MTH (0144) 584 - Numerical Calculus and Applications

Credits: 3.00

Students will learn the key concepts of numerical computations. Focus is placed on numerical methods for nonlinear equations, optimization, interpolation and approximation, differentiation and integration, ordinary differential equations, boundary-value problems, and Fourier transforms.

Free Note: Open only to students in the M.S. in Mathematics.

Students will:

●   Explain approximations in scientific computing; nonlinear equations. This will be assessed by Quiz 1 and Exam 1.
●   Apply optimization in 1-D; nonlinear least squares; constrained optimization. This will be assessed by Quiz 3 and Exam 2.
●   Explain how to utilize polynomial interpolation; piecewise polynomial interpolation. This will be assessed by Quiz 2 and Exam 1.
●   Apply numerical integration and differentiation; Richardson extrapolation. This will be assessed by Quiz 4 and Exam 2.
●   Solve initial value problems using: single-step methods; multi-step methods; Runge-Kutta methods. This will be assessed by Quiz 5 and the final exam.
●   Solve boundary-value problems; shooting method; finite-difference methods; finite element methods. This will be assessed by Quiz 6 and the final exam.
●   Use trigonometric interpolation; Fourier transform. This will be assessed by the final exam.
●   Solve large systems; direct sparse linear solvers; multigrid methods. This will be assessed by the final exam.