Engineering Mathematics

Learning Outcomes

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• Mathematical methods used in technical engineering subjects (shared with ELEC1300).

Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Show logical thinking in problem solving.
• Apply a range of numerical and computational methods (shared with ELEC1300).

Transferable and Generic Skills

Having successfully completed this module you will be able to:

• Represent mathematical concepts in sketches and visual forms.
• Demonstrate organisational and time-management skills.
• Interpret mathematical results and their implications in an engineering context.
• Construct mathematical models that capture the key features of an engineering problem.
• Record consistent learning and revision activities.

Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Apply appropriate methods of mathematical analysis.
• Critically analyse and solve engineering problems.

Integration

• Line integrals and conservative vector fields.
• Green’s Theorem in the Plane
• Surface and triple Integrals
• Stokes’s theorem
• Divergence Theorem of Gauss
• Boundary and initial conditions.

Ordinary Differential Equations

• Constant coefficient linear ODEs. Euler equations.
• Homogeneous linear ODE with constant coefficients
• Nonhomogeneous ODEs

Matrix algebra:

• rank; eigenvalues and eigenvectors; Symmetric, Skew-Symmetric, and Orthogonal Matrices; Eigenbases. Diagonalization. Quadratic Forms

Further Calculus:

• Chain rule for partial derivatives; higher partial derivatives; total differentials and small errors
• Partial Differential Equations.
• Separation of variables
• Use of Fourier Series
• Two-Dimensional Wave Equations
• Rectangular Membrane. Double Fourier Series
• Heat Equation and the Laplacian
• Solution by Fourier Series.
• Steady Two-Dimensional Heat Problems.
• Laplace’s Equation in Cylindrical and Spherical Coordinates.

Numerical Mathematics

• Discrete numerics, sampling, DFT
• Numerical approximation, numerical integration, numerical differentiation
• Use of MATLAB in numerical caculaitons: curve fitting, numerical simulation of solutions to equations

Systems

• Systems of ODEs as Models in Engineering Applications
• Basic Theory of Systems of ODEs.
• Matrix Solutions to coupled second order ODEs
• Nonhomogeneous Linear Systems of ODEs
• The method of reduction of order.
• The method of variation of parameters.
• Sturm-Liouville Theory. Examples of Sturm-Liouville problems.
• Eigenfunction expansions.

Taught using a blended approach, incorporating “flipped mode” teaching and traditional problem classes.

• Comprehensive explanatory video lectures on each topic
• Case study recordings
• Weekly discussion tutorials and seminars
• Case study based problem sheets
• Weekly intensive problem classes – problem sheets worked on
• Self-study notes for each topic.
• Self-testing on each block
• Mini-test at end of each block
• Past examination papers and solutions.
• Computing Labs on data analysis and numerical Computation

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.

Repeat

An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.