• Student home
• Student news
• Student events
• New students' welcome
• Studying at York
  • Enrolment
  • Manage your studies
    • Enrol or re-enrol
    • Your student record
    • Your timetable
    • Change your plan
    • Programmes and modules
      • Programme specifications
      • Elective modules
      • Module catalogue
    • University study spaces
  • Student Visa holders
  • Study skills
  • Assessment and examination
  • Academic progress issues
  • Graduation
• York Futures
• Health and wellbeing
• Support and advice
• York Graduate Research School
• Work, volunteering and career planning
• Accommodation
• Study and work abroad
• IT and online services
• Finance
• Campus and city life
• If things go wrong

Partial Differential Equations I - MAT00040H

« Back to module search

• Department: Mathematics
• Module co-ordinator: Dr. Konstantin Ilin
• Credit value: 10 credits
• Credit level: H
• Academic year of delivery: 2021-22
  • See module specification for other years: 2018-19 2019-20 2020-21

Related modules

Module will run

Occurrence	Teaching cycle
A	Autumn Term 2021-22

Module aims

A partial differential equation (PDE) is a differential equation that contains an unknown function and its partial derivatives. PDEs are used to describe a wide range of natural processes. Examples include fluid mechanics, elasticity theory, electrodynamics, quantum mechanics, etc. PDEs also play an important role in other areas of mathematics such as analysis and differential geometry.

The aim of this module is to give an introduction to the basic properties of PDEs and to the basic analytical techniques to solve them.

Module learning outcomes

At the end of the module students should

• be able to determine the type of a second order PDE
• be able to solve simplest first order PDEs
• understand what are well-posed initial (and/or boundary) value problems for classical PDEs such as the wave equation, the Laplace equation and the heat (diffusion) equation
• know basic analytical techniques for solving the above classical equations

Module content

Syllabus

• Introduction: what is a PDE, first-order linear PDEs, initial and boundary conditions, well-posed problems, types of second-order PDEs.
• Wave equation: d'Alembert’s formula, causality and energy, reflection of waves.
• Heat (diffusion) equation: maximum principle, heat equation on the whole line and on the half-line
• Laplace equation: maximum principle, Poisson’s formula, rectangular domain

 

Academic and graduate skills

• Academic skills: the techniques taught are used in many areas of pure and applied mathematics.

• Graduate skills: through lectures, examples, classes, students will develop their ability to assimilate, process and engage with new material quickly and efficiently. They develop problem solving-skills and learn how to apply techniques to unseen problems.

Assessment

Task	Length	% of module mark
Online Exam Partial Differential Equations I	N/A	100

Special assessment rules

None

Reassessment

Task	Length	% of module mark
Online Exam Partial Differential Equations I	N/A	100

Module feedback

Current Department policy on feedback is available in the undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

Indicative reading

W.A.Strauss, Partial Differential Equations. An Introduction. John Wiley & Sons. 1992.