Aims:
To give an introduction to some of the basic methods of numerical analysis via a widely used scientific computing package.
Detailed Information
Course Description: Link to Official Course Descriptor.
Pre-requisites: none.
Location: Malaysia.
Semester: 2.
Syllabus:
- Introduction: What is scientific computing? Approximate versus exact solutions of mathematical problems.
- Introduction to scientific computing software: Basic operations, vectors and matrices, plotting graphs of functions, loops, conditional statements.
- Solution of nonlinear algebraic equations: Approximating solutions of f(x)=0 using, e.g., the bisection, Newtonand fixed-point methods.
- Polynomial Interpolation: Approximating functions of one variable by polynomials.
- Numerical Integration: Approximating integrals of functions of one or more variables using, e.g., Newton-Cotesmethods, composite quadrature rules, Gaussian quadrature.
- Numerical Differentiation: Approximating derivatives using finite differences, e.g., forward, backward and central difference methods.
- Direct methods for solving linear systems: Approximating solutions of Ax=b using, e.g., Gaussian eliminationand LU and Cholesky decompositions.
- Iterative methods for solving linear systems: Approximating solutions of Ax=b using, e.g., Jacobi, Gauss-Seidel, SOR and Krylov subspace methods.
- Iterative methods for solving eigenvalue problems: Approximating eigenvalues and eigenvectors using, e.g. power, inverse power, QR and Krylov subspace methods.
Learning Outcomes: Subject Mastery
• Basic understanding of numerical analysis and the numerical approximation of solutions of mathematical problems.
• Use of mathematical techniques for approximating derivatives, integrals and the solutions of nonlinear equations.
• Ability to approximate and interpolate a function.
• Be able to solve a linear system by standard direct methods.
• Be able to carry out iterative algorithms for the solution of linear systems and eigenvalue problems.
• Appreciate the value of careful analysis of algorithms for efficiency and accuracy.
Learning Outcomes: Personal Abilities
• Ability to use computer software to solve mathematical problems.
• The ability to critically assess sources and types of errors in problems.
• Critical awareness of the power of abstraction in understanding physical situations.
• Ability to use computer simulations to understand abstract systems and approximate real-world problems.
• Organize complex calculations in a clear manner.
• Be aware of the importance of understanding errors.
• Be able to present a written account of technical material.
Assessment Methods: Due to covid, assessment methods for Academic Year 2021-22 may vary from those noted on the official course descriptor. Please see the Computer Science Course Weightings and the Maths Course Weightings for 2020-21 Semester 1 assessment methods.
SCQF Level: 9.
Credits: 15.