CAAM 336 – Differential Equations in Science and Engineering


MWF 1:00-1:50 p.m. in Duncan Hall 1070

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LectureDateTopics/Sections CoveredHomework Additional Material
1 Mon 8/24   Chapter 1 — Classification of differential equations. Ch. 1 Exercises 1–10.
2 Wed 8/26 2.1 — Derivation of the heat equation. bar_bc.m
3 Fri 8/28 2.1.1, 2.1.2 — Heat Equation: forcing terms, boundary conditions, initial conditions, steady state.
Due at 1:00:
Ch. 1 Exercises 2,4,6,8,10.
(You should do all of them, but only hand in the evens.)
bar_bc_ss.m
4 Mon 8/31 2.3 — Vibrating Strings: the wave equation.
Java applet showing string vibrations by Paul Fastad.
5 Wed 9/2 3.1 — Vector spaces and linear operators.
Due at 1:00:
hw2.pdf
Solutions: sol2.pdf
vib_string1.m, vib_string2.m
6 Fri 9/4 3.1 — More on Vector spaces and linear operators.
Finite difference approximation.
Required reading: finite_difference.pdf
Mon 9/7 Labor Day
7 Wed 9/9 Finite differences (required reading: finite_difference.pdf).
3.2 — Subspaces, null space, range.
Due at 1:00:
hw3.pdf
Solutions: sol3.pdf
finite_diff_bessel.m
8 Fri 9/11 3.3, 3.4 — Basis, linear independence, and orthogonality.
9 Mon 9/14 3.4 — Orthogonality and projections.
10 Wed 9/16 3.4 — Best approximation.
Begin 3.5 — Eigenvalues and eigenvectors.
Due at 1:00:
hw4.pdf
Solutions: sol4.pdf
proj_example1.m
11 Fri 9/18 3.5 — The spectral method. lecture11.pdf
12 Mon 9/21 5.1 — The analogy between BVPs and linear systems; symmetric operators (Definition 5.4 and subsequent examples).
5.2 — The spectral method.
13 Wed 9/23 5.1, 5.2 continued.
Due at 1:00:
hw5.pdf
Solutions: sol5.pdf
14 Fri 9/25 5.2, 5.3 — The spectral method for solving BVPs.
15 Mon 9/28 5.3 — Convergence of Fourier series. Inhomogeneous boundary conditions.
16 Wed 9/30 5.3 — More examples.
Due at 1:00:
hw6.pdf
Solutions: sol6.pdf
17 Fri 10/2 Fourier series recap.
5.4 — Weak formulation.
18 Mon 10/5 5.4, 5.5 — Weak formulation and the Galerkin method.
19 Wed 10/7 5.5, 5.6 — The Galerkin method, finite elements.
Due at 1:00:
hw7.pdf
Solutions: sol7.pdf
20 Fri 10/9 5.6 — Piecewise linear finite elements. galerkin_example1.m
hat.m, fem_demo1.m
Mon 10/12 Midterm Recess
21 Wed 10/14 5.6 continued.
Due at 1:00:
hw8.pdf
Solutions: sol8.pdf
22 Fri 10/16 6.1.6 — Homogeneous heat equation; separation of variables.
23 Mon 10/19 More heat equation:
6.1.0, 6.1.1 — Fourier series methods.
6.1.3 — Inhomogeneous heat equation with homogeneous Dirichlet conditions.
6.1.4 — Inhomogeneous Dirichlet conditions.
Begin 6.2 — Homogeneous Neumann conditions.
24 Wed 10/21 6.2 — Heat equation with homogeneous Neumann conditions. Fourier cosine series.
25 Fri 10/23 6.3 — Periodic boundary conditions and the full Fourier series.
Due at 5:00:
exam1.pdf
exam1_practice_problems.pdf
26 Mon 10/26 6.3 continued.
27 Wed 10/28 6.4.0 — Finite element method for the heat equation.
Due at 1:00:
hw9.pdf
Solutions: sol9.pdf
28 Fri 10/30 4.2, 4.3 — ODE and linear homogeneous systems (review).
4.4 — Matrix exponentials, Euler's method.
29 Mon 11/2 4.5 — Backward Euler method.
30 Wed 11/4 4.5 continued. euler_demo.m
31 Fri 11/6 6.4, 6.5 — Finite elements and Neumann conditions.
Due at 1:00:
hw10.pdf
Solutions: sol10.pdf
32 Mon 11/9 6.5 continued.
33 Wed 11/11 6.5 continued.
34 Fri 11/13 7.1 — Infinite string: d'Alembert's solution. For a careful derivation of a model of a vibrating string, see:
Stuart S. Antman, The equations for large vibrations of strings, American Math. Monthly 87 (1980) 359--370.
35 Mon 11/16 7.1 continued.
7.2 — Homogeneous wave equation: separation of variables.
36 Wed 11/18 7.2 — The Fourier method for the wave equation.
Due at 1:00:
hw11.pdf
Solutions: sol11.pdf
hw11prob6.m
wave_DirichletIBVP.m
37 Fri 11/20 7.3 — FEM for the wave equation.
7.4 (especially 7.4.2) — Resonance.
38 Mon 11/23 Finish ch. 7.
8.1 — 2 and 3 dimensions, the Divergence Theorem.
39 Wed 11/25
Fri 11/27 Thanksgiving Recess
40 Mon 11/30
41 Wed 12/2
Due at 1:00:
hw12.pdf
42 Fri 12/4
exam2.pdf
Exam 2 Due at 5 p.m., Wednesday, Dec 16

Any student with a disability requiring accommodation in this course is encouraged
to contact the instructor during the first week of class, and also to contact
Disability Support Services in the Ley Student Center.