| M612 as an Online Course (8:52) |
| Compact Embeddings (4:46) |
| Difference Quotients (8:07) |
| The Space H-1 (8:27) |
| Full Lecture PDF (12 pages) |
| Second Order Elliptic PDE (10:28) |
| Weak Solutions (11:50) |
| Full Lecture PDF (13 pages) |
| The Lax-Milgram Theorem (8:31) |
| Proof of the Lax-Milgram Theorem (12:44) |
| Full Lecture PDF (15 pages) |
| The Main Energy Estimate (11:16) |
| Existence of Weak Solutions (5:44) |
| The Terminology ''Energy Estimates'' (6:54) |
| Full Lecture PDF (13 pages) |
| Adjoint Operators on Hilbert Spaces (7:27) |
| The Fredholm Alternative for Compact Operators (5:21) |
| The Fredholm Alternative for Elliptic Operators (10:52) |
| Full Lecture PDF (12 pages) |
| Proof of Theorem 6.2.4, Part I (12:15) |
| Proof of Theorem 6.2.4, Part II (13:44) |
| Full Lecture PDF (14 pages) |
| Spectral Theory for Compact Operators (3:38) |
| The Resolvent for Elliptic Operators: Theorem 6.2.5 (11:03) |
| The Resolvent for Elliptic Operators: Theorem 6.2.6 (11:50) |
| Full Lecture PDF (19 pages) |
| Interior Regularity: Overview (5:23) |
| Interior Regularity: Theorem 6.3.1, Part I (7:23) |
| Interior Regularity: Theorem 6.3.1, Part II (9:51) |
| Full Lecture PDF (31 pages) |
| University Reading Day |
| Interior Regularity: Theorem 6.3.1, Part III (20:38) |
| Interior Regularity: Theorem 6.3.1, Part IV (17:06) |
| Higher Interior Regularity (7:49) |
| Boundary Regularity, Part I (20:15) |
| Full Lecture PDF (33 pages) |
| Boundary Regularity, Part II (23:29) |
| Boundary Regularity, Part III (9:59) |
| Higher Boundary Regularity (3:28) |
| Function Spaces Involving Time: Classcial Theory (13:43) |
| Function Spaces Involving Time: Bochner Integration (6:14) |
| Function Spaces Involving Time: Lp (0,T; X) (9:35) |
| Full Lecture PDF (18 pages) |
| Second Order Parabolic PDE: Energy Estimates (24:33) |
| Second Order Parabolic PDE: Existence of Weak Solutions (17:33) |
| Full Lecture PDF (23 pages) |