Web Page for Math 412
Partial Differential Equations
Syllabus
Homework
HW #1, due Feb. 3: Chapter 1, Problems 2, 6, 7; Section 2.1, Problems 4, 7, 8, 11 (read 2.1.3); Section 2.3: 7.
HW #2, due Feb. 15: Section 3.1, Problem 5 [Hint: determine whether or not the set is a subspace of C[0,1] for (a)-(c) and of C(R) for (d) & (e)]; Section 3.2, Problems 1, 7; Section 3.3, Problem 9; Section 3.4, Problems 1, 10; Section 3.5, Problem 2.
HW #3, due March 1:
Section 5.1, Problem 7;
Section 5.2, Problems 1, 3, 7 a, 11 a;
Section 5.3, Problems 2 a&b, 4 d.
HW #4, due March 13:
Section 5.3, Problems 4 a&c. Also provide plots of the series solutions using modifications of codes 2 & 4 below.
Section 5.5, Problem 7.
Section 5.6, Problems 3 (modify FEM_Ex5_19.m for part b), 5 (modify FEM_Ex5_18.m for the error tests).
HW #5, due March 31:
Unless Matlab code is specifically asked for, include only paper print offs of the output.
Section 6.1, Problems 4, 8 (use ODE soln on p. 91). For the plots, modify HeatSineIBVPsnapshot.m, which plots a snap shot of the solution to Example 6.1 for a fixed t value.
Section 6.2, Problems 2 with requested graphs (for this modify HeatCosineIBVPsnapshot.m), 7 and 8.
HW #6, due April 14:
Section 6.4, Problems 8, 10. Modify HeatFEM.m.
Section 6.5, Problems 6 (note that (a) and (b) are written problems and (c) requires an m-file). Modify HeatFEM.m, making use of FEM_Ex6_10.m.
Section 7.1, Problems 1, 2. Include snapshots of solutions in your write-up.
Final Exam, due by noon on May 12: Final.pdf.
Computer Cods/Labs:
1. Plotting Fourier sine series: FourierSineCompare.m, FourierSine.m
2. Plotting sine series solutions of the BVP -u''=f, u(0)=u(L)=0: FourierSineBVPsoln.m, FourierSineBVPsolnHW.m
3. Plotting quarter-cosine series solutions of the BVP -u''=f, u'(0)=u(L)=0, defined in 5.3 4d (p. 164): FourierQuarterCosineBVPsolnHW.m, FourierQuarterCosine.m
4. Plotting quarter-sine series solutions of the BVP -u''=f, u(0)=u'(L)=0, defined in Example 5.11 (p. 156): FourierQuarterSineBVPsolnEx5_11.m, FourierQuarterSine.m
**Lab, March 10: FEM_Ex5_18.m, FEM_Ex5_19.m
5. Plotting solutions of the heat equation, Ex 6.1: HeatSineIBVPsoln.m
6. Plotting solutions of the diffusion equation, Ex 6.2: DiffusionSineIBVPsoln.m
7. Plotting solutions of the heat equation with Neumann BCs, Ex 6.4: HeatCosineIBVPsoln.m, FourierCosine.m
8. Solving the heat equation using FEM (Example 6.8), HeatFEM.m.
9. FEM for the with Neumann BCs: FEM_Ex6_10.m
10. Plotting solutions of the homogeneous wave equation, Ex 7.3: HomogWaveSineIBVPsoln.m.
11. Plotting solutions of the non-homogeneous wave equation, Ex 7.4: NonHomogWaveSineIBVPsoln.m.
Exams