Lecture 1: Difference Methods for Ordinary Differential Equations

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Lecture 2: Finite Differences, Accuracy, Stability, Convergence

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Lecture 3: The One-way Wave Equation and CFL / von Neumann Stability

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Lecture 4: Comparison of Methods for the Wave Equation

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Lecture 5: Second-order Wave Equation (including leapfrog)

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Lecture 6: Wave Profiles, Heat Equation / point source

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Lecture 7: Finite Differences for the Heat Equation

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Lecture 8: Convection-Diffusion / Conservation Laws

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Lecture 9: Conservation Laws / Analysis / Shocks

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Lecture 10: Shocks and Fans from Point Source

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Lecture 11: Level Set Method

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Lecture 12: Matrices in Difference Equations (1D, 2D, 3D)

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Lecture 13: Elimination with Reordering: Sparse Matrices

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Lecture 14: Financial Mathematics / Black-Scholes Equation

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Lecture 15: Iterative Methods and Preconditioners

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Lecture 16: General Methods for Sparse Systems

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Lecture 17: Multigrid Methods

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Lecture 18: Krylov Methods / Multigrid Continued

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Lecture 19: Conjugate Gradient Method

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Lecture 20: Fast Poisson Solver

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Lecture 21: Optimization with constraints

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Lecture 22: Weighted Least Squares

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Lecture 23: Calculus of Variations / Weak Form

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Lecture 24: Error Estimates / Projections

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Lecture 25: Saddle Points / Inf-sup condition

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Lecture 26: Two Squares / Equality Constraint Bu = d

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Lecture 27: Regularization by Penalty Term

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Lecture 28: Linear Programming and Duality

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Lecture 29: Duality Puzzle / Inverse Problem / Integral Equations

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