MA319 Half Unit
Partial Differential Equations
This information is for the 2020/21 session.
Teacher responsible
Simon, Robert
Availability
This course is available on the BSc in Business Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Economics and BSc in Mathematics, Statistics and Business. This course is available with permission as an outside option to students on other programmes where regulations permit and to General Course students.
Pre-requisites
Students must have completed Further Mathematical Methods (MA212) and Real Analysis (MA203).
Course content
The aim of the course is the study of partial differential equations. The focus will be on first order quasilinear equations, and second order linear equations. The method of characteristics for solving first order quasilinear equations will be discussed. The three main types of linear second order partial differential equations will be considered: parabolic (diffusion equation), elliptic (Laplace equation), and hyperbolic (wave equation). Techniques for solving these for various initial and boundary value problems on bounded and unbounded domains, using eigenfunction expansions (separation of variables, and elementary Fourier series), and integral transform methods (Fourier and Laplace transforms) will be treated. Elementary distributional calculus and the notion of weak solutions will also be considered. Applications and examples, such as the solution technique for Black-Scholes option pricing, will be discussed throughout the course.
Teaching
This courseis delivered through a combination of classes and lectures totalling 30 hours across Lent Term. This year, some or all of this teaching will be delivered through a combination of virtual classes and delivered as online videos.
Formative coursework
Students will be expected to produce 10 problem sets in the LT.
Written answers to set problems will be expected on a weekly basis.
Indicative reading
- S.J. Farlow. Partial Differential Equations for Scientists and Engineers. Dover, 1993.
- J.D. Logan. Applied Partial Differential Equations. Second Edition. Springer, 2004.
- W. Strauss. Partial Differential Equations. An Introduction. Second Edition. John Wiley, 2008.
Lecture notes will be provided.
Assessment
Exam (100%, duration: 2 hours) in the summer exam period.
Important information in response to COVID-19
Please note that during 2020/21 academic year some variation to teaching and learning activities may be required to respond to changes in public health advice and/or to account for the situation of students in attendance on campus and those studying online during the early part of the academic year. For assessment, this may involve changes to mode of delivery and/or the format or weighting of assessments. Changes will only be made if required and students will be notified about any changes to teaching or assessment plans at the earliest opportunity.
Key facts
Department: Mathematics
Total students 2019/20: 28
Average class size 2019/20: 14
Capped 2019/20: No
Value: Half Unit
Personal development skills
- Self-management
- Problem solving
- Communication
- Application of numeracy skills
- Specialist skills
