| CODE | PHY1134 | ||||||||
| TITLE | Introduction to Numerical Methods | ||||||||
| UM LEVEL | 01 - Year 1 in Modular Undergraduate Course | ||||||||
| MQF LEVEL | 5 | ||||||||
| ECTS CREDITS | 2 | ||||||||
| DEPARTMENT | Physics | ||||||||
| DESCRIPTION | This unit provides an in-depth exploration of fundamental numerical techniques essential for solving complex mathematical problems encountered in various fields. Emphasizing practical applications, the course equips students with the necessary tools and methodologies to effectively approximate and solve mathematical problems using numerical approaches. Through a combination of theoretical concepts and hands-on applications, students will develop a strong foundation in numerical methods to tackle real-world problems with precision and accuracy. The unit will include: - Determining the roots of an equation using Bisection method, Newton-Raphson and the direct iteration method; - Solving systems of linear equations using Gaussian elimination, Jacobi iteration and Gauss-Seidel iteration; - Numerical integration using Euler’s Method, the trapezoidal rule and Simpson’s rule; - Numerical differentiation using backward, forward and central differences; formulae for the first and second derivatives; - Solving first and second order differential equations using simple finite difference techniques; introduction to Runge-Kutta methods; - Introduction to linear regression. Study-unit Aims: • Develop an understanding of the fundamentals of various numerical methods and their role in approximating solutions for a wide range of mathematical problems; • Develop skills in implementing numerical techniques to efficiently determine roots of equations, solve systems of linear equations, and numerically integrate functions; • Assist students with applying numerical differentiation and finite difference methods to analyze and solve differential equations, gaining insights into their behaviour and solutions; • Explore the principles of linear regression and its practical applications in data analysis and predictive modeling. Learning Outcomes: 1. Knowledge & Understanding By the end of the study-unit the student will be able to: • Apply various numerical methods to find roots of equations, solve linear systems, and perform numerical integration, and explain practical applications of these methods in real-world scenarios; • Implement numerical differentiation techniques and finite difference methods to approximate derivatives and solve differential equations numerically; • Utilize linear regression to analyze data, build predictive models, and interpret the results to draw meaningful conclusions; • Evaluate and compare different numerical methods, considering their accuracy, efficiency, and suitability for specific types of problems. They will articulate the strength and limitations of each method in various contexts. 2. Skills By the end of the study-unit the student will be able to: • Ability to apply various numerical methods to solve complex mathematical problems and make informed decisions based on the results obtained; • Capacity to critically analyze numerical data and evaluate the accuracy and reliability of results obtained from different numerical techniques; • Proficiency in evaluating the applicability and limitations of numerical methods, fostering a deeper understanding of their implications in diverse problem-solving scenarios. Main Text/s and any supplementary readings: Main Text: - Course notes will be provided to the students Supplementary Text: - Gerald, C.F. and Wheatley, P.O., Applied Numerical Analysis, 7 edition, Pearson Education. |
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| ADDITIONAL NOTES | Pre-Requisite qualifications: Advanced Level Mathematics Co-Requisite Study-unit: PHY1133 |
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| STUDY-UNIT TYPE | Lecture | ||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Jonathan Farrugia |
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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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