Course Description

This course provides an overview and covers the fundamentals of scientific and numerical computing. Topics include numerical analysis and computation, symbolic computation, scientific visualization, architectures for scientific computing, and applications of scientific computing.



Course topics include

1. Computer arithmetic: floating point numbers, rounding errors, relative and absolute errors, cancelation, numerical instability.

Solving systems of linear equations: Gaussian elimination, LU decomposition, pivoting, QR decomposition, Cholesky decomposition, norms, condition numbers, iterative methods.

Solving nonlinear equations: bisection method, Newton's method, the secant method.

2. Optimization(optional): golden section search, the steepest descent method, Newton's method the conjugate gradient method.

Interpolation(optional): interpolation for approximation, Lagrange interpolation, Newton interpolation, Hermite interpolation, piecewise polynomial interpolation.

3. Numerical differentiation and integration: forward difference approximation, Richardson extrapolation, the composite rule, Newton-Cotes quadrature, Gaussian quadrature.

4. Stochastic simulation(optional): random numbers, random number generators, nonuniform distributions, low-discrepancy sequences.

Eigenvalue computation(optional): Jacobi method, the power method, singular value decomposition.

5. Symbolic computation(optional): symbolic computation, exact arithmetic, computer algebra.

Assessment

6 programming assignments: 25%

6 written assignments: 25%

Final examination: 50%

Grading

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Teaching Skills & Others

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