Assignment 4
Assignment due: end of term
Documents
Assignment 4 [PDF]
Solutions 4 [PDF]
Topics assessed include:
- Q1: Energy arguments
- Q2-3: Maximum principle for the heat equation
- Q4-8: Fourier transforms
- Q9: Showing that the Fourier transform of an L1 function is not always in L1 itself
Assignment 3
Assignment due: 2024-11-22
Documents
Assignment 3 [PDF]
Solutions 3 [PDF]
Topics assessed include:
- Q1: Reflection method
- Q2: Inhomogeneous wave equation
- Q3: A useful result for Fourier series.
- Q4: Separable variables: wave equation
- Q5: Separable variables: heat equation
- Q6: Separable variables: Laplace's equation
Assignment 2
Assignment due: 2024-11-08
Documents
Assignment 2 [PDF]
Solutions 2 [PDF]
Topics assessed include:
- Q1: Classification of second order PDEs
- Q2: Causality for the wave equation (domain of dependence, domain of influence)
- Q3: d'Alembert's formula (application with specific functions)
- Q4: Method of characteristics revisited
Assignment 1
Assignment due: 2024-10-25
Documents
Assignment 1 [PDF]
Solutions 1 [PDF]
Topics assessed include:
- Q1: ODEs recap
- Q2: Classification of PDEs (linearity, order, homogeneous)
- Q3: Straightforward PDEs (solveable through integration)
- Q4: Method of characteristics with constant coefficients. This video should be helpful.
- Q5,6,7: Method of characteristics with variable coefficients. This video should be helpful.
- Q8: Method of characteristics: the general case. This video should be helpful.
Aseiniad 4
Dychwelwch yr aseiniad erbyn:
Ffeiliau
Aseiniad 4 [PDF]
Datrysiadau 4 [PDF]
Ymhlith y pynciau a aseswyd mae:
- C1: Dadleuon egni
- C2-3: Yr Egwyddor Macsimwm
- C4-8: Cyfrifo trawsffurfiau Fourier
- C9: Dangos nad yw trawsffurf Fourier ffwythiant L1 yn L1 bob tro
Aseiniad 3
Dychwelwch yr aseiniad erbyn: 2024-11-22
Ffeiliau
Aseiniad 3 [PDF]
Datrysiadau 3 [PDF]
Ymhlith y pynciau a aseswyd mae:
- C1: Dull adlewyrchiad
- C2: Hafaliad ton anhomogenaidd
- C3: Canlyniad defnyddiol ar gyfer cyfresi Fourier
- C4: Gwahanu newidynnau: hafaliad ton
- C5: Gwahanu newidynnau: hafaliad gwres
- C6: Gwahanu newidynnau: hafaliad Laplace
Aseiniad 2
Dychwelwch yr aseiniad erbyn: 2024-11-08
Ffeiliau
Aseiniad 2 [PDF]
Datrysiadau 2 [PDF]
Ymhlith y pynciau a aseswyd mae:
- C1: Dosbarthu hafaliadau differol rhannol trefn dau (parabolig, eliptig, hyperbolig)
- C2: Achosiaeth ar gyfer hafaliad ton (parth y dibyniaeth, parth y dylanwad)
- C3: Fformiwla d'Alembert (cymhwysiad gyda ffwythiannau penodol)
- C4: Dull nodweddion: ailymweld
Aseiniad 1
Dychwelwch yr aseiniad erbyn: 2024-10-25
Ffeiliau
Aseiniad 1 [PDF]
Datrysiadau 1 [PDF]
Ymhlith y pynciau a aseswyd mae:
- C1: Ymarfer datrys hafaliadau differol cyffredin
- C2: Dosbarthu hafaliadau differol rhannol (llinoledd, trefn, homogenedd)
- C3: Hafaliadau differol rhannol syml (gellir eu datrys trwy integru)
- C4: Dull nodweddion gyda chyfernodau cyson. Dylai'r fideo yma fod yn ddefnyddiol.
- C5,6,7: Dull nodweddion gyda chyfernodau newidiol. Dylai'r fideo yma fod yn ddefnyddiol.
- C8: Dull nodweddion: yr achos cyffredinol. Dylai'r fideo yma fod yn ddefnyddiol.