A collection of problems on mathematical physics:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Pergamon Press
1964
|
| Series: | International series of monographs on pure and applied mathematics
52 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 770 S. Ill., graph. Darst. |
Staff View
MARC
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| 240 | 1 | 0 | |a Sbornik zadač po matematičeskoj fizike |
| 245 | 1 | 0 | |a A collection of problems on mathematical physics |c B. M. Budak ; A. A. Samarskij and A. N. Tikhonov |
| 264 | 1 | |a Oxford [u.a.] |b Pergamon Press |c 1964 | |
| 300 | |a XII, 770 S. |b Ill., graph. Darst. | ||
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| 490 | 1 | |a International series of monographs on pure and applied mathematics |v 52 | |
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Record in the Search Index
| _version_ | 1826400932405968896 |
|---|---|
| adam_text |
CONTENTS
Paget
TRANSLATION EDITOR'S NOTE x
PREFACE xi
CHAPTER I. CLASSIFICATION AND REDUCTION TO
CANONICAL FORM OF SECOND ORDER
PARTIAL DIFFERENTIAL EQUATIONS
1. The equation for a function of two independent variables
a11uxx+2aliuxy+a22uyy+b1ux+b!.Uy+cu = f(x,y) 1 163
1. The equation with variable coefficients 1 163
2. The equation with constant coefficients 2 168
2. The equation with constant cosffisients for a function of n
independent variables 3 168
CHAPTER II. EQUATIONS OF HYPERBOLIC TYPE
1. Physical problems reducible to equations of hyperbolic type;
statement of boundary value problems 4 171
1. Free vibrations in a non resistant medium; equations with
constant coefficients, 5 171
2. Forced vibrations and vibrations in a resistant medium;
equations with constant coefficients 8 186
3. Vibration problems leading to equations with continuous
variable coefficients 10 188
4. Problems leading to equations with discontinuous coeffi¬
cients and similar problems (piecewise homogeneous media,
etc.) 11 190
5. Similarity of boundary value problems 15 201
2. Method of travelling waves (D'Alembert's method) 17 208
1. Problems for an infinite string 18 208
2. Problems for a semi infinite region 20 216
3. Problems for an infinite line, consisting of two homogeneous
semi infinite lines; 25 231
4. Problems for a finite segment 26 235
3. Method of separation of variables 28 248
1. Free vibrations in a non resistant medium 29 248
2. Free vibrations in a resistant medium 31 260
t The number of the pages referring to the answers and solutions is given
in italics
M
Vi CONTENTS
3. Forced vibrations under the action of distributed and con¬
centrated forces in a non resistant medium and in a resistant
medium 32 264
4. Vibrations with inhomogeneous media and other conditions
leading to equations with variable coefficients; calculations
with concentrated forces and masses 37 291
4. Method of integral representations 39 296
1. The method of the Fourier integral 39 296
1*. Transition to a finite interval by the method of images 44 311
2. Riemann's method. 45 312
CHAPTER III. EQUATIONS OF PARABOLIC TYPE
1. Physical problems leading to equations of parabolic type; state¬
ment of boundary value problems 47 317
1. Homogeneous media; equations with constant coefficients 48 318
2. Inhomogeneous media; equations with variable coefficients
and matching conditions 50 323
3. Similarity of boundary value problems 51 326
2. Method of separation of variables 52 331
1. Homogeneous isotropic media. Equations with constant co¬
efficients 52 331
(a) Problems of heat conduction with constant boundary
conditions 52 331
(b) Problems of heat conduction with variable boundary
conditions and free terms, dependent on x and / 55 340
(c) Problems of diffusion 57 345
(d) Problems of electrodynamics 57 347
2. Inhomogeneous media. Equations with variable coefficients
and matching conditions 58 348
3. Method of integral representations and source functions 59 351
1. Homogeneous isotropic media. Application of the Fourier
integral ] transform to problems on the infinite line and
the semi infinite line 59 351
2. Homogeneous isotropic media. Calculation of Green's
functions 61 555
(a) Infinite straight line 61 355
(b) Semi infinite straight line 63 358
(c) Finite segment 68 367
3. Inhomogeneous media; equations with piecewise continuous
