9)
14.5 Intersection of Linear Affine Varieties
258(11)
15 Euclidean Affine Linear Geometry 269(24)
15.1 Euclidean Affine Spaces
269(3)
15.2 Orthogonality Between Linear Affine Varieties
272(4)
15.3 The Distance Between Linear Affine Varieties
276(7)
15.4 Bundles of Lines and of Planes
283(4)
15.5 Symmetries
287(6)
16 Conic Sections 293(36)
16.1 Conic Sections as Geometric Loci
293(5)
16.2 The Equation of a Conic in Matrix Form
298(3)
16.3 Reduction to Canonical Form of a Conic: Translations
301(6)
16.4 Eccentricity: Part 1
307(2)
16.5 Conic Sections and Kepler Motions
309(1)
16.6 Reduction to Canonical Form of a Conic: Rotations
310(8)
16.7 Eccentricity: Part 2
318(5)
16.8 Why Conic Sections
323(6)
Appendix A: Algebraic Structures 329(14)
Index 343
Giovanni Landi is Professor of Mathematical Physics at the University of Trieste. He is a leading expert of noncummutative geometry, and board member of several journals in the field. He has also written the monograph "An Introduction to Noncommutative Spaces and their Geometries" published by Springer (1997). Alessandro Zampini works at the University of Luxemburg, where he gives a course on linear algebra and analytic geometry.
Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
Püsilink: https://www.kriso.ee/db/97833197836116e.html