Bamberg P.G. — A Course in Mathematics for Students of Physics, Vol. 2 :: Электронная библиотека попечительского совета мехмата МГУ

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Bamberg P.G. — A Course in Mathematics for Students of Physics, Vol. 2

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Название: A Course in Mathematics for Students of Physics, Vol. 2

Автор: Bamberg P.G.

Аннотация:

After the basic theories of differential and integral calculus are explained, they are applied to interesting problems in optics, electronics (networks), electrostatics, wave dynamics and finally, to classical thermodynamics.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1990

Количество страниц: 841

Добавлена в каталог: 29.03.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Absolute temperature      773 780 783
Abstract temperature      777
Adiabatic curve      778
Adiabatic enclosure      772 778
Adiabatic interaction      778
Ampere      408
Ampere’s Law      631 688
antisymmetric      536
Bilinear function      535
Bilinear function, alternating      535
Binomial measure      803
Bose — Einstein statistics      803
Bosons      803
Bott periodicity      685
Boundaries      421
Boundary map      420 503
Boundary operator      415 503
Boundary value problems      474
Boyle’s law      791
Calculus of residues      715
Capacitance      408
Capacitive networks      469
Capacitor      408
Caratheodory’s theorem      771
Caratheodory’s theorem, statement of proof of      771 850
Carnot cycle      784
Cauchy integral formula      719 721
Cauchy principal value      737
Cauchy — Riemann equations      711
Cauchy’s residue theorem      717
Cauchy’s Theorem      710
Causality      691
Chains      419
Change of variables formula      546
chemical potential      799
Circuit theory      407
Circuits, linear passive      408
Classical phase space      804
Clifford algebras      658 673 675
Co-chain      429
Cohomology      520
Commutative diagram      533
Complexes, higher dimensional      502
Conductance      411
Conductivity      615
Configurational variables      777
Contour integrals      735
Coulomb      407
Creation and annihilation operators      657
Current      407
CYCLE      420
D operator      539—541
de Broglie’s formula      762
De Rham cohomology      565
Diathermal contact      775
Dielectric coefficient      596
dielectric constant      599
Dielectric displacement      588
Diode      409
Dirac algebra      600
Dirichlet integral      646
Dirichlet problem      476 591 604
Dirichlet problem, solution      479 608
Dirichlet’s principle      605
Doctrine of latent and specific heat      787
Domain of dependence      691
Domain of influence      691
Einstein’s formula      762
Electric field strength      588
Electrical screening, principle of      592
Electromagnetic Lagrangian      697
Electromotive force      409
Electrostatic energy      600
Electrostatics, equations of      597 599
Empirical temperature      777
Energy momentum tensor      697 700
Enthalpy      792
Entries, to a circuit      467
entropy      773 780 783 797 814
Equilibrium states      775 816 819
Equipotential      593
Essential singularity      729
Euler characteristic      508
Euler’s theorem      508 518
Exterior algebra      535—9
Face      502
Farad      408
Faraday’s law of induction      686
Fermi — Dirac statistics      803
fermions      803
Filter      446
First law of thermodynamics      772 778
Flow      618
Formal transpose      586
Fourier inversion formula      763
Fourier series      743
Fourier transform      763
Fresnel integrals      735
Fundamental formula of differential calculus      628 633
Fundamental theorem of algebra      724
Gamma distribution      822
Gamma function      750
Gas constant      790
Gaussian Integrals      758
Gaussian measure, continuous      804
Gaussian measure, discrete      804
Gauss’ law      471 588
Graph, oriented      419
Green’s formulas      483 601
Green’s functions      482 606
Green’s reciprocity theorem      466 467 487
Group velocity      761
Harmonic functions      602
Heat      778
Helmholtz equation      702
Henry      408
Holomorphic functions      711—5
Homology      505
Homology, invariance      510
Huyghen’s principle      703
Ideal gas      791
Impedance      418
Incoming wave      701
Inductance      408
inductor      408
Intensive variables      800
Interior product      621
Internal energy      772 778 812
Isotherms      778
k-chains      503
k-form      537 539

k-form, closed      564
k-form, exact      564
k-form, integration      541
Kirchhoffs theorem      428 444
Kirchhoff’s current law      411 420 434 615 628
Kirchhoff’s laws      410
Kirchhoff’s tree method      461 463
Kirchhoff’s voltage law      411 429 434
Lagrangian formulation      698
Lagrangian submanifold      794
Lagrangian submanifold, generating function      795
Laplace operator on k-forms      647
Laplace’s equation      473
Laplace’s method      750
Laplace’s principle      755
Laplacian      472 646
Latent heat      787
Laurent expansion      743
Laurent series      743
Lie derivative      626
Lie derivative of a k-form, formula      628
Lie derivative of a k-form, properties      627
Lienard — Wiechert potential      696
Liouville’s theorem      724
Lorentz force      700
Magnetic excitation      631
Magnetic lines of force      630
Magnetism      628
Magnetostatics, laws of      631
Massieu function      796 814
Maximum entropy principle      797
Maxwell — Boltzmann distribution      819
Measure      801
Meromorphic function      717
mesh      415
Mesh current method      416 427 435
Method of images      491
Minimum energy principle      797
Mollier diagram      793
n-complex      503
Networks, electrical      407
Node      413
Node potential method      417 435
Noether’s theorem      698
Normal modes      445
Null curve      769
Observables (in classical statistical mechanics)      808 823
Occupancy      803
Ohm      408
Ohm’s Law      408 615
One-chains      419
One-dimensional complex      419
One-parameter group      618
Orthogonal projection, Weyl’s method of      458 604
Outgoing wave      701
Partition function      814 823
Partition of unity      559 562
Path      415
Permeability      631
Planck function      794
Poincare’s Lemma      568 569
Poisson equation problem      475
Poisson integral formula      608
Poisson kernel      483 485
Poisson’s equation      472
Poisson’s equation, solution      479 607
Pole      717
Power      407
Poynting vector      700
Principle of removable singularities      721
Probability measure      802
Progressing wave      700
Pushforward, of a measure      806
Quantum logic      831
Quantum state      831
Quaternions      660
Ramification      733
Random walk      485
Reduced wave equation      702
Resistance      409
resistivity      615
resistor      408
Resistor, in parallel      411
Resistor, in series      413
Resistor, linear      409
Resistor, non-linear      409
Resonance, in circuit theory      418
Resonant frequencies      445
Restricted coboundary map      431
Retarded potentials      696
Reversible curve      778
Rouche theorem      728
Second law of thermodynamics      773 780
Short circuit      418
Solid angle      586
Specific heat      787
Speed of sound      788
Star operator      641
Star operator in $\mathbb{R}^3$       597
Star operator in spacetime      643 644
Star shaped      569
State      775
State, statistical      802 823 832
Stationary phase, method of      755
Stirling’s formula      750
Stokes’ Theorem      553
system      775 822
Tellegen’s theorem      430
Tensor algebras      671
Tensor products      664
Thermal equilibrium      777
Thermistor      409
Thermometer      777
Torus      513
TREE      424
Trees and projections      426
Trilinear      536
Two-cell      502
Two-complex      502
Vector field      617
Vertex      413
Volt      408
Voltage      407
Voltage vector      429
Watt      408
Wave equation, homogeneous, one-dimensional      689
Wave equation, homogeneous, three-dimensional      692
Wave equation, inhomogeneous      695
Wave front      700
Wedge product      535 538
Zero-chains      419
Zeroth law of thermodynamics      777

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