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UCL Mechanical Engineering
Faculty of Engineering Sciences


ENGS103P Mathematical Modelling and Analysis I

Traditional Engineering programmes often teach Engineering Mathematics theory in isolation from engineering practice. Whilst students taught through such programmes often exhibit detailed understanding of mathematical concepts, they struggle to apply their newly acquired mathematical knowledge to solving engineering problems. In contrast to this, the Mathematical Modelling and Analysis I (MMA I) module utilises mathematical modelling and simulation techniques as a pedagogic tool to integrate the acquisition and practice of mathematical concepts. This approach is underpinned by a suite of online mathematical support resources as well as a walk-in student-led Engineering Mathematics Support team.

Code: ENGS103P
Alt Codes: None
Title: Mathematical Modelling and Analysis
Level: 1
UCL Credits/ECTS: 0.5/7.5
Start: September
End: December
Taught By: Dr. Abel Nyamapfene (Module Coordinator)


  • None


  • Examination (40%)
  • E-assessment (20%)
  • Discipline-specific coursework (40%)
    • Online quizzes
    • Generic mathematics problems
    • Discipline-specific mathematical problem solving and analysis


The mathematical concepts covered by the MMA I module are similar to those covered by more traditional first year Engineering Mathematics modules. However, unlike the traditional modules, the MMA I reinforces the engineering utility of these concepts by using relevant engineering-oriented titles rather than mathematics oriented titles.

Syllabus Item Summary of Intended Learning Outcomes
Building Mathematical Models Introduces basic mathematical models  and their implementation using MATLAB
Employ assumptions to simplify systems Introduces the art of estimation and approximation in Engineering analysis and decision-making.
 Engineering calculus  Reviews basic mathematical calculus with an emphasis on engineering applications
 Engineering uncertainty  Introduces statistics and probability  concepts and their significance and application to practical engineering
Analysing data  Introduces data modelling and fitting, including regression analysis, within engineering practice
Representing engineering systems and signals using complex numbers  Introduces the theory of complex numbers as a tool for modelling and analysing bimodal engineering quantities
Describing the world in 3-D, matrices and linear algebra  Describing the world in 3-D, Matrices and Linear algebra Introduces vectors, matrices and linear algebra and their importance in handling and manipulating multi-dimensional engineering data.
Engineering system modelling: Calculus and differential equations  Introduces and uses calculus and differential equations to model and analyse dynamic engineering systems

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 mathematical concepts, including Calculus, Linear Algebra and Differential Equations 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;
  • Use estimation, approximation and dimensional analysis to reduce complexity;
  • 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.

ENGS103P Mathematical Modelling and Analysis I

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