MA40203: Theory of partial differential equations
[Page last updated: 23 October 2023]
Academic Year:  2023/24 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Masters UG & PG (FHEQ level 7) 
Period: 
 Semester 2

Assessment Summary:  EX 100% 
Assessment Detail:  
Supplementary Assessment: 
 Likeforlike reassessment (where allowed by programme regulations)

Requisites: 
Before taking this module you must take MA20223 AND take MA30252

Learning Outcomes: 
Students should be able to state definitions, and state and prove theorems, in the analysis of partial differential equations. They should be able to apply maximum principles to questions of existence, uniqueness, symmetry and boundedness/blowup for solutions of PDE.

Aims:  To introduce students to modern PDE theory through the study of qualitative properties of solutions, principally those that derive from Maximum Principles. The treatment will be rigorous and will lead to specific nonlinear examples.

Skills:  Numeracy T/F, A
Problem Solving T/F, A
Written Communication F (on problem sheets).

Content:  Weak maximum principles for twice continuously differentiable solutions of linear elliptic PDE; interior ball property, Hopf boundary point lemma, strong maximum principles. Applications might include; uniqueness of solutions of linear Poisson equations; symmetry of nonnegative solutions of nonlinear Poisson equation in a ball; Perron approach to existence. Maximum principles for parabolic equations; comparison theorem for nonlinear case. Applications might include: bounds for diffusive Burgers' equation via upper solutions; proof of blowup for nonlinear diffusion equations via lower solutions; connection with similarity solutions; systems of reactiondiffusion equations.

Course availability: 
MA40203 is Optional on the following courses:
Department of Computer Science
 USCMAFM14 : MComp(Hons) Computer Science and Mathematics (Year 4)
 USCMAAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 5)
 USCMAKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 5)
Department of Mathematical Sciences
 RSMAAFM16 : Integrated PhD Statistical Applied Mathematics
 TSMAAFM17 : MRes Statistical Applied Mathematics
 TSMAAFM16 : MSc Statistical Applied Mathematics
 USMAAFB15 : BSc(Hons) Mathematical Sciences (Year 3)
 USMAAAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
 USMAAKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
 USMAAFB13 : BSc(Hons) Mathematics (Year 3)
 USMAAAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
 USMAAKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
 USMAAFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
 USMAAAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
 USMAAKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
 USMAAAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
 USMAAKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
 USMAAFM14 : MMath(Hons) Mathematics (Year 3)
 USMAAFM14 : MMath(Hons) Mathematics (Year 4)
 USMAAAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
 USMAAKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
 USMAAKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)
Department of Physics
 USXXAFM01 : MSci(Hons) Mathematics and Physics (Year 4)
 USXXAAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 5)
 USXXAKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 5)

Notes:  This unit catalogue is applicable for the 2023/24 academic year only. Students continuing their studies into 2024/25 and beyond should not assume that this unit will be available in future years in the format displayed here for 2023/24.
 Courses and units are subject to change in accordance with normal University procedures.
 Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any prerequisite rules.
 Find out more about these and other important University terms and conditions here.
