|
 Academic Year:
| 2015/6 |
| Owning Department/School:
| Department of Mathematical Sciences |
| Credits:
| 6 |
| Level:
| Intermediate (FHEQ level 5) |
| Period: |
Semester 1 |
| Assessment Summary:
| CW 25%, EX 75% |
| Assessment Detail: |
|
| Supplementary Assessment: |
MA20222 Mandatory extra work (where allowed by programme regulations) |
| Requisites: |
While taking this module you must take MA20216 AND take MA20218
Before taking this module you must take MA10207 AND take MA10208 AND take MA10209 AND take MA10210 AND take XX10190 |
| Description:
| 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. 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 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: 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
MA20222 is Optional on the following programmes:Department of Computer Science
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