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Section 5.1: Background for programming projects, introduction to the
solution of initial value problems |
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Section 5.2: Derivations of Euler's method, definition of
convergence |
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Section 5.2-5.3: Error bounds and
asymptotic error estimate for Euler's method, local truncation error, global
error |
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Section 5.2-5.4: Convergence proof for
Euler's method, derivation of Runge-kutta methods |
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Section 5.4: Runge-Kutta methods cont,
derivation of the general second order Runge-Kutta methods |
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Section AS: Timestep estimation, model
problem analysis, intervals of absolute stability |
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Section AS: Timestep estimation for
general equations |
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Section 5.11: Implicit methods
(Trapezoidal rule, Backward Euler), comparison of ODE methods |
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Section 5.11: Implicit methods,
solving the implicit equations, stiff differential equations |
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Section 5.6: Overview of multistep
methods |
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Section 5.9: Numerical methods for
systems of ODE's |
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Section 5.9: Results on numerical
methods for systems, convergence results, error bounds, asymptotic error
estimates, regions of absolute stability. |
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Section 11.3: Two point boundary
values problems, finite difference approximation |
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Section 7.1 11.3: Review of vector and
matrix norms, error estimates for linear two-point boundary value problem |
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Section 11.4: Programming
consideration for two point boundary value problems |
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Section 7.3: Iterative methods for the
solution of linear systems of equations, Gauss-Jacobi method |
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Section 7.3: Iterative methods cont,
Gauss-Seidel methd, error analysis for iterative methods |
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Section 7.1-4: Error analysis for
iterative methods cont, relationship between error and the residual,
stopping criterion |
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Section 7.3-4: Convergence results for
iterative methods, condition number |
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Section 8.1: Discrete least squares approximation,
construction of the normal equations |
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Section 8.1, DLS: Derivation of the normal
equations, matrix/vector formulation of the discrete least squares
problem |
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Section DLS: Using the QR decomposition to solve
normal equations, relation of QR to Gram-Schmidt. |
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Section 8.5: Introduction to discrete Fourier
approximation |
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Section 8.5: Fourier approximation cont, complex
form of the discrete Fourier approximation |
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Section 8.6: The fast Fourier transform |
