Applied computational physics:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Weitere Verfasser: | |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Oxford University Press
2018
|
| Ausgabe: | First edition |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Literaturangaben |
| Beschreibung: | xxi, 913 Seiten Illustrationen, Diagramme |
| ISBN: | 9780198708636 9780198708643 |
Internformat
MARC
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| 245 | 1 | 0 | |a Applied computational physics |c Joseph F. Boudreau and Eric. S. Swanson ; with contributions from Riccardo Maria Bianchi |
| 250 | |a First edition | ||
| 264 | 1 | |a Oxford |b Oxford University Press |c 2018 | |
| 300 | |a xxi, 913 Seiten |b Illustrationen, Diagramme | ||
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| 653 | 0 | |a Quantum theory / Data processing | |
| 653 | 0 | |a Physics / Computer simulation | |
| 653 | 0 | |a Quantum theory / Computer simulation | |
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Datensatz im Suchindex
| _version_ | 1804178134921117696 |
|---|---|
| adam_text | Contents
A
1 Building programs in a Linux environment 1
1.1 The editor., the compiler, and the make system 3
LL1 Troubleshooting mysterious problems 6
1.2 A quick tour of input and output 7
1.3 Where to find information on the C++ standard library 9
1.4 Command line arguments and return values 9
1.5 Obtaining numerical constants from input strings 11
1.6 Resolving shared libraries at run time 11
1.7 Compiling programs from multiple units 12
1.8 Libraries and library tools 16
1.9 More on Makefile 18
1.10 The subversion source code management system (SVN) 20
1.10.1 The SVN repository 21
1.10.2 Importing a project into SVN 22
1.10.3 The basic idea 22
1.11 Style guide: advice for beginners 25
1.12 Exercises 27
Bibliography 29
2 Encapsulation and the C++ class 30
2.1 Introduction 3 0
2.2 The representation of numbers 31
2.2.1 Integer datatypes 32
2.2.2 Floating point datatypes 33
2.2.3 Special floating point numbers 34
2.2.4 Floating point arithmetic on the computer 36
2.3 Encapsulation: an analogy 37
2.4 Complex numbers 38
2.5 Classes as user defined datatypes 43
2.6 Style guide: defining constants and conversion factors in one place 45
2.7 Summary 47
2.8 Exercises 48
Bibliography 49
3 Some useful classes with applications 51
3.1 Introduction 51
3.2 Coupled oscillations 52
xii Contents
3.3 Linear algebra with the Eigen package 54
3.4 Complex linear algebra and quantum mechanical scattering
from piecewise constant potentials 57
3.4.1 Transmission and reflection coefficients 59
3.5 Complex linear algebra with Eigen 60
3.6 Geometry 63
3.6.1 Example: collisions in three dimensions 64
3.7 Collection classes and strings 65
3.8 Function objects 67
3.8.1 Example: root finding 70
3.8.2 Parameter objects and parametrized functors 74
3.9 Plotting 76
3.10 Further remarks 7 7
3.11 Exercises 78
Bibliography 83
4 Interpolation and extrapolation 84
4.1 Lagrange interpolating polynomial 85
4.2 Evaluation of the interpolating polynomial 87
4.2.1 Interpolation in higher dimensions 89
4.3 Spline interpolation 90
4.3.1 The cubic spline 90
4.3.2 Coding the cubic spline 93
4.3.3 Other splines 94
4.4 Extrapolation 95
4.5 Taylor series, continued fractions, and Pade approximants 97
4.6 Exercises 102
Bibliography 106
5 Numerical quadrature 107
5.1 Some example problems 108
5.1.1 One-dimensional periodic motion 108
5.1.2 Quantization of energy 110
5.1.3 Two body central force problems 111
5.1.4 Quantum mechanical tunneling 112
5.1.5 Moments of distributions 113
