Undergraduate Programme and Module Handbook 2024-2025

# Module PHYS2611: MATHEMATICAL METHODS IN PHYSICS

## Department: Physics

### PHYS2611: MATHEMATICAL METHODS IN PHYSICS

Type | Open | Level | 2 | Credits | 20 | Availability | Available in 2024/2025 | Module Cap | Location | Durham |
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#### Prerequisites

- Foundations of Physics 1 (PHYS1122) AND ((Single Mathematics A (MATH1561) and Single Mathematics B (MATH1571)) OR (Calculus I (MATH1061) and Linear Algebra I (MATH1071))).

#### Corequisites

- None

#### Excluded Combination of Modules

- Analysis in Many Variables II (MATH2031).

#### Aims

- This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.
- It supports the Level 2 modules Foundations of Physics 2A (PHYS2611) and Foundations of Physics 2B (PHYS2621) by supplying the necessary mathematical tools.

#### Content

- The syllabus contains:
- Index notation.
- Matrices and vector spaces.
- Fourier series.
- Fourier transforms.
- Laplace transforms.
- Vector calculus.
- Line and surface integrals.
- Key concepts in probability.
- Conditional probability (Bayes’s rule).
- Probability distribution.
- Introduction to Bayesian inference.
- Hypothesis testing.
- Higher order ODEs.
- Series solution of ODEs.
- Special functions.
- PDEs: separation of variables.
- PDEs: general and particular solutions.

#### Learning Outcomes

Subject-specific Knowledge:

- Having studied this module students will be familiar with some of the key results of vector integral and vector differential calculus, multivariable calculus and orthogonal curvilinear coordinates, Fourier analysis, the use of matrices, the fundamental concepts in probability and the Bayesian approach to data analysis, with important mathematical tools for solving ordinary and partial differential equations occurring in a variety of physical problems.

Subject-specific Skills:

- In addition to the acquisition of subject knowledge, students will be able to apply the principles of physics to the solution of predictable and unpredictable problems.
- They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation.

Key Skills:

#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

- Teaching will be by lectures and tutorial-style workshops.
- The lectures provide the means to give a concise, focused presentation of the subject matter of the module. The lecture material will be defined by, and explicitly linked to, the contents of recommended textbooks for the module, making clear where students can begin private study. When appropriate, the lectures will also be supported by the distribution of written material, or by information and relevant links online.
- Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills.
- Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at other mutually convenient times.
- Student performance will be summatively assessed through a written examination and an online test and formatively assessed through problem exercises and a progress test. The written examination and online test will provide the means for students to demonstrate the acquisition of subject knowledge and the development of their problem-solving skills. The problem exercises, progress test and workshops will provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.

#### Teaching Methods and Learning Hours

Activity | Number | Frequency | Duration | Total/Hours | |
---|---|---|---|---|---|

Lectures | 40 | 2 per week | 1 hour | 40 | |

Workshops | 18 | Weekly | 1 hour | 18 | |

Preparation and Reading | 142 | ||||

TOTAL | 200 |

#### Summative Assessment

Component: Examination | Component Weighting: 60% | ||
---|---|---|---|

Element | Length / duration | Element Weighting | Resit Opportunity |

Written examination | 2 hours | 100% | |

Component: Online tests | Component Weighting: 40% | ||

Element | Length / duration | Element Weighting | Resit Opportunity |

Online tests | 100% |

#### Formative Assessment:

Problem exercises and self-assessment; progress test, workshops (not compulsory) and problems solved therein.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University