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Faculty Handbook 2019-2020

# Module Description

Please ensure you check the module availability box for each module outline, as not all modules will run each academic year.

## Department: Physics

### PHYS2611: MATHEMATICAL METHODS IN PHYSICS

Type Level Credits Availability Module Cap Open 2 20 Available in 2019/20 Durham

#### Prerequisites

• (Foundations of Physics 1 (PHYS1122) OR Physics for Geoscientists (GEOL1121)) AND ((Single Mathematics A (MATH1561) and Single Mathematics B (MATH1571)) OR (Calculus and Probability I (MATH1061) and Linear Algebra I (MATH1071))).

• 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:
• Vector algebra.
• Matrices and vector spaces.
• Vector calculus.
• Line and surface integrals.
• Fourier series.
• Fourier transforms.
• Laplace transforms.
• Higher order ODEs.
• Series solution of ODEs.
• PDEs: general and particular solutions.
• PDEs: separation of variables.
• Special functions.

#### Learning Outcomes

Subject-specific Knowledge:
• Having studied this module students will be familiar with some of the key results of vectors, vector integral and vector differential calculus, multivariable calculus and orthogonal curvilinear coordinates, Fourier analysis, orthogonal functions, the use of matrices, and 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 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 on DUO.
• 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 an examination and formatively assessed through problem exercises and progress tests. The examination 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 tests 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 Contact 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: 100%
Element Length / duration Element Weighting Resit Opportunity
Written Examination 3 hours 100%

#### Formative Assessment:

Problem exercises and self-assessment; two progress tests, 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