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COMPUTATIONAL PHYSICS

Adolfo AVELLA COMPUTATIONAL PHYSICS

0512600004
DEPARTMENT OF PHYSICS "E. R. CAIANIELLO"
EQF6
PHYSICS
2024/2025

OBBLIGATORIO
YEAR OF COURSE 2
YEAR OF DIDACTIC SYSTEM 2017
SPRING SEMESTER
CFUHOURSACTIVITY
648LESSONS
ADOLFO AVELLA T Curriculum
Objectives
THE COURSE HAS THE OBJECTIVE TO INTRODUCE THE STUDENTS TO THE USE OF THE BASIC COMPUTATIONAL TOOLS NEEDED TO STUDY FROM THE SIMPLEST TO THE MOST COMPLEX PHYSICAL, BUT ALSO STATISTICAL AND BIOLOGICAL, SYSTEMS.

KNOWLEDGE AND UNDERSTANDING:
THE COURSE WILL PROVIDE THE STUDENT WITH THE BASIC KNOWLEDGE OF THE FUNDAMENTAL NUMERICAL METHODS FOR SOLVING DIFFERENT TYPES OF PROBLEMS IN PHYSICS AND THE ABILITY TO UNDERSTAND/LEARN BY HIMSELF THE RELATED ADVANCED CONCEPTS. THE COURSE INCLUDES THE USE OF FORTRAN 95/2003/2008 AS MODERN PROGRAMMING LANGUAGE AND THE LEARNING OF BOTH THE SYNTAX OF THE LANGUAGE AND OF THE DIFFERENT PROGRAMMING PARADIGMS (PROCEDURAL, MODULAR, OBJECT-ORIENTED) THAT IT SUPPORTS, SO THAT THE STUDENT CAN UNDERSTAND/LEARN OTHER MODERN LANGUAGES BY HIMSELF.

