MATH 412-200/501/502 "Theory of Partial Differential Equations", Fall 2017

Course information

• Instructor: Dr G.Berkolaiko, office: Blocker 625c, email: berko AT math.tamu.edu
• Lectures: MWF 11:30-12:20pm BLOC 117 (Section 502)
  MWF 12:40-1:30pm BLOC 161 (Sections 200/501)
• Office hours: M 2-3pm and T 10-11
• Course description (first day handout)
• Exam Dates: midterm Friday, Oct 20 (class time); final Thursday, Dec 7, 10am-12noon in Blocker 150.

Homework assignments

Solutions and grades will be posted on eCampus.

Problems with * are compulsory for the honors section students only. Regular section students are encourage to solve them too; please mark your homework with a big star so that I can provide feedback to you!

HW 1 (due Wed, Sept 6) solutions available

1.3: 1;
1.4: 1bfg, 4, 7ba, 10;

HW 2 (due Wed, Sep 13)

1.5: 5, 9a, 12, 14;
2.2: 4;
2.3: 1ace, 2a, 3ab, 5, 7*;
2.4: 3, 4, 6;

HW 3 (due Wed, Sep 27)

2.5: 1b, 3, 5ad, 7a, 12 (integrate by parts), 14, 15d;
4.4: 8-12
3.2: 1ac, 4;

HW 4 (due Wed, Oct 4)

3.3: 4, 15;
3.4: 1, 2*, 3a (use the formula for sine series coefficients and integrate by parts using 3.4.1), 9, 12

HW 5 (due Wed, Oct 11)

12.2: 3, 4, 5acd;
(*) Additional questions

HW 6 (due Wed, Oct 18)

12.3: 5, 6*;
12.4: 2, 4;
12.5: 1b (use (4.4.11) and (4.4.13) as the answer for part (a));

HW 7 (due Wed, Nov 1)

10.3: 1, 5-8, 18*;

HW 8 (due Wed, Nov 8)

10.4: 3-5;

HW 9 (due Fri, Nov 17)

9.2: 3;
9.3: 1, 2, 4cd;

HW 10

9.3.5abc;
Use the Green's function we derived (equation (11.2.32)) in the representation formula (11.2.24) to derive the d'Alambert's solution (12.3.13) for the wave equation (12.3.1),(12.3.6),(12.3.7).

Extras

• Past exams: midterm 2010, final 2010.
• Matlab simulations:
  • Animating solution of a simple heat equation with fixed ends: animate_heat_eq.m.
  • Exploring Fourier series: compare_FS.m, compare_FsineS.m, compare_FcosS.m.
  • Animating solutions of the wave equation: animate_wave_eq.m
  • Animating Green's function for the heat equation with 0 boundary: animate_gf_heat_eq_bc0.m
  • Animating solution to wave equation with a non-homogeneous boundary: wave_nh_boundary.m
• More material:
  • Prerequisites review (notes from Oct 16 class, courtesy of Christina Rigsby).
  • Notes on derivation of Laplacian (and gradient) in polar coordinates.
  • Notes on different forms of the general solution of \(y'' = ay\), ExtraNotes_ExponentialSolutions.pdf.
  • Notes on method of characteristics.

Course news

• Material covered (midterm): Chapters 1, 2, 3, 4.1-4.4, 12.1-12.5.
• Pre-exam review: Blocker 605AX, Thursday Oct 19, 3-4pm.

This file was last modified on Wednesday, 10-Jan-2024 15:58:00 CST.