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Steeb W.-H. — Problems and Solutions in theoretical and mathematical physics. Volume 1. Introductory level
Steeb W.-H. — Problems and Solutions in theoretical and mathematical physics. Volume 1. Introductory level

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Название: Problems and Solutions in theoretical and mathematical physics. Volume 1. Introductory level

Автор: Steeb W.-H.


This book is a collection of problems with detailed solutions which will prove valuable to students and research workers in mathematics, physics, engineering and other sciences. The topics range in difficulty from elementary to advanced level. Almost all the problems are solved in detail and most of them are self-contained. All relevant definitions are given. Students can learn important principles and strategies required for problem solving. Teachers will find this text useful as a supplement, since important concepts and techniques are developed through the problems. The material has been tested in the author's lectures given around the world.
The book is divided into two volumes. Volume I presents the introductory problems, for undergraduate and advanced undergraduate students. In Volume II, the more advanced problems, together with detailed solutions, are collected, to meet the needs of graduate students and researchers. The problems included cover most of the new fields in theoretical and mathematical physics, such as Lax representation, Bäcklund transformation, soliton equations, Lie-algebra-valued differential forms, the Hirota technique, the Painlevé test, the Bethe ansatz, the Yang-Baxter relation, chaos, fractals, complexity, etc.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 238

Добавлена в каталог: 31.10.2010

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Предметный указатель
Anticommutator      75
Arithmetic mean      196
Bargmann representation      173
Body centered cubic lattice      51
Boundary value problems      130
Cantor series      18
Cauchy sequence      218
Cayley's theorem      54
Chain rule      79
Chaotic behaviour      78
Characteristic function      15
Chebyshev polynomials      32 182
Chordal distance      175
Commutator      29
Complete elliptic integral      183
Concave function      217
Conservation law      138
Constrained extrema      107
Continuous spectrum      73
Contracting mapping      208
Convex function      217
Convex set      215
Cumulant expansion      15
Cusp catastrophe      100
De Moivre's theorem      4 16
Denumerable      102
Discrete Fourier Transform      19 121
Discriminant      99
Displayed harmonic oscillator      173
Distributive law for intersections      213
Driven damped harmonic oscillator      1
Eccentricity      184
Eigenvalue equation      57
ellipse      183
Entire function      173
Face centered cubic lattice      52
Fibonacci numbers      113
Formula of Rodrigues      190
Fourier approximation      26
Fourier expansion      200
Fourier transform      157
Generating functions      117
Geometric mean      196
Geometric series      5
Gibbs inequality      194
Gram — Schmidt algorithm      62
Green's theorem      202
Hamilton's equations of motion      131
Heisenberg equation of motion      49
Hermite polynomial      179
Hermitian matrix      34
Hilbert space      74
Hilbert — Schmidt operator      198
Hypergeometric equation      91
Idempotent law of intersection      213
Imaginary quotient      3
Imaginary remainder      3
Invariant      80
Jacobi identity      35
Kirchhoff's law      119
Kronecker delta      20
L'Hospital rule      103
Lagrange multiplier rule      107
Lagrange multipliers      107
Lagrange's theorem      54
Laurent series      170 227
Lebesgue integral      153
Legendre polynomials      181 190
Legendre transformation      86
Leibniz's rule      185
Line element      183
Linear diffusion equation      93
Logistic map      78
Lorentz transformation      79
Metric tensor field      183
Modified Emden equation      88
Moebius transformation      178
Motion of a charge      126
Nonsingular      29
Order of a finite group      54
Order of an element      54
Orthogonal      60
Parameter differentiation      142
Parseval's equation      162
Pauli matrices      44
Permutation matrices      53
Polar coordinates      141
Principle branch      1
Principle of inclusion and exclusion      213
Principle of Mathematical Induction      16
Product rule      17
Rademacher function      204
Reciprocal basis      51
Residue theorem      166
Ricatti equation      140
Schroedinger equation      138
Separation ansatz      133
Sine-Gordon equation      94
Skew-Hermitian matrix      38
Slack variables      222
Spherical coordinates      136
Spherical distance      175
Step function      143
Stereographic projection      175
Stirling number      122
Summation by parts      111
Tent map      78
Three dimensional wave equation      136
Time-independent Schroedinger equation      133
Unbounded operators      207
Van der Waals equation      98
Variation of constants      127
Walsh function      204
Wave equation      134
Weierstrass function      187
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