Lecture notes were made available before each class session. Lecture slides were presented during the session. The class was taught concurrently to audiences at both MIT and the National University of Singapore, using audio and video links between the two classrooms, as part of the Singapore-MIT Alliance.
LECTURE SLIDES | LECTURE NOTES |
---|---|
Numerical Methods for Partial Differential Equations (PDF) | (PDF - 1.0 MB) |
Finite Difference Discretization of Elliptic Equations: 1D Problem (PDF) | (PDF - 1.6 MB) |
Finite Difference Discretization of Elliptic Equations: FD Formulas and Multidimensional Problems (PDF) | (PDF - 1.0 MB) |
Finite Differences: Parabolic Problems (PDF) | (PDF) |
Solution Methods: Iterative Techniques (PDF) | (PDF - 1.0 MB) |
Iterative Methods: Multigrid Techniques (PDF) | (PDF) |
Finite Difference Discretization of Hyperbolic Equations: Linear Problems (PDF - 1.7 MB) | (PDF - 2.4 MB) |
Hyperbolic Equations: Scalar One-Dimensional Conservation Laws (PDF) | (PDF - 1.4 MB) |
Numerical Schemes for Scalar One-Dimensional Conservation Laws (PDF) | (PDF - 1.4 MB) |
Finite Element Methods for Elliptic Problems; Variational Formulation: The Poisson Problem (PDF) | (PDF - 1.2 MB) |
Discretization of the Poisson Problem in IR^{1}: Formulation (PDF) | (PDF - 1.5 MB) |
Discretization of the Poisson Problem in IR^{1}: Theory and Implementation (PDF - 1.9 MB) | (PDF - 2.5 MB) |
FEM for the Poisson Problem in IR^{2} (PDF) | (PDF - 1.6 MB) |
Numerical Methods for PDEs, Integral Equation Methods, Lecture 1: Discretization of Boundary Integral Equations (PDF - 1.0 MB) | (PDF) |
Numerical Methods for PDEs, Integral Equation Methods, Lecture 2: Numerical Quadrature (PDF) | (PDF) |
Numerical Methods for PDEs, Integral Equation Methods, Lecture 3: Discretization Convergence Theory (PDF) | (PDF) |
Numerical Methods for PDEs, Integral Equation Methods, Lecture 4: Formulating Boundary Integral Equations (PDF) | (PDF) |
Numerical Methods for PDEs, Integral Equation Methods, Lecture 5: First and Second Kind Potential Equations (PDF) | |
Numerical Methods for PDEs, Integral Equation Methods, Lecture 6: Discretization and Quadrature (PDF) |