coefficients and matching conditions 69 376
CHAPTER IVi EQUATIONS OF ELLIPTIC TYPE
1. Physical problems leading to equations of elliptic type, and
the statement of boundary value problems 71 381
CONTENTS vii
1. Boundary value problems for Laplace's and Poisson's equa¬
tion in a homogeneous medium 71 381
2. Boundary value problems for Laplace's equation in inhomo
geneous media 72 387
2. Simplest problems for Laplace's and Poisson's equations 74 392
1. Boundary value problems for Laplace's equation 74 392
2. Boundary value problems for Poisson's equation 76 399
3. The source function 77 400
1. The source function for regions with plane boundaries 78 402
2. The source function for regions with spherical (circular)
and plane boundaries 79 411
3. The source function in inhomogeneous media 80 419
4. The method of separation of variables 81 425
1. Boundary value problems for a circle, ring and sector 81 425
2. Boundary value problems for strips, rectangles, plane layers
and parallelepipeds 85 445
3. Problems requiring the application of cylindrical functions 87 458
4. Problems requiring the application of spherical and cylin¬
drical functions 89 475
5. Potentials and their application 92 490
CHAPTER V. EQUATIONS OF PARABOLIC TYPE
1. Physical problems leading to equations of parabolic type;
statement of boundary value problems 96 506
2. The method of separation of variables 98 511
1. Boundary value problems not requiring the application of
special functions 98 511
(a) Homogeneous media 98 511
(b) Inhomogeneous media 101 519
2. Boundary value problems requiring the application of special
functions 102 523
(a) Homogeneous media 102 523
(b) Inhomogeneous media; central factors 105 538
3. The method of integral representations 106 546
1. The application of the Fourier integral 106 546
2. The formation and application of Green's functions 109 557
CHAPTER VI. EQUATIONS OF HYPERBOLIC TYPE
1. Physical problems leading to equations of hyperbolic type;
statement of boundary value problems 115 565
2. The simplest problems; different methods of solution 120 574
3. The method of separation of variables 126 586
Vlii CONTENTS '
1. Boundary value problems not requiring the application of
special functions 126 586
(a) Homogeneous media 126 586
(b) Inhomogeneous media 128 591
2. Boundary value problems requiring the application of special
functions 128 593
(a) Homogeneous media 128 593
(b) Inhomogeneous media 134 620
4. The method of integral representations 134 621
1. The application of the Fourier integral 134 621
(a) The Fourier transform 134 621
(b) The Fourier Bessel (Hankel) transform 135 626
2. Formation and application of the functions of the effect
of concentrated sources 137 631
(a) Green's functions for an impulse 137 631
(b) Source functions of continuously acting concentrated
sources 138 637
CHAPTER VII. EQUATIONS OF ELLIPTIC TYPE Au+cu = f
1. Problems for the equation A«—xa« = —/ 140 644
2. Some problems on natural vibrations 142 649
1. Natural vibrations of strings and rods 142 649
2. Natural vibrations of volumes 144 659
3. Propagation and radiation of sound 146 676
1. Point source 147 678
2. Radiation of membranes, cylinders and spheres 148 685
3. Diffraction by a cylinder and sphere 150 696
4. Steady state electromagnetic vibrations 151 703
1. Maxwell's equations. Potentials. Green Ostrogradskirs vector
formulae 151 703
2. Propagation of electromagnetic waves and vibrations in
resonators 155 710
3. Radiation of electromagnetic waves 156 721
4. Antenna on the plane earth 158 729
SUPPLEMENT
I. Different orthogonal systems of coordinates 741
1. Rectangular coordinates 741
2. Cylindrical coordinates 742
3. Spherical coordinates 742
4. Elliptic coordinates 743
5. Parabolic coordinates 743
6. Ellipsoidal coordinates 744
7. Degenerate ellipsoidal coordinates 745
CONTENTS ix
8. Toroidal coordinates 745
9. Bipolar coordinates 746
10. Spheroidal coordinates 748
11. Paraboloidal coordinates 748
II. Some formulae of vector analysis 748
III. Special functions 749
1. Trigonometric functions 749
2. Hyperbolic functions 749
3. The error integral 749
4. Gamma functions 750
5. Elliptic functions 750
6. Bessel functions 751
7. Legendre polynomials 753
8. The hypergeometric function F{a,@,y) 754
