Mathematics for Electronics & Electrical Engineering Part II

Learning Outcomes

Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Show logical thinking in problem solving
• Solve a variety of mathematical problems relevant to engineering

Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Demonstrate organisational and time-management skills
• Write up in an accurate, coherent and logical manner your solutions to a range of mathematical problems

• Fourier Series.

Orthogonality relations. 2L periodic functions. Half-range series. Solutions to periodically forced ODEs.

• Fourier Transforms.

Fourier transform and inverse transform. Sine and cosine transform. Properties of the Fourier transform. The discrete Fourier transform.

• Eigenvalues, eigenvectors and eigenfunctions.

Matrix eigenvalue problems. Solution to systems of coupled ODEs. Symmetric matrices.

• Linear ODEs and Sturm-Liouville problems.

Boundary and initial conditions. Constant coefficient linear ODEs. Euler equations. The method of reduction of order. The method of variation of parameters. Sturm-Liouville Theory. Examples of Sturm-Liouville problems. Eigenfunction expansions.

• Partial differential equations

Classification of second-order linear PDEs. The technique of separation of variables with application to wave equations, diffusion equations, and Laplace’s equation.

• Vector calculus

The gradient, divergence and curl operators. Directional derivatives. Line integrals and conservative vector fields. Stokes’s theorem and the Divergence theorem. Alternative coordinate systems.

Teaching methods include

• Standard “chalk and talk” lectures, using either blackboard or whiteboard, tutorials, coursework problems, material on Blackboard.

Learning activities include

• Individual study.
• Note-taking at lecture classes.
• Working through coursework assignments and submitting to specified deadlines.
• Preparation for a written examination.

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.