LEADER 05147nam 22007335 450 001 9910254635603321 005 20251116150247.0 010 $a3-319-27265-9 024 7 $a10.1007/978-3-319-27265-8 035 $a(CKB)3710000000627467 035 $a(SSID)ssj0001656869 035 $a(PQKBManifestationID)16438111 035 $a(PQKBTitleCode)TC0001656869 035 $a(PQKBWorkID)14988498 035 $a(PQKB)11770551 035 $a(DE-He213)978-3-319-27265-8 035 $a(MiAaPQ)EBC6310511 035 $a(MiAaPQ)EBC5594679 035 $a(Au-PeEL)EBL5594679 035 $a(OCoLC)945632196 035 $a(PPN)192774158 035 $a(EXLCZ)993710000000627467 100 $a20160321d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aBasic Concepts in Computational Physics /$fby Benjamin A. Stickler, Ewald Schachinger 205 $a2nd ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XVI, 409 p. 95 illus.) 300 $aIncludes Index. 311 08$a3-319-27263-2 327 $aSome Basic Remarks -- Part I Deterministic Methods -- Numerical Differentiation -- Numerical Integration -- The KEPLER Problem -- Ordinary Differential Equations ? Initial Value Problems -- The Double Pendulum -- Molecular Dynamics -- Numerics of Ordinary Differential Equations - Boundary Value Problems -- The One-Dimensional Stationary Heat Equation -- The One-Dimensional Stationary SCHRÖDINGER Equation -- Partial Differential Equations -- Part II Stochastic Methods -- Pseudo Random Number Generators -- Random Sampling Methods -- A Brief Introduction to Monte-Carlo Methods -- The ISING Model -- Some Basics of Stochastic Processes -- The Random Walk and Diffusion Theory -- MARKOV-Chain Monte Carlo and the POTTS Model -- Data Analysis -- Stochastic Optimization -- Appendix: The Two-Body Problem -- Solving Non-Linear Equations. The NEWTON Method -- Numerical Solution of Systems of Equations -- Fast Fourier Transform -- Basics of Probability Theory -- Phase Transitions -- Fractional Integrals and Derivatives in 1D -- Least Squares Fit -- Deterministic Optimization. 330 $aThis new edition is a concise introduction to the basic methods of computational physics. Readers will discover the benefits of numerical methods for solving complex mathematical problems and for the direct simulation of physical processes. The book is divided into two main parts: Deterministic methods and stochastic methods in computational physics. Based on concrete problems, the first part discusses numerical differentiation and integration, as well as the treatment of ordinary differential equations. This is extended by a brief introduction to the numerics of partial differential equations. The second part deals with the generation of random numbers, summarizes the basics of stochastics, and subsequently introduces Monte-Carlo (MC) methods. Specific emphasis is on MARKOV chain MC algorithms. The final two chapters discuss data analysis and stochastic optimization. All this is again motivated and augmented by applications from physics. In addition, the book offers a number of appendices to provide the reader with information on topics not discussed in the main text. Numerous problems with worked-out solutions, chapter introductions and summaries, together with a clear and application-oriented style support the reader. Ready to use C++ codes are provided online. 606 $aPhysics 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aComputer science$xMathematics 606 $aChemistry, Physical and theoretical 606 $aNumerical and Computational Physics, Simulation$3https://scigraph.springernature.com/ontologies/product-market-codes/P19021 606 $aMathematical and Computational Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T11006 606 $aComputational Mathematics and Numerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M1400X 606 $aTheoretical and Computational Chemistry$3https://scigraph.springernature.com/ontologies/product-market-codes/C25007 615 0$aPhysics. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 0$aComputer science$xMathematics. 615 0$aChemistry, Physical and theoretical. 615 14$aNumerical and Computational Physics, Simulation. 615 24$aMathematical and Computational Engineering. 615 24$aComputational Mathematics and Numerical Analysis. 615 24$aTheoretical and Computational Chemistry. 676 $a530.1 700 $aStickler$b Benjamin A.$4aut$4http://id.loc.gov/vocabulary/relators/aut$0791786 702 $aSchachinger$b Ewald$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254635603321 996 $aBasic Concepts in Computational Physics$92527079 997 $aUNINA