Skip to main content

Trinity College Dublin, The University of Dublin

Trinity Menu Trinity Search



You are here Courses > Undergraduate > Courses & Modules

MAU33E01 Engineering mathematics V

Module Code MAU33E01
Module Title Engineering mathematics V
Semester taught Semester 1
ECTS Credits 5
Module Lecturer Prof. Tristan McLoughlin
Module Prerequisites MAU22E02 Engineering mathematics IV

Assessment Details

  • This module is examined in a 2-hour examination at the end of Semester 1.
  • Continuous assessment contributes 20% towards the overall mark.
  • Re-assessment, if needed, consists of 100% exam.

Contact Hours

11 weeks of teaching with 3 lectures and 1 tutorial per week.

Learning Outcomes

On successful completion of this module, students will be able to

  • Calculate the coefficients of the Fourier series for a variety of functions and use them to solve various differential equations.
  • Calculate the Fourier transforms of simple functions and apply the Fourier transform to solve the heat and wave equations over infinite domains.
  • Solve the heat, wave and Laplace equations, subject to various boundary conditions, using either separation of variables or Fourier methods.
  • Solve linear optimization problems using the simplex and two-phase simplex methods.
  • Find the dual of a given linear programming problem and use the duality theorems to solve it.

Module Content

  • Fourier methods: definition of complex and real Fourier series, applying Fourier series to solve ordinary differential equations, even and odd half-range expansions, Fourier transform, interpretation of Fourier modes as frequencies, convolution.
  • Partial differential equations: Laplace equation, heat equation, wave equation, D'Alembert's solution, fundamental solution, separation of variables, applying Fourier analysis to initial value problems.
  • Linear programming: Solving linear optimization problems using the simplex and two-phase simplex methods. How to find the dual of a given linear programming problem and how to use the duality theorems to solve it.

Recommended Reading

  • Advanced engineering mathematics by Erwin Kreyszig.