Courses - Faculty of Engineering
Engineering Science
Stage I
Mathematical Modelling 1
Introduction to mathematical modelling. Differentiation and integration (polynomials, trigonometric, exponential, logarithmic, and rational functions). Integration by parts, substitution and partial fractions. Differential equations and their solutions (including Euler's method). Vector and matrix algebra, transformations, solving systems of linear equations. Modelling using probability.
Restriction: ENGSCI 211, 213, 311, 313, 314
Stage II
Mathematical Modelling 2
First and second order ordinary differential equations and solutions. Laplace transforms. Taylor series and series in general. Multivariable and vector calculus including divergence, gradient and curl. Further linear algebra. Eigenvalues and eigenvectors. Fourier series. Application of the techniques through appropriate modelling examples. Introductory data analysis and statistics.
Prerequisite: ENGGEN 150, or ENGSCI 111, or a B+ grade or higher in MATHS 108 or 110, or a B+ grade or higher in MATHS 120 and 130
Restriction: ENGSCI 213
Computational Techniques and Computer Systems
Introduction to computer architecture and computational techniques. Data representation, memory, hardware, interfacing, and limitations. Numerical computation and algorithms, coding design and paradigms.
Prerequisite: ELECTENG 101 and ENGGEN 131, and ENGGEN 150 or ENGSCI 111
Corequisite: ENGSCI 211 or 213
Modelling and Analytics in Operations Research
Emphasises the relationship between business and industrial applications and their associated operations research models. Software packages will be used to solve practical problems. Topics such as: linear programming, transportation and assignment models, network algorithms, queues, inventory models, simulation, analytics and visualisation will be considered.
Prerequisite: 15 points at Stage I in Engineering General or Engineering Science or Mathematics or Statistics
Restriction: STATS 255
Engineering Science Design I
Introduction to concepts of model design for engineering problems, including model formulation, solution procedures, validation, and shortcomings, with examples from topics in computational mechanics, operations research and data science. Further development of problem-solving skills, group project work, and group communication skills. The use of computational models to support design-focused decision making while considering ethical, societal, cultural, and environmental factors.
Prerequisite: ENGGEN 115 and ENGSCI 233
Corequisite: ENGSCI 211 or 213
Stage III
Image and Digital Signal Processing
Fundamentals of image processing and digital signal processing. One dimensional signals and digital filters. Digital filtering with FIR and IIR filters and the Digital Fourier Transform (DFT). Two-dimensional signals, systems and analysis methods. 2D images, spatial sampling, grey-scale quantification, point operations, spatial operations, high pass filtering, sharpening images, noisy images, nonlinear image processing.
Prerequisite: ENGSCI 211 or 213
Mathematical Modelling 3
A selection from: ordinary differential equations, systems of equations, analytical and numerical methods, non-linear ODEs, partial differential equations, separation of variables, numerical methods for solving PDEs, models for optimisation, industrial statistics, data analysis, regression, experimental design reliability methods.
Prerequisite: ENGSCI 211
Restriction: ENGSCI 313, 314
Mathematical Modelling 3ECE
Complex Analysis, including complex numbers, analytic functions, complex integration, Cauchy's theorem, Laurent series, residue theory; Laplace transforms; Modelling with partial differential equations, including electronic and electrical applications; Fourier Analysis, Fourier transform, Fast Fourier transform; Optimisation, including unconstrained and constrained models, linear programming and nonlinear optimisation.
Prerequisite: ENGSCI 211
Restriction: ENGSCI 311, 314
Mathematical Modelling 3ES
Mathematical modelling using ordinary and partial differential equations, calculus of variations and statistical methods. Topics include: eigenvalues, eigenvectors, systems of equations, stability, separation of variables, wave and heat equations, Euler-Lagrange equation, Hamilton’s Principle, probability, random variables, common distributions, Poisson process, exploratory data analysis, confidence intervals, hypotheses tests, linear models including one-way and two-way ANOVA, ANCOVA and multiple regression, introduction to logistic regression.
Prerequisite: ENGSCI 211
Restriction: ENGSCI 311, 313, 321
Computational Techniques 2
Methods for computing numerical solutions of mathematical models and data analytics problems with focus on translating algorithms to computer code. A selection of topics from numerical solution of linear and non-linear equations, eigen problems, ordinary and partial differential equations, databases, inverse problems and parameter estimation.
Prerequisite: ENGSCI 233
Corequisite: ENGSCI 311 or 313 or 314
Mathematical and Computational Modelling in Mechanics
Development of macroscopic models of physical systems using fundamental mathematical techniques and physical laws. Topics include vector and tensor calculus including indicial notation and integral theorems, conservation laws, control volumes and constitutive equations, continuum assumptions, isotropy and homogeneity. Possible applications include deformation, strain and stress, fluid flow, electromagnetism, reactive chemical transport, and kinetics.
Prerequisite: BIOMENG 221 or MECHENG 242, and ENGSCI 211 or 213
Restriction: BIOMENG 321
Computational Design for Physical Systems
Integrate sustainability and environmental considerations into computational engineering. This will develop skills in: analysing complexity and selecting an appropriate model representation of the physical problem; choosing the correct computational tool with which to solve the model; designing and executing appropriate numerical experiments using the chosen tool; validating, interpreting and communicating the simulation results. Enhance skills in sustainable decision-making and addressing environmental challenges.
