Unit information: Applied Linear Algebra in 2020/21

Unit name	Applied Linear Algebra
Unit code	EMAT20012
Credit points	10
Level of study	I/5
Teaching block(s)	Teaching Block 2 (weeks 13 - 24)
Unit director	Dr. Szalai
Open unit status	Not open
Pre-requisites	EMAT10100, EMAT10704, EMAT10007, EMAT10006,
Co-requisites	EMAT20920
School/department	School of Engineering Mathematics and Technology
Faculty	Faculty of Engineering

Description including Unit Aims

The unit will teach some practical aspects of matrix linear algebra that is applicable to engineering problems such as in large-scale data analysis and solution of linear differential equations. By the end of the unit the students will be able to understand the theory behind techniques to tackle large scale linear problems in the context of specific applications, such as data fitting, model reduction and model prediction. Also how to apply these methods to practical problems via numerical implementation.

Intended Learning Outcomes

Upon successful completion of the unit students will be able to:

1. understand the basic properties of matrix linear algebra systems that arise in engineering problems, including dimension, structure, sparsity and spectral properties.
2. reason about the solutions of linear equations and regression problems, including whether to expect a unique solution.
3. choose an appropriate solution technique for a linear equation of arbitrary size, including the idea of both direct and iterative solvers.
4. reason about linear transformations and calculate their eigenvalues and singular values in the context of engineering applications.
5. use matrix algebra to construct the solutions of systems of linear differential equations that arise as mathematical models of physical or engineering systems, and to gain a qualitative understanding of their dynamics.

Teaching Information

Teaching will be delivered through a combination of synchronous and asynchronous sessions, including lectures, supported by live online sessions, problem sheets and self-directed exercises. The unit will be supported by weekly workshops, which will provide blended learning involving class discussion, problem solving, and/or group presentations. Students will be expected to actively participate in the workshops, and engage with readings, self-directed exercises, and problem-solving activities

Assessment Information

The unit is assessed by 100% coursework, as follows:

3 x worksheets (20% each)

1 x worksheet (40%)

Worksheets will assess all ILOs.

Reading and References

• Gilbert Strang: Introduction to Linear Algebra Wellesley-Cambridge Press.
• Stephen Boyd & Lieven Vandenberghe: Introduction to Applied Linear Algebra, Cambridge University Press