Unit Code: MTH810

Unit Name: Scientific Computing

Description: Scientific computing has become an indispensable tool in many branches of research and is vitally important for studying a wide range of physical and social phenomena. This course is a practical introduction to computational problem-solving, including both mathematical analyses of numerical algorithms (numerical analysis) and practical problem-solving. In addition to computational techniques, the course includes theoretical development and implementation, efficiency, and accuracy issues in using algorithms and interpreting results. The aim is to give students a basic understanding of floating-point arithmetic, the implementation of algorithms used to solve numerical problems, and a familiarity with current numerical computing environments. There will be a significant programming component in the course. Students will be expected to implement a range of numerical methods in homework assignments to get hands-on experience with modern scientific computing. Topics include linear systems, linear least squares, eigenvalue problems, nonlinear equations, optimization algorithms, interpolation, numerical integration and differentiation, and differential equations.

Learning Target Outcomes: As a result of successfully completing this course, the student will be able to: 1. Analyse key properties of numerical algorithms, such as stability and convergence using standard techniques. 2. Transform scientific problems into generic computational models and understand how various error sources influence the accuracy and reliability of the models and the computed results. 3. Use fundamental mathematical techniques relevant to the analysis of scientific computing methods. 4. Analyse essential algorithms relevant to real-world scientific computing. 5. Demonstrate a capacity for rigorous analysis in sophisticated scientific computing and visualization environments. 6. Develop and use a high-level programming language to solve scientific computing problems with proficiency and confidence.

Prerequisite: Minimum Entry Requirements of the programme

Prerequisite Sentence: N/A

Credit Point: 30

Offered In: Semester 1,2