Mathematical Methods for Engineers II (Spring 2006) (M-I-T)

• Lecture 1: Difference Methods for Ordinary Differential Equations (M-I-T)
• Lecture 2: Finite Differences, Accuracy, Stability, Convergence (M-I-T)
• Lecture 3: The One-way Wave Equation and CFL / von Neumann Stability (M-I-T)
• Lecture 4: Comparison of Methods for the Wave Equation (M-I-T)
• Lecture 5: Second-order Wave Equation (including leapfrog) (M-I-T)
• Lecture 6: Wave Profiles, Heat Equation / point source (M-I-T)
• Lecture 7: Finite Differences for the Heat Equation (M-I-T)
• Lecture 8: Convection-Diffusion / Conservation Laws (M-I-T)
• Lecture 9: Conservation Laws / Analysis / Shocks (M-I-T)
• Lecture 10: Shocks and Fans from Point Source (M-I-T)
• Lecture 11: Level Set Method (M-I-T)
• Lecture 12: Matrices in Difference Equations (1D, 2D, 3D) (M-I-T)
• Lecture 13: Elimination with Reordering: Sparse Matrices (M-I-T)
• Lecture 15: Iterative Methods and Preconditioners (M-I-T)
• Lecture 16: General Methods for Sparse Systems (M-I-T)
• Lecture 17: Multigrid Methods (M-I-T)
• Lecture 18: Krylov Methods / Multigrid Continued (M-I-T)
• Lecture 19: Conjugate Gradient Method (M-I-T)
• Lecture 20: Fast Poisson Solver (M-I-T)
• Lecture 21: Optimization with constraints (M-I-T)
• Lecture 22: Weighted Least Squares (M-I-T)
• Lecture 23: Calculus of Variations / Weak Form (M-I-T)
• Lecture 24: Error Estimates / Projections (M-I-T)
• Lecture 25: Saddle Points / Inf-sup condition (M-I-T)
• Lecture 26: Two Squares / Equality Constraint Bu = d (M-I-T)