(Last Updated:03 May 2017)

**Total Credits: **20

**Level: **Level 4

**Target Students: **Students taking the MSc Scientific Computing and the MSc Financial and Computational Mathematics in the School of Mathematical Sciences; Also available to Year 4 MMath students and other MSc students.

**Taught Semesters:**

Semester | Assessment |
---|---|

Spring | Assessed by end of Spring Semester |

**Prerequisites: **For MMath students, G12INM is a pre-requisite. MSc students should have a solid background in mathematics, including calculus, linear algebra, and ordinary differential equations as covered by the entry requirements. Some programming experience (Matlab, C++, Python, etc) is expected.

Mnem | Title |
---|---|

G12INM | Introduction to Numerical Methods |

**Corequisites: **None.

**Summary of Content: **Four major topics for the computational solution of problems in applied mathematics are considered in this module:

- Approximate theory,
- numerical solution of nonlinear problems,
- numerical solution of ODEs and
- numerical solution of PDEs.

- Approximations theory, multivariate polynomial approximation
- Numerical differentiation and numerical solution of ODEs
- Introduction to PDEs, finite difference methods and FFT (Fast Fourier Tranforms) for PDEs
- Numerical solution of (systems of) nonlinear equations.

**Method and Frequency of Class: **

Activity | Number Of Weeks | Number of sessions | Duration of a session |
---|---|---|---|

Lecture | 12 weeks | 1 per week | 2 hours |

Workshop | 12 weeks | 1 per week | 1 hour |

Activities may take place every teaching week of the Semester or only in specified weeks. It is usually specified above if an activity only takes place in some weeks of a Semester

One 2-hour class and one 1-hour class per week timetabled centrally, which is used for lectures, example and problem classes.

**Method of Assessment: **

Assessment Type | Weight | Requirements |
---|---|---|

Exam 1 | 60 | 2.5 hour written examination |

Coursework 1 | 20 | Assessed coursework including a computing component |

Coursework 2 | 20 | Assessed coursework including a computing component |

**Convenor: **

Dr K van der Zee

**Education Aims: **This module introduces computational methods for solving problems in applied mathematics. Students taking this module will develop knowledge and understanding to design, justify and implement relevant computational techniques and methodologies.

**Learning Outcomes: **A student who completes this module successfully should be able to:

L1 - *Formulate and analyse polynomial approximations;*

L2 - *Formulate and analyse computational methods for the solution of nonlinear equations;*

L3 - *Formulate and analyse relevant numerical methods for ODEs and PDEs;*

L4 - *Implement computational algorithms using a sophisticated programming language.*

**Offering School: **Mathematical Sciences

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