| CODE | PHY2160 | |||||||||
| TITLE | Introduction to Computational Physics | |||||||||
| UM LEVEL | 02 - Years 2, 3 in Modular Undergraduate Course | |||||||||
| MQF LEVEL | 5 | |||||||||
| ECTS CREDITS | 4 | |||||||||
| DEPARTMENT | Physics | |||||||||
| DESCRIPTION | This study-unit constitutes an introductory course in numerical computation as applied to problems in physics. Study-unit Aims The theoretical part of the study-unit will provide: - a description of the bisection method, the Newton-Raphson method and the direct iteration method for determining the roots of an equation, together with an analysis of the rate of convergence and the errors involved in these methods; - a description of how to solve linear algebraic equations using Gaussian elimination, Jacobi iteration and Gauss-Seidel iteration; - a description of how to solve non-linear algebraic equations using the Newton-Raphson method in two dimensions; - the definition and a description of the use of finite difference operators; - a description of how to interpolate a set of data using the Newton-Gregory forward fitting formula, Lagrangian interpolation and Spline interpolation; - a description of how to integrate numerically using the trapezoidal rule, Simpson’s rule, the Euler’s method, the modified Euler method, the Runge-Kutta method; - the derivation of the central difference formulae for the first and second derivatives; - the application of the finite difference method to partial differential equations; - a brief introduction to Monte Carlo techniques. The practical part of the study-unit will provide: - a description of the components of a computer; - a review of the available programming languages; - a description of the notion of pseudocode; - a description of how to use a computer as a calculator; - a description of how to use iterative techniques to solve problems; - a description of how to define a tolerance so as to determine the convergence of the solution; - guided implementation of the various techniques introduced in the taught part of the study-unit; - a discussion of the practical steps to take in order to debug a program. Learning Outcomes 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: - demonstrate the power of numerical techniques in obtaining approximate solutions to physics problems that do not have an analytical solution; - explain the basic principles underlying the various techniques described in the course; - identify the various errors that result from the application of these techniques; - demonstrate the concepts of iteration and convergence; - appreciate the utility of a computer in the application of these techniques to real problems. 2. Skills: By the end of the study-unit the student will be able to: - use the bisection method, the Newton-Raphson method and the direct iteration method to determine the roots of a given equation; - write a program that determines the roots of a given equation using the bisection method, the Newton-Raphson method and the direct iteration method; - determine the rate of convergence and the error in a given iterative method; - use Gaussian elimination, Jacobi iteration and Gauss-Seidel iteration to solve linear algebraic equations; - write a programme that uses the Gaussian elimination, Jacobi iteration and Gauss-Seidel iteration to solve linear algebraic equations; - use the Newton-Raphson in two dimensions to solve a given set of two non-linear algebraic equations; - write a program that uses the Newton-Raphson in two dimensions to solve a given set of two non-linear algebraic equations; - calculate the value of the finite difference operators for a given set of data; - write a program that calculates the value of the finite difference operators for a given set of data; - determine the order of the best interpolating polynomial for a given set of data; - write a program that determines the order of the best interpolating polynomial for a given set of data; - use the Newton-Gregory forward fitting formula, Lagrangian interpolation and Spline interpolation to determine an interpolation function for a given set of data; - write a program that uses the Newton-Gregory forward fitting formula, Lagrangian interpolation or Spline interpolation to determine an interpolation function for a given set of data; - use the trapezoidal rule, Simpson’s rule, the Euler’s method, the modified Euler method, the Runge-Kutta method to integrate a given function numerically; - write a program that uses the trapezoidal rule, Simpson’s rule, the Euler’s method, the modified Euler method or the Runge-Kutta method to integrate a given function numerically; - determine the finite difference form of a given differential equation using the central difference equations; - write a program that uses the finite difference form of a given differential equation to solve numerically the given differential equation; - write programs that solve numerically the system to a given tolerance; - write simple Monte-Carlo programs to solve appropriate probablistic problems; - debug a program he/she has written. Main Text/s and any supplementary readings Recommended textbook: Gerald, C.F. and Wheatley, P.O., Applied Numerical Analysis, 7 edition, Pearson Education Suggested reading: Pang, T, An Introduction to Computational Physics, 2nd Edition, Cambridge University Press Vesily, F.J., Computational Physics: an introduction, 2nd Edition, Kluwer Academic Devries P.L, and Hasbun J.E. , A First Course in Computational Physics, 2nd Edition, J. Wiley and Sons |
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| ADDITIONAL NOTES | Pre-Requisite: Basic knowledge of Mathematics including calculus. | |||||||||
| STUDY-UNIT TYPE | Lecture and Practical | |||||||||
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The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the description above applies to study-units available during the academic year 2024/5. It may be subject to change in subsequent years. |
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