Modules

Core Module Information
Module title: Mathematical Methods I
SCQF level: 07:
SCQF credit value: 20.00
ECTS credit value: 10
Module code: ELE07110
Module leader: Stathis Tingas
School School of Computing, Engineering and the Built Environment
Subject area group: Engineering and Mathematics
Prerequisites

Requisites: Pre-requisite: [Module ELE07102] Foundation Mathematics
Description of module content:

This module develops the single-variable calculus and ordinary differential equation methods needed to analyse engineering systems. Students extend their foundation mathematics through implicit and parametric differentiation, local linearisation using first-order Taylor approximation, integration using partial fractions, separable and linear first-order ordinary differential equations, numerical solution of first-order ordinary differential equations using Euler's method, and second-order ordinary differential equations with real and complex roots and external forcing.The mathematics is taught through engineering contexts drawn across mechanical, electrical/electronic and energy systems. Students learn to identify the common mathematical structure beneath different physical problems, develop reliable handwritten analytical methods, and use MATLAB to visualise behaviour, explore parameters, compare analytical and numerical results, and investigate model limitations.A consistent Challenge -» Abstract -» Solve -» Explore -» Verify & Transfer learning cycle is used across the module. This supports active participation, mathematical fluency, scientific computing, verification of results and transfer of mathematical understanding between engineering contexts. Generative AI may be used selectively as a fallible source for critical verification, but does not replace independent mathematical reasoning.
Learning Outcomes for module:

Upon completion of this module you will be able to

LO1: Apply differentiation and integration techniques to engineering problems.

LO2: Construct and evaluate linear approximations of nonlinear engineering relationships.

LO3: Solve and interpret first- and second-order ordinary differential equation models using analytical and numerical methods.

LO4: Analyse engineering problems by selecting and verifying appropriate analytical and computational methods, recognising their limitations.
Full Details of Teaching and Assessment
2026/7, Trimester 2, In Person,
VIEW FULL DETAILS
Occurrence: 001
Primary mode of delivery: In Person
Location of delivery: MERCHISTON
Partner:
Member of staff responsible for delivering module: Stathis Tingas
Module Organiser:


Student Activity (Notional Equivalent Study Hours (NESH))
Mode of activityLearning & Teaching ActivityNESH (Study Hours)NESH Description
Face To Face Lecture 20 Challenge + Abstract + guided teaching. Engineering question, short explicit teaching blocks, worked examples, prediction/concept questions and return to the opening challenge.
Face To Face Tutorial 20 Solve stage using Core -» Apply -» Challenge. Individual paper-and-pencil mathematics remains central, with bounded engineering applications, peer reasoning where useful and rapid feedback.
Face To Face Centrally Time Tabled Examination 2 The exam evaluates students’ understanding of core mathematical and engineering principles and their ability to apply this knowledge to the solution of complex problems. Through a series of timed questions, students will be expected to formulate and analyse mathematical models, drawing justified conclusions based on first principles and logical reasoning.
Online Guided independent study 136 Reading, analytical and MATLAB practice, preparation for workshops/labs and assessments, revision, and consolidation of mathematical and computational methods.
Face To Face Supervised time in studio/workshop 20 Explore + Verify & Transfer. MATLAB visualisation, parameter variation, analytical/numerical comparison, numerical ODE solution, verification of supplied outputs and cross-context transfer. Starter code may be used so programming syntax does not become a hidden prerequisite.
Face To Face Tutorial 2 Revision class
Total Study Hours200
Expected Total Study Hours for Module200


Assessment
Type of Assessment Weighting % LOs covered Week due Length in Hours/Words Description
Report 50 1~2~3~4 Week 7 , WORDS= 1000 w An individual, bounded engineering mathematics investigation released in Week 2 and submitted in Week 7. It is important that you can demonstrate that you have learnt and can independently apply the reasoning undertaken in this assessment, and your mark for this component will be confirmed through a compulsory verification task (see below). The assessment provides evidence of application of mathematical knowledge to engineering problems [M1], formulation and analysis leading to substantiated conclusions and recognition of assumptions and limitations [M2], and selection and application of appropriate analytical and computational techniques, including MATLAB, with verification of their results and limitations [M3].
Centrally Time Tabled Examination 50 1~2~3~4 Exam Period HOURS= 2 hours The centrally timetabled examination provides protected individual evidence of mathematical competence across the whole module. It assesses clean analytical mathematics, selection of appropriate methods, interpretation of engineering results, and verification or diagnosis of supplied mathematical and computational outputs. The examination covers all learning outcomes, with greater emphasis on material not substantially evidenced in Assessment 1, including Euler's method and the second-order ODE block.Where appropriate, computational understanding may be assessed through supplied numerical or MATLAB-style outputs (as opposed to running a live environment), and/or by assessing the correctness of a supplied GenAI responseThe examination assesses students' ability to apply mathematical knowledge to engineering problems [M1], formulate and analyse problems and justify conclusions [M2], and select, interpret and verify appropriate analytical and computational approaches while recognising limitations [M3].
Class Test 0 1~2~3~4 Week 8 HOURS= 60 minutes You will undertake a compulsory learning verification assessment under controlled conditions following submission of your engineering mathematics coursework (above) to evaluate your understanding of the analytical and computational methods used in your submitted work. To support inclusive approaches to assessment, you will have an option to choose the mode of verification. Verification carries no separate weighting but may result in an adjustment to the coursework mark and must be undertaken for the mark for the report to be recorded. Clear information around the mode of assessment and adjustments associated with verification will be detailed in your assessment brief.
Component 1 subtotal: 50
Component 2 subtotal: 50
Module subtotal: 100

Indicative References and Reading List - URL:
ELE07110 / ELE07410 Mathematical models I
ELE07110 Mathematical Methods I
 

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