## MA20222: Numerical analysis

[Page last updated: 28 April 2022]

Owning Department/School: Department of Mathematical Sciences
Credits: 6 [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Intermediate (FHEQ level 5)
Period:
Semester 1
Assessment Summary: CW 25%, EX 75%
Assessment Detail:
• Coursework (CW 25%)
• Examination (EX 75%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this unit you must take XX10190 or MA10265 or MA10275 or MA10276 or CM10228. Students will need to be able to program in Python.
Learning Outcomes: After taking this unit, students should 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 in Python.
* Write the relevant mathematical arguments in a precise and lucid fashion.

Aims: To give an introduction to numerical analysis, including the role of numerical analysis as the foundation for scientific computing. To develop general mathematical skills and to enable students to take final year courses on numerical analysis.

Skills: Numeracy T/F A Problem Solving T/F A Computation skills T/F A Written and Spoken Communication F (in tutorials).

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).

Programme availability:

#### MA20222 is Compulsory on the following programmes:

Department of Mathematical Sciences
• USMA-AFB13 : BSc(Hons) Mathematics (Year 2)
• USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 2)
• USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 2)
• USMA-AFB20 : BSc(Hons) Mathematics, Statistics, and Data Science (Year 2)
• USMA-AAB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Study year abroad (Year 2)
• USMA-AKB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Industrial Placement (Year 2)

#### MA20222 is Optional on the following programmes:

Department of Computer Science
• USCM-AFB20 : BSc(Hons) Computer Science and Mathematics (Year 3)
• USCM-AAB20 : BSc(Hons) Computer Science and Mathematics with Study year abroad (Year 4)
• USCM-AKB20 : BSc(Hons) Computer Science and Mathematics with Year long work placement (Year 4)
• USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 3)
• USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 3)
• USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 3)
Department of Mathematical Sciences
• USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 2)
• USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 3)
• USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 2)
• USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
• USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 2)
• USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
• USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 2)
• USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
• USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 2)
• USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
• USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 2)
• USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
• USMA-AFB05 : BSc(Hons) Statistics (Year 3)
• USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
• USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 2)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
• USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 2)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 2)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)

 Notes: This unit catalogue is applicable for the 2022/23 academic year only. Students continuing their studies into 2023/24 and beyond should not assume that this unit will be available in future years in the format displayed here for 2022/23. Programmes 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.