Overview

Prerequisites

• MA1115
• MA2121

Learning Outcomes

A student who successfully completes this course will have developed/acquired the following skills/knowledge:

• Possess a basic working knowledge of floating-point numbers and arithmetic. Understand floating-point round-off and its consequences, including catastrophic cancellation. Be able to define the term “machine epsilon.”
• Understand the difference between absolute and relative error. Know when each is appropriate to use and why.
• Be able to implement basic numerical algorithms for root finding, including fixed-point iterations, Newton’s method, the secant method, and bisection.
• Be able to implement basic piecewise interpolation schemes.
• Be able to implement finite difference schemes for approximating derivatives of functions.
• Be able to implement composite Newton–Cotes quadrature methods, including Riemann sums, the trapezoid rule, and Simpson’s rule.
• Be able to implement various methods for solving initial-value problems (IVPs), including one-step methods (e.g., Euler’s method and Runge–Kutta methods), and multistep methods. Know the differences between one-step and multistep methods and those between implicit and explicit methods and the relative merits of each.
• Implement Lagrange schemes for polynomial interpolation, including barycentric schemes. Know the differences between Lagrange interpolation and piecewise interpolation and their relative merits. Implement Chebyshev interpolation.
• Implement trigonometric interpolation. Understand the connection between trigonometric interpolation and the discrete Fourier transform.
• Develop a basic understanding of orthogonal polynomials and their role in continuous least-squares fitting and Gauss quadrature.
• Implement basic methods for solving boundary-value problems, including finite difference methods and spectral collocation.