5.1.6 Integrals of statistical mechanics 115
5.2 Quadrature formulae 118
5.2.1 Accuracy and convergence rate 124
5.3 Speedups and convergence tests 126
5.4 Arbitrary abscissas 128
5.5 Optimal abscissas 129
5.6 Gaussian quadrature 132
5.7 Obtaining the abscissas 135
Contents xiii
5.7.1 Implementation notes 137
5.8 Infinite range integrals 139
5.9 Singular integrands 140
5.10 Multidimensional integrals 141
5.11 A note on nondimensionalization 142
5.11.1 Compton scattering 142
5.11.2 Particle in a finite one-dimensional well 143
5.11.3 Schrodinger equation for the hydrogen atom 144
5.12 Exercises 145
Bibliography 150
6 How to write a class 151
6.1 Some example problems 152
6.1.1 A stack of integers 152
6.1.2 The Jones calculus 152
6.1.3 Implementing stack 154
6.2 Constructors 160
6.3 Assignment operators and copy constructors 162
6.4 Destructors 165
6.5 const member data and const member functions 166
6.6 Mutable member data 167
6.7 Operator overloading 167
6.8 Friends 170
6.9 Type conversion via constructors and cast operators 171
6.10 Dynamic memory allocation 174
6.10.1 The “big four” 176
6.11 A worked example: implementing the Jones calculus 181
6.12 Conclusion 190
6.13 Exercises 191
Bibliography 195
7 Monte Carlo methods 196
7.1 Multidimensional integrals 197
7.2 Generation of random variates 198
7.2.1 Random numbers in C++11 198
7.2.2 Random engines 199
7.2.3 Uniform and nonuniform variates 200
7.2.4 Histograms 202
7.2.5 Numerical methods for nonuniform variate generation 204
7.2.6 The rejection method 204
7.2.7 Direct sampling (or the transformation method) 207
7.2.8 Sum of two random variables 210
7.2.9 The Gaussian (or normal) distribution 211
7.3 The multivariate normal distribution, x2 and correlation 212
xiv Contents
7 A Monte Carlo integration 216
7.4.1 Importance sampling 219
7.4.2 Example 220
7.5 Markov chain Monte Carlo 221
7.5.1 The Metropolis-Hastings algorithm 223
7.5.2 Slow mixing 223
7.5.3 Thermalization 225
7.5.4 Autocorrelation 227
7.5.5 Multimodality 228
7.6 The heat bath algorithm 229
7.6.1 An application: Ising spin systems 229
7.6.2 Markov chains for quantum problems 231
7.7 Where to go from here 232
7.8 Exercises 233
Bibliography 239
8 Percolation and universality 240
8.1 Site percolation 241
8.1.1 The cluster algorithm 241
8.1.2 Code verification 244
8.1.3 The percolation probability 244
8.2 Fractals 249
8.3 Scaling and critical exponents 252
8.3.1 The correlation length and the anomalous dimension 253
8.3.2 Additional scaling laws 256
8.4 Universality and the renormalization group 258
8.4.1 Coarse graining 260
8.4.2 Monte Carlo renormalization group 263
8.5 Epilogue 264
8.6 Exercises 265
Bibliography 27 2
9 Parallel computing 274
9.1 High performance computing 274
9.2 Parallel computing architecture 278
9.3 Parallel computing paradigms 279
9.3.1 MPI 279
9.3.2 openMP 285
9.3.3 C++11 concurrency library 289
9.4 Parallel coding 299
9.5 Forking subprocesses 300
9.6 Interprocess communication and sockets 302
9.7 Exercises 308
Bibliography 310
Contents xv
10 Graphics for physicists 312
10.1 Graphics engines 312
10.1.1 3d libraries and software 313
10.1.2 Generating graphics 314
10.1.3 The Open Inventor/Coin3d toolkit 315
10.2 First steps in a 3d world-3d visualization 316
10.2.1 The basic skeleton of a 3d application 316
10.2.2 A three-dimensional greeting to the world 318
10.2.3 A colorful spherical world 321
10.2.4 Deleting nodes in the scene graph 322
10.3 Finding patterns-Testing random number generators 322
10.4 Describing nature’s shapes-fractals 326
