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MA22037: Numerical analysis

[Page last updated: 03 June 2024]

Academic Year: 2024/25
Owning Department/School: Department of Mathematical Sciences
Credits: 10 [equivalent to 20 CATS credits]
Notional Study Hours: 200
Level: Intermediate (FHEQ level 5)
Period:
Semester 2
Assessment Summary: CWRI 25%, EXCB 75%
Assessment Detail:
  • Mini project (CWRI 25%)
  • Examination (EXCB 75%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must take MA12004 OR take MA12011 OR take MA12013
You must have experience with Python programme (e.g. MA12003 or MA12008 or similar) to take this module.
Learning Outcomes: By the end of the unit, you will be able to:
  • Demonstrate knowledge of computational methods for the approximation of functions, integrals, and solutions to systems of equations (e.g., linear equations and ordinary differential equations).
  • Understand the approximation theory of some computational methods.
  • Implement and use these methods for solving problems on a computer.



Synopsis: You will study the algorithms that are used in computational science. You will develop an understanding of the complexity and convergence behaviour of algorithms for solving linear systems of equations and representing complex functions. This will be supported by computational experiments in Python.

Content: Introduction: What is numerical analysis? Floating-point numbers and rounding error. Concepts of convergence and accuracy (e.g., absolute and relative errors, order of convergence). Nonlinear systems of equations: The fixed-point theorem and root-finding problem. Examples including Newton's method. Approximation of functions: Polynomial interpolation and error analysis. Applications to numerical integration (e.g., Newton-Cotes formulae, Gauss quadrature, composite rules) and the numerical solution of initial-value problems for ODEs (e.g., the Euler and theta-methods; stability, consistency, and convergence). Linear systems of equations: Matrix norms and condition numbers. Iterative methods (e.g., Jacobi and Gauss-Seidel) vs direct methods (e.g., row-reduction methods and Gaussian elimination). Least-squares problems and the singular-value decomposition.

Course availability:

MA22037 is Optional on the following courses:

Department of Computer Science
  • USCM-AFB32 : BSc(Hons) Computer Science and Mathematics (Year 2)
  • USCM-AKB32 : BSc(Hons) Computer Science and Mathematics with professional placement (Year 2)
  • USCM-AKB32 : BSc(Hons) Computer Science and Mathematics with study abroad (Year 2)
Department of Economics
  • UHES-AFB12 : BSc(Hons) Economics and Mathematics (Year 2)
  • UHES-AKB12 : BSc(Hons) Economics and Mathematics with professional placement (Year 2)
  • UHES-AKB12 : BSc(Hons) Economics and Mathematics with professional placement and study abroad (Year 2)
  • UHES-AKB12 : BSc(Hons) Economics and Mathematics with study abroad (Year 2)
Department of Mathematical Sciences
  • USMA-AFB30 : BSc(Hons) Mathematics (Year 2)
  • USMA-AFB32 : BSc(Hons) Mathematics and Statistics (Year 2)
  • USMA-AKB32 : BSc(Hons) Mathematics and Statistics with professional placement (Year 2)
  • USMA-AKB32 : BSc(Hons) Mathematics and Statistics with study abroad (Year 2)
  • USMA-AFB33 : BSc(Hons) Mathematics, Statistics and Data Science (Year 2)
  • USMA-AKB33 : BSc(Hons) Mathematics, Statistics and Data Science with professional placement (Year 2)
  • USMA-AKB33 : BSc(Hons) Mathematics, Statistics and Data Science with study abroad (Year 2)
  • USMA-AKB30 : BSc(Hons) Mathematics with professional placement (Year 2)
  • USMA-AKB30 : BSc(Hons) Mathematics with study abroad (Year 2)
  • USMA-AFM30 : MMath(Hons) Mathematics (Year 2)
  • USMA-AKM30 : MMath(Hons) Mathematics with professional placement (Year 2)
  • USMA-AKM31 : MMath(Hons) Mathematics with study abroad (Year 2)
Department of Physics
  • USPH-AFB26 : BSc(Hons) Mathematics and Physics (Year 2)
  • USPH-AKB26 : BSc(Hons) Mathematics and Physics with professional placement (Year 2)
  • USPH-AKB26 : BSc(Hons) Mathematics and Physics with study abroad (Year 2)
  • USPH-AFM26 : MSci(Hons) Mathematics and Physics (Year 2)
  • USPH-AKM26 : MSci(Hons) Mathematics and Physics with professional placement (Year 2)
  • USPH-AKM26 : MSci(Hons) Mathematics and Physics with study abroad (Year 2)

Notes:

  • This unit catalogue is applicable for the 2024/25 academic year only. Students continuing their studies into 2025/26 and beyond should not assume that this unit will be available in future years in the format displayed here for 2024/25.
  • Courses and units are subject to change in accordance with normal University procedures.
  • Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.
  • Find out more about these and other important University terms and conditions here.