APPLYING KNOWLEDGE AND UNDERSTANDING:
THE COURSE AIMS TO DEVELOP THE STUDENT'S ABILITY TO SOLVE, IN A PROFESSIONAL MANNER, DIFFERENT TYPES OF PROBLEMS IN PHYSICS THROUGH THE USE OF NUMERICAL METHODS AND ALGORITHMS AND THEIR ENCODING IN TERMS OF COMPUTER PROGRAMS. IN PARTICULAR, THE STUDENT WILL DEVELOP THE CAPABILITY TO OUTLINE A PHYSICAL PROBLEM, TO SELECT/DEVELOP NUMERICAL METHODS AND RELATED ALGORITHMS FOR ITS RESOLUTION ACCORDING TO THEIR EFFICIENCY, STABILITY AND PRECISION, AND THEIR DEMAND FOR COMPUTING RESOURCES, TO DRAFT THE CORRESPONDING CODE IN A MODERN PROGRAMMING LANGUAGE, TO INTERPRET CRITICALLY THE PROCESSED DATA AND COMMUNICATE THE RESULTS IN A CLEAR AND EXPRESSIVE MANNER. HE WILL ALSO BECOME FAMILIAR WITH COMPILERS (GFORTRAN), DEVELOPMENT ENVIRONMENTS (LINUX, BASH, EMACS), GRAPHICS APPLICATIONS (GNUPLOT) AND SCIENTIFIC TEXTS PROCESSORS (LYX) FOR THE PRACTICAL APPLICATION OF THE KNOWLEDGE GAINED.
Prerequisites
KNOWLEDGE OF THE BASIC TOPICS IN CLASSICAL PHYSICS (MECHANICS, THERMODYNAMICS, ELECTROMAGNETISM, OPTICS), ANALYTICAL GEOMETRY, LINEAR ALGEBRA AND CALCULUS (SERIES, FUNCTIONS, LIMITS, DERIVATIVES, INTEGRALS).
Contents
LECTURES (IN THE CLASSROOM):
1. COMPUTER AND SCIENCE / PHYSICS: MATHEMATICAL COMPLEXITY OF PHYSICAL PROBLEMS (MATHEMATICAL METHODS), NUMERICAL METHODS, ALGORITHMS, PROGRAMMING LANGUAGES AND PARADIGMS (2H).
2. ERRORS AND UNCERTAINTIES IN COMPUTING: MODELS OF HARDWARE AND SOFTWARE REPRESENTATION OF NUMBERS, PRECISION, TYPES OF ERROR (OVERFLOW, UNDERFLOW, ROUND-OFF SIMPLE AND ACCUMULATION), STABILITY, IEEE STANDARD (4H).
3. APPROXIMATION AND NUMERICAL ANALYSIS OF REAL FUNCTIONS: INTERPOLATION (LAGRANGE, AITKEN), DIFFERENTIATION (AT N POINTS, RECURSIVE) INTEGRATION (TRAPEZOIDS, SIMPSON, RECURSIVE) ZERI (BISECTION, NEWTON-RAPHSON, SECANT), EXTREMES. APPLICATION TO PHYSICAL PROBLEMS (10H).
4. ORDINARY DIFFERENTIAL EQUATIONS: PROBLEMS WITH INITIAL CONDITIONS, METHODS OF EULER AND PICARD, PREDICTOR-CORRECTOR METHODS, RUNGE-KUTTA METHODS, EIGENVALUE PROBLEM AND BOUNDARY CONDITIONS, LINEAR EQUATIONS AND STURM-LIOUVILLE PROBLEM. APPLICATION TO PHYSICAL PROBLEMS (4H).
5. MATRIX CALCULUS: SIMPLE OPERATIONS WITH MATRICES, SYSTEMS OF LINEAR EQUATIONS, ZEROES AND EXTREMES OF FUNCTIONS OF SEVERAL VARIABLES, EIGENVALUE PROBLEMS, LANCZOS ALGORITHM. APPLICATION TO PHYSICAL PROBLEMS (4H).
TUTORIALS (LABORATORY CLASSES):
1. FORTRAN 95/2003/2008: SUPPORTED PARADIGMS OF PROGRAMMING, MODELING OF THE PHYSICAL PROBLEM, DESIGN OF THE CODE, BASIC AND ADVANCED SYNTAX OF THE LANGUAGE, MODULARITY, GENERIC AND OBJECT ORIENTED PROGRAMMING (16H).
2. DEVELOPER ENVIRONMENT: OPERATING SYSTEM (LINUX), SHELL (BASH), EDITOR (EMACS), COMPILER (GFORTRAN), GRAPHICS APPLICATION (GNUPLOT), EDITOR OF SCIENTIFIC TEXTS (LYX) (8H).
Teaching Methods
THE COURSE INCLUDES 24 HOURS OF FRONTAL LECTURES IN CLASSROOM FINALIZED TO THE LEARNING OF THE BASIC KNOWLEDGE ABOUT NUMERICAL METHODS AND PROGRAMMING AND 36 HOURS OF FRONTAL PRACTICAL LECTURES IN LABORATORY FOCUSED ON THE ILLUSTRATION OF THE PROCESS OF MODELING THE PHYSICAL PROBLEM UNDER CONSIDERATION, THE SELECTION AND DEVELOPMENT OF NUMERICAL METHODS AND ALGORITHMS NECESSARY FOR ITS NUMERICAL SOLUTION, THE DESIGN OF THE CODE ACCORDING TO THE CHOSEN PROGRAMMING PARADIGM, THE CONCRETE DRAFTING OF THE CODE IN FORTRAN 95/2003/2008 (SYNTAX OF THE LANGUAGE), ITS COMPILATION, EXECUTION, AND RELATED COLLECTION AND GRAPHICAL REPRESENTATION OF THE RESULTS.
Verification of learning
THE ASSESSMENT AND EVALUATION OF THE STUDENT'S LEVEL OF LEARNING WILL TAKE PLACE THROUGH A FINAL TEST THAT WILL CONSIST IN THE ORAL DISCUSSION OF A RESEARCH PROJECT, ASSIGNED AT THE END OF THE COURSE TO A GROUP OF TWO/THREE STUDENTS, CONCERNING THE SOLUTION OF A PHYSICAL PROBLEM NOT MENTIONED IN THE COURSE, BUT SOLVED BY THE NUMERICAL METHODS COVERED DURING THE COURSE. THE ORAL DISCUSSION IS AIMED AT ASSESSING THE LEVEL OF THEORETICAL KNOWLEDGE, THE AUTONOMY OF ANALYSIS AND JUDGMENT, AS WELL AS THE STUDENT'S PRESENTATION SKILLS.

THE EVALUATION LEVEL IS ASSIGNED TAKING INTO ACCOUNT THE EFFICIENCY OF THE METHODS USED, THE COMPLETENESS AND ACCURACY OF THE ANSWERS, AS WELL AS THE CLARITY IN THE PRESENTATION.