10.4.1 Shared nodes 331
10.5 Animations 335
10.5.1 Coin engines: a rotating world 335
10.5.2 Coin sensors: an orbiting planet 338
10.6 The Inventor system 339
10.7 Exercises 340
Bibliography 342
11 Ordinary differential equations 343
11.1 Introduction 344
11.2 Example applications 345
11.2.1 Projectile motion with air resistance 345
11.2.2 Motion of a charged particle in a magnetic field 346
11.2.3 Simple nonlinear systems: the Lorenz model 347
11.2.4 The Lagrangian formulation of classical mechanics 348
11.2.5 The Hamiltonian formulation of classical mechanics 350
11.2.6 The Schrodinger equation 351
11.3 A high-level look at an ODE solver 353
11.3.1 A simple integrator class 354
11.3.2 Example: the harmonic oscillator 357
11.4 Numerical methods for integrating ordinary differential equations 358
11.4.1 The Euler method 359
11.4.2 The midpoint method 361
11.4.3 The trapezoid method 361
11.4.4 The 4th order Runge-Kutta method 361
11.4.5 Properties of nth order Runge-Kutta methods 362
11.5 Automated solution of classical problems 368
11.5.1 Taking partial derivatives with GENFUNCTIONs 368
11.5.2 Computing and solving the equations of motion 370
11.5.3 A classical Hamiltonian solver 371
11.6 Adaptive step size control 373
xvi Contents
11.6.1 Step doubling 375
11.6.2 Embedded Runge Kutta methods 379
11.7 Symplectic integration schemes 383
11.7.1 Symplectic transformations 386
11.8 Symplectic integrators of first and higher order 390
11.9 Algorithmic inadequacies 393
11.9.1 Stability 393
11.9.2 Solution mixing 394
11.9.3 Multiscale problems 395
11.10 Exercises 396
Bibliography 401
12 Polymorphism 402
12.1 Example: output streams 404
12.2 Inheritance 406
12.3 Constructors and destructors 407
12.4 Virtual functions 409
12.5 Virtual destructors 413
12.6 Pure virtual functions and abstract base classes 415
12.7 Real example: extending the GenericFunctions package 416
12.8 Object-oriented analysis and design 421
12.9 Exercises 421
Bibliography 423
13 Nonlinear dynamics and chaos 424
13.1 Introduction 424
13.2 Nonlinear ordinary differential equations 426
13.3 Iterative maps 429
13.3.1 The logistic map 430
13.3.2 The Henon map 435
13.3.3 The quadratic map 436
13.4 The nonlinear oscillator 438
13.4.1 The Lyapunov exponent 440
13.5 Hamiltonian systems 443
13.5.1 The KAM theorem 444
13.5.2 The Henon-Heiles model 445
13.5.3 Billiard models 447
13.6 Epilogue 449
13.7 Exercises 450
Bibliography 453
14 Rotations and Lorentz transformations 455
14.1 Introduction 455
14.2 Rotations 456
Contents xvii
14.2.1 Generators 457
14.2.2 Rotation matrices 458
14.3 Lorentz transformations 460
14.4 Rotations of vectors and other objects 463
14.4.1 Vectors 463
14.4.2 Spinors 464
14.4.3 Higher dimensional representations 465
14.5 Lorentz transformations of four-vectors and other objects 467
14.5.1 Four-vectors 467
14.5.2 Weyl spinors 468
14.5.3 Dirac spinors 470
14.5.4 Tensors of higher order 473
14.6 The helicity formalism 474
14.7 Exercises 479
Bibliography 482
15 Simulation 483
15.1 Stochastic systems 483
15.2 Large scale simulation 484
15.3 A first example 486
15.4 Interactions of photons with matter 488
15.5 Electromagnetic processes 491
15.5.1 Bremsstrahlung 491
15.5.2 Electromagnetic showers 493
15.5.3 The need for simulation toolkits 493
15.6 Fundamental processes: Compton scattering 494
15.7 A simple experiment: double Compton scattering 501
15.8 Heavier charged particles 503
15.9 Conclusion 505
15.10 Exercises 506
Bibliography 510
16 Data modeling 511
16.1 Tabular data 512
16.2 Linear least squares (or x2) fit 514