IV. Tables of the error integral and roots of some characteristic
equations 755
REFERENCES 759
INDEX 763
A list of other volumes published in this series
appears on pages 769 and 770. |
| any_adam_object | 1 |
| author | Budak, Boris Michajlovič 1917-1972 Samarskij, Aleksandr A. 1919-2008 Tichonov, Andrej N. 1906-1993 |
| author_GND | (DE-588)1067945512 (DE-588)107587351 (DE-588)172417775 |
| author_facet | Budak, Boris Michajlovič 1917-1972 Samarskij, Aleksandr A. 1919-2008 Tichonov, Andrej N. 1906-1993 |
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| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV001928533 |
| illustrated | Illustrated |
| indexdate | 2025-03-12T15:01:00Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001256889 |
| oclc_num | 990535 |
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| physical | XII, 770 S. Ill., graph. Darst. |
| publishDate | 1964 |
| publishDateSearch | 1964 |
| publishDateSort | 1964 |
| publisher | Pergamon Press |
| record_format | marc |
| series | International series of monographs on pure and applied mathematics |
| series2 | International series of monographs on pure and applied mathematics |
| spelling | Budak, Boris Michajlovič 1917-1972 Verfasser (DE-588)1067945512 aut Sbornik zadač po matematičeskoj fizike A collection of problems on mathematical physics B. M. Budak ; A. A. Samarskij and A. N. Tikhonov Oxford [u.a.] Pergamon Press 1964 XII, 770 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series of monographs on pure and applied mathematics 52 Mathematische fysica gtt Physique mathématique - Problèmes et exercices Vergelijkingen (wiskunde) gtt Mathematische Physik Mathematical physics Problems, exercises, etc Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Physik (DE-588)4045956-1 s Mathematische Methode (DE-588)4155620-3 s DE-604 Mathematische Physik (DE-588)4037952-8 s Samarskij, Aleksandr A. 1919-2008 Verfasser (DE-588)107587351 aut Tichonov, Andrej N. 1906-1993 Verfasser (DE-588)172417775 aut International series of monographs on pure and applied mathematics 52 (DE-604)BV001888024 52 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001256889&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Budak, Boris Michajlovič 1917-1972 Samarskij, Aleksandr A. 1919-2008 Tichonov, Andrej N. 1906-1993 A collection of problems on mathematical physics International series of monographs on pure and applied mathematics Mathematische fysica gtt Physique mathématique - Problèmes et exercices Vergelijkingen (wiskunde) gtt Mathematische Physik Mathematical physics Problems, exercises, etc Mathematische Physik (DE-588)4037952-8 gnd Mathematische Methode (DE-588)4155620-3 gnd Physik (DE-588)4045956-1 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4155620-3 (DE-588)4045956-1 (DE-588)4143389-0 |
| title | A collection of problems on mathematical physics |
| title_alt | Sbornik zadač po matematičeskoj fizike |
| title_auth | A collection of problems on mathematical physics |
| title_exact_search | A collection of problems on mathematical physics |
| title_full | A collection of problems on mathematical physics B. M. Budak ; A. A. Samarskij and A. N. Tikhonov |
| title_fullStr | A collection of problems on mathematical physics B. M. Budak ; A. A. Samarskij and A. N. Tikhonov |
| title_full_unstemmed | A collection of problems on mathematical physics B. M. Budak ; A. A. Samarskij and A. N. Tikhonov |
| title_short | A collection of problems on mathematical physics |
| title_sort | a collection of problems on mathematical physics |
| topic | Mathematische fysica gtt Physique mathématique - Problèmes et exercices Vergelijkingen (wiskunde) gtt Mathematische Physik Mathematical physics Problems, exercises, etc Mathematische Physik (DE-588)4037952-8 gnd Mathematische Methode (DE-588)4155620-3 gnd Physik (DE-588)4045956-1 gnd |
| topic_facet | Mathematische fysica Physique mathématique - Problèmes et exercices Vergelijkingen (wiskunde) Mathematische Physik Mathematical physics Problems, exercises, etc Mathematische Methode Physik Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001256889&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001888024 |
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