#### Prerequisites
* (Foundations of Physics 1 (PHYS1122) OR Physics for Geoscientists (GEOL1121)) 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:
* 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 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 an open-book examination and formatively assessed through problem exercises and a progress test. The open-book 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 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.
More information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS2611
