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UCL Mechanical Engineering
Faculty of Engineering Sciences


ENGS203P Mathematical Modelling and Analysis II

Mathematical Modelling and Analysis II (MMA II) follows from MMA I and utilises mathematical modelling and simulation techniques as a pedagogic tool to integrate the acquisition and practice of mathematical concepts. It is delivered by Lectures followed by smaller group workshops led by each department. This approach is underpinned by a suite of online mathematical support resources as well as a walk-in student-led Engineering Mathematics Support team. The module aims to provide the core mathematics, modelling and analysis skills that underpin studies in engineering through a blended learning and teaching programme of mathematics that:

  • Emphasises the modelling of engineering systems and the analysis of data
  • Integrates mathematics theory and engineering practice
Code: ENGS203P
Alt Codes: None
Title: Mathematical Modelling and Analysis II
Level: 2
UCL Credits/ECTS: 0.5/7.5
Start: September
End: April
Taught By: Dr. Abel Nyamapfene (Module Coordinator)



  • MMA I or Equivalent


  • Examination (60%)
  • E-assessment and discipline-specific coursework (40%)


  1. Series and Transforms
    1. Polynomial approximations
    2. Taylor, Maclaurin and Fourier Series
    3. Laplace and Fourier Transforms
  2. Partial Differential Equations (PDEs)
    1. First order PDEs
    2. Second order PDEs
  3. Vector Calculus, Matrices, Eigenvectors and Eigenvalues
    1. Line and multiple integrals
    2. Matrix decomposition
    3. Eigenvalues and Eigenvectors
    4. Least squares formulation in matrix form
  4. Advanced Statistics and Data Analysis
    1. Hypothesis Testing, Estimation, Regression Analysis and Experimental Design
    2. Discrete Statistics

ENGS203P Mathematical Modelling and Analysis II

Intended Learning Outcomes

Upon completion of this module students should be able to:

  • Recognise the connections between mathematics and engineering, and how mathematical ideas are embedded in engineering contexts
  • Represent real-world systems from engineering in a mathematical framework
  • Identify and draw upon a range of advanced mathematical concepts, including Vector Calculus, Matrices and Eigenvectors/Values, Statistics, Series and Transforms, and Partial Differential Equations (PDEs) to analyse specific problems and identify the appropriate mathematics to realise a solution
  • Employ appropriate computer programming and modelling techniques and statistical analysis to efficiently solve and evaluate the performance of engineering systems
  • Relate the behaviour of the output of mathematical models to the underlying physical or conceptual models of interest
  • Carry our engineering problem solving both collaboratively in a team and independently
  • Present and interpret mathematical results in effective and appropriate ways to varied audiences, including non-mathematical engineering audiences
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