16.3 Function minimization in data modeling 516
16.3.1 The quality of a x2 fit 522
16.3.2 A mechanical analogy 523
16.4 Fitting distributions 523
16.4.1 x2 fit to a distribution 524
16.4.2 Binned maximum likelihood fit to a distribution 527
16.5 The unbinned maximum likelihood fit 529
16.5.1 Implementation 530
16.5.2 Construction of normalized PDFs 533
xviii Contents
16.6 Orthogonal series density estimation 534
16.7 Bayesian inference 538
16.8 Combining data 540
16.9 The Kalman filter 543
16.9.1 Example: fitting a polynomial curve 545
16.9.2 Complete equations 546
16.10 Exercises 550
Bibliography 554
17 Templates, the standard C++ library, and modern C++ 556
17.1 Generic type parameters 557
17.2 Function templates 558
17.3 Class templates 5 60
17.3.1 Class template specialization 561
17.4 Default template arguments 563
17.5 Non-type template parameters 563
17.6 The standard C++ library 565
17.6.1 Containers and iterators 566
17.6.2 Algorithms 575
17.7 Modern C++ 577
17.7.1 Variadic templates 578
17.7.2 Auto 580
17.7.3 Smart pointers 581
17.7.4 Range-based for loop 582
17.7.5 Nullptr 583
17.7.6 Iterators: nonmember begin and end 583
17.7.7 Lambda functions and algorithms 584
17.7.8 Initializer lists 586
17.8 Exercises 590
Bibliography 593
18 Many body dynamics 594
18.1 Introduction 594
18.2 Relationship to classical statistical mechanics 595
18.3 Noble gases 597
18.3.1 The Verlet method 598
18.3.2 Temperature selection 603
18.3.3 Observables 605
18.4 Multiscale systems 608
18.4.1 Constrained dynamics 611
18.4.2 Multiple time scales 614
18.4.3 Solvents 616
18.5 Gravitational systems 616
18.5.1 N-Body simulations of galactic structure 618
Contents xix
18.5.2 The Barnes-Hut algorithm 620
18.5.3 Particle-mesh methods 625
18.6 Exercises 627
Bibliography 640
19 Continuum dynamics 642
19.1 Introduction 643
19.2 Initial value problems 643
19.2.1 Differencing 644
19.2.2 Continuity equations 645
19.2.3 Second order temporal methods 648
19.2.4 The Crank-Nicolson method 648
19.2.5 S econd order equations 650
19.2.6 Realistic partial differential equations 651
19.2.7 Operator splitting 652
19.3 The Schrödinger equation 655
19.4 Boundary value problems 658
19.4.1 The Jacobi method 659
19.4.2 Successive over-relaxation 662
19.5 Multigrid methods 664
19.6 Fourier techniques 667
19.6.1 The fast Fourier transform 669
19.6.2 The sine transform 670
19.6.3 An application 672
19.7 Finite element methods 673
19.7.1 The variational method in one dimension 674
19.7.2 Two-dimensional finite elements 675
19.7.3 Mesh generation 677
19.8 Conclusions 684
19.9 Exercises 685
Bibliography 699
20 Classical spin systems 701
20.1 Introduction 701
20.2 The Ising model 702
20.2.1 Definitions 703
20.2.2 Critical exponents and finite size scaling 704
20.2.3 The heat bath algorithm and the induced magnetization 706
20.2.4 Reweighting 709
20.2.5 Autocorrelation and critical slowing down 710
20.2.6 Cluster algorithms 713
20.3 The Potts model and first order phase transitions 717
20.4 The planar XY model and infinite order phase transitions 720
20.5 Applications and extensions 724
xx Contents
20.5.1 Spin glasses 724
20.5.2 Hopfield model 725
20.6 Exercises 726
Bibliography 730
21 Quantum mechanics I-few body systems 732
21.1 Introduction 732
21.2 Simple bound states 733
21.2.1 Shooting methods 734
21.2.2 Diagonalization 735
21.2.3 Discretized eigenproblems 735
21.2.4 Momentum space methods 737
21.2.5 Relativistic kinematics 739
21.3 Quantum Monte Carlo 740
21.3.1 Guided random walks 740
21.3.2 Matrix elements 745
21.4 Scattering and the T-matrix 750
