| Class | Date | Main Topic | References |
| 1 | Tu 01/31 | Overview of prototype problems for the semester | Evans (Ch. 1) |
| 2 | Th 02/02 | Theory of elliptic partial differential equations | Evans (Sec. 2.2) |
| 3 | Tu 02/07 | Theory of parabolic partial differential equations | Evans (Sec. 2.3) |
| 4 | Th 02/09 | The finite difference method for elliptic problems | Braess (Ch. I) |
| 5 | Tu 02/14 | Linear solvers and Matlab programming | |
| 6 | Th 02/16 | Theory of the finite difference method for elliptic problems | Braess (Ch. I) |
| 7 | Tu 02/21 | Theory of the finite difference method for elliptic problems | Braess (Ch. I) |
| 8 | Th 02/23 | Test 1 (the finite difference method) | |
| 9 | Tu 02/28 | Introduction to the FEM for elliptic problems | |
| 10 | Th 03/02 | The weak form of elliptic PDEs | |
| 11 | Tu 03/07 | Weak derivatives and Sobolev spaces and their norms | Braess (Sec. II.1) |
| 12 | Th 03/09 | General theory of elliptic bilinear forms | Braess (Sec. II.2) |
| 13 | Tu 03/14 | Céa's lemma and Galerkin orthogonality | Braess (Sec. II.4) |
| We 03/15 | 12:00-01:00 CIRC Software Workshop on FEMLAB | in Room ENG 122 | |
| 14 | Th 03/16 | More on weak formulation and introduction to FEMLAB | |
| Tu 03/21 | Spring Break | ||
| Tu 03/21 | Spring Break | ||
| 15 | Tu 03/28 | Standard finite element spaces and their properties | Braess (Sec. II.5) |
| 16 | Th 03/30 | Implementation details of finite element methods | |
| Fr 03/31 | The Finite Element Circus at UMBC | in Room BIOL 120 | |
| Sa 04/01 | The Finite Element Circus at UMBC | in Room BIOL 120 | |
| 17 | Tu 04/04 | Approximation theory for finite element spaces | Braess (Sec. II.6) |
| 18 | Th 04/06 | Convergence analysis for the FEM for elliptic problems | Braess (Sec. II.7) |
| 19 | Tu 04/11 | Introduction to FEMLAB's scripting language | |
| 20 | Th 04/13 | Test 2 (the finite element method) | |
| 21 | Tu 04/18 | The method of lines for parabolic problems (FEM and FD) | |
| 22 | Th 04/20 | The finite element method for parabolic problems | Thomée (Ch. 1) |
| 23 | Tu 04/25 | Theory of the finite element method for parabolic problems | Thomée (Ch. 1) |
| 24 | Th 04/27 | Theory of hyperbolic partial differential equations | Strikwerda (1.1-1.2) |
| 25 | Tu 05/02 | Finite differences for the scalar transport equation | Strikwerda (1.3-1.4) |
| 26 | Th 05/04 | Theory for FD for the scalar transport equation | Strikwerda (1.5-1.6) |
| 27 | Tu 05/09 | Numerical methods for stiff systems of ODEs | Shampine & Reichelt |
| 28 | Th 05/11 | Numerical methods for stiff systems of ODEs | Shampine & Reichelt |
| 29 | Tu 05/16 | Review and discussion | |
| Th 05/18 | 01:00-03:00 Project Presentations | Note date and time! | |