Related Course/s:

Aims & Objectives:

• Solve eigenvalue problems
• Use eigenvalue techniques to solve differential equations
• Calculate gradients of scalar functions
• Calculate the divergence and curl of vector fields
•  Calculate multiple integrals
• Apply Green’s theorem and Stoke’s theorem
• Calculate numerical solutions of ordinary differential equations
• Apply finite difference methods to obtain numerical solutions of Laplace’s equation and heat conduction equation
• Use Mathematica in all of the above areas

Teaching Methods:

Lectures (36 hrs), Tutorials (12 hrs), Computer Laboratories (12 hrs)

Assessment:

Tests/Assignments (30-45%), Examination (55-70%)

Generic Skills Outcomes:

• Ability to apply knowledge of basic science and engineering fundamentals
• Ability to communicate effectively, not only with engineers but also with the community at large
• Ability to undertake problem identification, formulation and solution

Content:

• Matrix analysis: The eigenvalue problem, numerical methods, reduction to canonical form, functions of a matrix, engineering application
  
• Numerical solution of ordinary differential equations: Initial value and boundary value problems, finite difference methods
  
• Solution of partial differential equations: Analytical solution: direct integration, method of separation of variables; numerical solution: finite difference methods for the Laplace equation and the heat conduction equation
  
• Vector calculus: Derivatives of a scalar point function, derivatives of a vector point function, line integrals, double integrals, surface integrals, volume integrals, Green's theorem in the plane, Gauss divergence theorem, Stokes theorem, engineering application

Note: The Mathematica package will be used in this unit.

Reading Materials:

Notes for the subject will be made available via Blackboard

References:

James, G. et al., Advanced Engineering Mathematics, Addison-Wesley, 1994.