21.4.1 Scattering via the Schrödinger equation 750
21.4.2 The T-matrix 752
21.4.3 Coupled channels 757
21.5 Appendix: Three-dimensional simple harmonic oscillator 761
21.6 Appendix: scattering formulae 763
21.7 Exercises 763
Bibliography 771
22 Quantum spin systems 773
22.1 Introduction 773
22.2 The anisotropic Heisenberg antiferromagnet 775
22.3 The Lanczos algorithm 778
22.3.1 The Lanczos miracles 779
22.3.2 Application of the Lanczos method
to the Heisenberg chain 781
22.4 Quantum Monte Carlo 785
22.5 Exercises 791
Bibliography 800
23 Quantum mechanics II-many body systems 802
23.1 Introduction 802
23.2 Atoms 803
23.2.1 Atomic scales 803
23.2.2 The product Ansatz 804
23.2.3 Matrix elements and atomic configurations 805
23.2.4 Small atoms 807
23.2.5 The self-consistent Hartee Fock method 809
Contents xxi
23.3 Molecules 814
23.3.1 Adiabatic separation of scales 815
23.3.2 The electronic problem 817
23.4 Density functional theory 824
23.4.1 The Kohn-Sham procedure 827
23.4.2 DFT in practice 828
23.4.3 Further developments 830
23.5 Conclusions 831
23.6 Appendix: Beyond Hartree-Fock 831
23.7 Exercises 836
Bibliography 842
24 Quantum field theory 844
24.1 Introduction 844
24.2 p4 theory 845
24.2.1 Evaluating the path integral 849
24.2.2 Particle spectrum 853
24.2.3 Parity symmetry breaking 856
24.3 Z2 Gauge theory 857
24.3.1 Heat bath updates 861
24.3.2 Average Plaquette and Polyakov loop 863
24.4 Abelian gauge theory: compact photons 865
24.4.1 Gauge invariance and quenched QED 867
24.4.2 Computational details 869
24.4.3 Observables 872
24.4.4 The continuum limit 875
24.5 SU(2) Gauge theory 877
24,5.1 Implementation 879
24.5.2 Observables 881
24.6 Fermions 886
24.6.1 Fermionic updating 890
24.7 Exercises 893
Bibliography 903
Index
905
Applied Computational Physics is a graduate-level text stressing three essential
elements: advanced programming techniques, numerical analysis, and physics.
The goal of the text is to provide students with essential computational skills
that they will need in their careers, and to increase the confidence with which
they write computer programs designed for their problem domain. The physics
problems give them an opportunity to reinforce their programming skills,
while the acquired programming skills augment their ability to solve problems
in physics! The C++ language is used throughout the text. Physics problems
include Hamiltonian systems, chaotic systems, percolation, critical phenomena,
few-body and multi-body quantum systems, quantum field theory, simulation
of radiation transport, and data modeling. The book, the fruit of a collaboration
between a theoretical physicist and an experimental physicist, covers a broad
diversity of topics from both viewpoints. Examples, program libraries, and
additional documentation can be found at the companion website. Hundreds
of original problems reinforce programming skills and increase the ability
to solve real-life physics problems at and beyond the graduate level.
JOSEPH F. BOUDREAU and ERIC S. SWANSON are both professors of Physics
at the Department of Physics and Astronomy, University of Pittsburgh, USA.
ALSO PUBLISHED BY
OXFORD UNIVERSITY PRESS
No; .: ; wSe ■ A • a! - s • s v. : L K
Ray Huffaker, Marco Bittelli, and Rodolfo Rosa
fiom C Ossie,-1 to Qua--. Vu-v Fields |§|
Laurent Baulieu, John lliopoulos, and Roland Seneor
Cover image: A simulation of percolatioV on a cubic lattice, in which distinct clusters are rendered
in different colors (center and upper righ ) and unoccupied sites appear as white spheres (lower left).