THE MINIMUM LEVEL OF EVALUATION (18) IS ASSIGNED WHEN THE STUDENT DEMONSTRATES A BARELY SUFFICIENT ABILITY IN THE APPLICATION OF THE NUMERICAL METHODS AND IN THE IDENTIFICATION OF THE METHODS TO CONTROL NUMERICAL ERROR, AND HAS A LIMITED KNOWLEDGE OF THE MAIN ALGORITHMS.

THE MAXIMUM LEVEL (30) IS ASSIGNED WHEN THE STUDENT DEMONSTRATES A COMPLETE AND IN-DEPTH KNOWLEDGE OF NUMERICAL METHODS AND ALGORITHMS AND SHOWS A REMARKABLE ABILITY TO IDENTIFY AND MANAGE THE SOURCES OF NUMERICAL ERROR PRESENT IN THE SPECIFIC PROBLEM HE/SHE HAS CHOSEN TO DEAL WITH.

PRAISE IS GIVEN WHEN THE CANDIDATE DEMONSTRATES SIGNIFICANT MASTERY OF THE THEORETICAL AND OPERATIONAL CONTENT AND SHOWS HOW TO PRESENT THE TOPICS WITH CONSIDERABLE MASTERY OF THE SPECIFIC TECHNICAL LANGUAGE AND AUTONOMOUS PROCESSING SKILLS EVEN IN CONTEXTS DIFFERENT FROM THOSE PROPOSED BY THE TEACHER.
Texts
COMPUTATIONAL PHYSICS: T. PANG; AN INTRODUCTION TO COMPUTATIONAL PHYSICS; CAMBRIDGE UNIVERSITY PRESS; CONTENUTI: 2ND ED. (2006), CODICI IN FORTRAN 90: 1ST ED. (1997). N.J. GIORDANO; COMPUTATIONAL PHYSICS; BENJAMIN CUMMINGS; 2ND ED. (2005). J. THIJSSEN; COMPUTATIONAL PHYSICS; CAMBRIDGE UNIVERSITY PRESS; 2ND ED. (2007). R.H. LANDAU, J. PAEZ, C.C. BORDEIANU; A SURVEY OF COMPUTATIONAL PHYSICS: INTRODUCTORY COMPUTATIONAL SCIENCE; PRINCETON UNIVERSITY PRESS (2008). P.L. DEVRIES , J.E. HASBUN; A FIRST COURSE IN COMPUTATIONAL PHYSICS; JONES & BARTLETT PUBLISHERS; 2ND ED. (2010). A. KLEIN; INTRODUCTORY COMPUTATIONAL PHYSICS; CAMBRIDGE UNIVERSITY PRESS; 2ND ED. (2010). R. FITZPATRICK; COMPUTATIONAL PHYSICS; LECTURE NOTES.
MATHEMATICAL METHODS: K.F. RILEY, M.P. HOBSON, AND S.J. BENCE; MATHEMATICAL METHODS FOR PHYSICS AND ENGINEERING; CAMBRIDGE UNIVERSITY PRESS; 3RD ED. (2006). S. HASSANI; MATHEMATICAL METHODS FOR STUDENTS OF PHYSICS AND RELATED FIELDS; SPRINGER SCIENCE+BUSINESS MEDIA, LLC; 2ND ED. (2009). H. SHIMA, AND T. NAKAYAMA; HIGHER MATHEMATICS FOR PHYSICS AND ENGINEERING; SPRINGER-VERLAG (2010).
NUMERICAL METHODS AND ALGORITHMS: W.H. PRESS, S.A. TEUKOLSKY, H.A. BETHE, W.T. VETTERLING, AND B.P. FLANNERY; NUMERICAL RECIPES - THE ART OF SCIENTIFIC COMPUTING; CAMBRIDGE UNIVERSITY PRESS; CONTENUTI: 3RD ED. (2007), CODICI IN FORTRAN 90: II VOL. OF 2ND ED. (1996).
FORTRAN 95/2003/2008: S.J. CHAPMAN; FORTRAN 95/2003 FOR SCIENTISTS AND ENGINEERS; MCGRAW-HILL; 3RD ED. (2008). M. METCALF, J. REID, M. COHEN; FORTRAN 95/2003 EXPLAINED; OXFORD UNIVERSITY PRESS (2004).
More Information
THE ATTENDANCE, ALTHOUGH NOT MANDATORY, IT IS STRONGLY RECOMMENDED. FOR A SATISFACTORY PREPARATION, IT IS REQUIRED, ON AVERAGE, TWO HOURS OF STUDY FOR EACH HOUR OF CLASS, BOTH FRONTAL AND LABORATORY ONES.
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