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Programme & Unit Catalogues

## MA20222: Numerical analysis

Owning Department/School: Department of Mathematical Sciences
Credits: 6
Level: Intermediate (FHEQ level 5)
Period: Semester 1
Assessment: CW 25%, EX 75%
Supplementary Assessment: MA20222 Mandatory extra work (where allowed by programme regulations)
Requisites: While taking this unit you must take MA20216 and take MA20218 and before taking this unit you must take MA10207 and take MA10208 and take MA10209 and take MA10210 and take XX10190
Description: Aims:
To teach those aspects of Numerical Analysis which are most relevant to a general mathematical training, and to lay the foundations for the more advanced courses in later years.

Learning Outcomes:
After taking this unit, students should be able to:
* Demonstrate knowledge of simple methods for the approximation of functions and integrals, solution of initial value problems for ordinary differential equations and the solution of linear systems
* Use basic methods for the analysis of the errors made in these methods.
* Show awareness of some of the relevant practical issues involved in their implementation, including coding of algorithms using MATLAB.
* Write the relevant mathematical arguments in a precise and lucid fashion.

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

Content:
MATLAB Programming for Numerical Analysis: Floating point numbers and rounding error.
Concepts of Convergence and Accuracy: Order of convergence, extrapolation and error estimation.
Approximation of Functions: Polynomial interpolation, error analysis.
Numerical Integration: Newton-Cotes formulae. Gauss quadrature. Composite formulae. Error analysis.
Numerical Solution of ODEs: Euler, Backward Euler, Trapezoidal and explicit Runge-Kutta methods. Stability. Consistency and convergence for one step methods. Error estimation and control.
Linear Algebraic Equations: Gaussian elimination, LU decomposition, pivoting, Matrix norms, conditioning, backward error analysis, iterative refinement.
Coding of algorithms: in MATLAB.
Programme availability:

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

Department of Mathematical Sciences
• USMA-AFB13 : BSc (hons) Mathematics (Full-time) - Year 2
• USMA-AKB14 : BSc (hons) Mathematics (Full-time with Thick Sandwich Placement) - Year 2
• USMA-AAB14 : BSc (hons) Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 2

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

Department of Computer Science
• USCM-AFM14 : MComp (hons) Computer Science and Mathematics (Full-time) - Year 3
• USCM-AKM14 : MComp (hons) Computer Science and Mathematics with Industrial Placement (Full-time with Thick Sandwich Placement) - Year 4
• USCM-AAM14 : MComp (hons) Computer Science and Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
Department of Mathematical Sciences
• USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 2
• USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 3
• USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 2
• USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 4
• USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 2
• USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USMA-AFB01 : BSc (hons) Mathematics and Statistics (Full-time) - Year 3
• USMA-AKB02 : BSc (hons) Mathematics and Statistics (Full-time with Thick Sandwich Placement) - Year 4
• USMA-AAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USMA-AFB05 : BSc (hons) Statistics (Full-time) - Year 2
• USMA-AFB05 : BSc (hons) Statistics (Full-time) - Year 3
• USMA-AKB06 : BSc (hons) Statistics (Full-time with Thick Sandwich Placement) - Year 2
• USMA-AKB06 : BSc (hons) Statistics (Full-time with Thick Sandwich Placement) - Year 4
• USMA-AAB06 : BSc (hons) Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 2
• USMA-AAB06 : BSc (hons) Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USMA-AFM14 : MMath Mathematics (Full-time) - Year 2
• USMA-AFM14 : MMath Mathematics (Full-time) - Year 3
• USMA-AAM15 : MMath Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 2

Notes:
* This unit catalogue is applicable for the 2013/4 academic year only. Students continuing their studies into 2014/15 and beyond should not assume that this unit will be available in future years in the format displayed here for 2013/14.
* Programmes and units are subject to change at any time, 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.