©Joe Boudreau and Eric Swanson.
OXFORD
UNIVERSITY PRESS
Y
ISBN 978-0-19-870863 i-6
9 780198 708636 )
www.oup.com
|
| any_adam_object | 1 |
| author | Boudreau, Joseph F. Swanson, Eric S. |
| author2 | Bianchi, Riccardo Maria |
| author2_role | ctb |
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| author_GND | (DE-588)1151471283 (DE-588)1153038374 (DE-588)1052667317 |
| author_facet | Boudreau, Joseph F. Swanson, Eric S. Bianchi, Riccardo Maria |
| author_role | aut aut |
| author_sort | Boudreau, Joseph F. |
| author_variant | j f b jf jfb e s s es ess |
| building | Verbundindex |
| bvnumber | BV044680214 |
| classification_rvk | SK 955 |
| classification_tum | PHY 016f |
| ctrlnum | (OCoLC)1021081616 (DE-599)BSZ495345024 |
| dewey-full | 530.0285 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.0285 |
| dewey-search | 530.0285 |
| dewey-sort | 3530.0285 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| edition | First edition |
| format | Book |
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| id | DE-604.BV044680214 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:59:09Z |
| institution | BVB |
| isbn | 9780198708636 9780198708643 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030077371 |
| oclc_num | 1021081616 |
| open_access_boolean | |
| owner | DE-706 DE-29T DE-19 DE-BY-UBM DE-703 DE-20 DE-11 DE-634 DE-91G DE-BY-TUM DE-83 |
| owner_facet | DE-706 DE-29T DE-19 DE-BY-UBM DE-703 DE-20 DE-11 DE-634 DE-91G DE-BY-TUM DE-83 |
| physical | xxi, 913 Seiten Illustrationen, Diagramme |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | Oxford University Press |
| record_format | marc |
| spelling | Boudreau, Joseph F. (DE-588)1151471283 aut Applied computational physics Joseph F. Boudreau and Eric. S. Swanson ; with contributions from Riccardo Maria Bianchi First edition Oxford Oxford University Press 2018 xxi, 913 Seiten Illustrationen, Diagramme txt rdacontent sti rdacontent n rdamedia nc rdacarrier Literaturangaben C++ (DE-588)4193909-8 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Computerphysik (DE-588)4273564-6 gnd rswk-swf Physics / Data processing Quantum theory / Data processing Physics / Computer simulation Quantum theory / Computer simulation Computerphysik (DE-588)4273564-6 s Mathematische Physik (DE-588)4037952-8 s DE-604 C++ (DE-588)4193909-8 s Swanson, Eric S. (DE-588)1153038374 aut Bianchi, Riccardo Maria (DE-588)1052667317 ctb Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030077371&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030077371&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Boudreau, Joseph F. Swanson, Eric S. Applied computational physics C++ (DE-588)4193909-8 gnd Mathematische Physik (DE-588)4037952-8 gnd Computerphysik (DE-588)4273564-6 gnd |
| subject_GND | (DE-588)4193909-8 (DE-588)4037952-8 (DE-588)4273564-6 |
| title | Applied computational physics |
| title_auth | Applied computational physics |
| title_exact_search | Applied computational physics |
| title_full | Applied computational physics Joseph F. Boudreau and Eric. S. Swanson ; with contributions from Riccardo Maria Bianchi |
| title_fullStr | Applied computational physics Joseph F. Boudreau and Eric. S. Swanson ; with contributions from Riccardo Maria Bianchi |
| title_full_unstemmed | Applied computational physics Joseph F. Boudreau and Eric. S. Swanson ; with contributions from Riccardo Maria Bianchi |
| title_short | Applied computational physics |
| title_sort | applied computational physics |
| topic | C++ (DE-588)4193909-8 gnd Mathematische Physik (DE-588)4037952-8 gnd Computerphysik (DE-588)4273564-6 gnd |
| topic_facet | C++ Mathematische Physik Computerphysik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030077371&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030077371&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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