Prerequisite: BIOMENG 321 or ENGSCI 343
Restriction: ENGSCI 746
Simulation Modelling for Process Design
Use of simulation models to design complex processes including consideration of cultural, environmental, societal and ethical factors as appropriate. Focus on practical problem solving, translational methods and the development of real-world modelling skills.
Prerequisite: ENGSCI 255 or STATS 255
Restriction: OPSRES 385
Engineering Science Design II
Application of computational engineering methods combined with optimisation techniques to complex engineering design problems. Group-based integrated design, prototype and test projects that include consideration of societal, ethical and professional engineering factors.
Prerequisite: BIOMENG 241 or ENGSCI 263
Restriction: ENGSCI 773
Optimisation in Operations Research
Linear programming, the revised simplex method and its computational aspects, duality and the dual simplex method, sensitivity and post-optimal analysis. Network optimisation models and maximum flow algorithms. Transportation, assignment and transhipment models, and the network simplex method. Introduction to integer programming.
Prerequisite: 15 points from ENGGEN 150, ENGSCI 111, MATHS 208, 250, 253, and 15 points from COMPSCI 101, ENGGEN 131, MATHS 162, STATS 220
Restriction: ENGSCI 765
Postgraduate 700 Level Courses
Research Project - Level 9
An investigation carried out under the supervision of a member of staff on a topic assigned by the Head of Department of Engineering Science. A written report on the work must be submitted.
To complete this course students must enrol in ENGSCI 700 A and B
Studies in Engineering Science
An advanced course on topics to be determined each year by the Head of Department of Engineering Science.
Prerequisite: Departmental approval
Advanced Mathematical Modelling
A selection of modules on mathematical modelling methods in engineering, including theory of partial differential equations, integral transforms, methods of characteristics, similarity solutions, asymptotic expressions, theory of waves, special functions, non-linear ordinary differential equations, calculus of variations, tensor analysis, complex variables, wavelet theory and other modules offered from year to year.
Prerequisite: 15 points from ENGSCI 311, 313, 314
Computational Algorithms for Signal Processing
Advanced topics in mathematical modelling and computational techniques, including topics on singular value decomposition, Principle Component Analysis and Independent Component Analysis, eigen-problems, and signal processing (topics on neural network models such as the multi-layer perception and self organising map).
Prerequisite: 15 points from ENGSCI 311, 313, 314
Mathematical Modelling for Professional Engineers
Mathematical modelling techniques required by professional engineers, such as partial and ordinary differential equations, differentiation and integration, vector calculus, linear algebra, analytical and numerical methods, industrial statistics, and data analysis.
Prerequisite: ENGSCI 211 or 213
Restriction: ENGSCI 311, 313, 314
Data-centric Engineering for Physical Systems
Mathematical modelling of complex physical systems, including model development, parameterisation and evaluation, illustrated using examples from current research and industry. Inverse problems and uncertainty quantification for physical models in engineering and science, including principles of uncertainty propagation for linear and nonlinear physical models given real-world data, and connections to physics-informed machine learning.
Prerequisite: 15 points from COMPSCI 101, ENGGEN 131, MATHS 162, 199; and either 15 points from ENGSCI 311, 313, 314, or MATHS 260 and either STATS 210 or 225
Computational Engineering for Physical Systems
Principles and practice for modelling complex physical systems. Applications in biomechanics, fluid mechanics and solid mechanics. Including topics such as large deformation elasticity theory applied to soft tissues, inviscid flow theory, compressible flows, viscous flows, meteorology, oceanography, coastal ocean modelling, mixing in rivers, fracture, composite materials and geomechanics. Underlying theories, computational techniques and industry applications explored using commercial software.
Prerequisite: BIOMENG 321 or ENGSCI 343
Waves and Fracture
Advanced topics in mechanics including: waves and wave motion with applications to acoustics, optics, fluid flow problems and shock discontinuities using numerical methods. Fracture: modes of, displacement discontinuity in linear elasticity, stress intensity factor, spectral solution methods, finite friction. Applications include: hydraulic fracturing, earthquakes, macroscale strength of materials.
Prerequisite: BIOMENG 321 or ENGSCI 343
Studies in Continuum Mechanics
An advanced course in continuum mechanics covering topics in the mechanics of solids and fluids and other continua.
Prerequisite: Departmental approval
Petroleum Engineering
Interdisciplinary introduction to topics in geology, geophysics, reservoir engineering, drilling and production engineering relevant to the production of oil and gas. Mathematical models of multiphase fluid flow in porous media. Reservoir engineering tools for analysis and forecasting of reservoir performance. Unconventional petroleum resources.
Prerequisite: 15 points from ENGSCI 311, 313, 314
Advanced Modelling and Simulation in Computational Mechanics
Solution of real-world continuum mechanics problems using computational tools commonly used in engineering practice. Develops skills in analysing complexity; selecting a model representation of the physical problem; choosing the correct computational tool to solve the model; designing and executing appropriate numerical experiments; validating, interpreting and communicating simulation results. Advanced solver methods, and modelling of advanced materials such as large-deformation elastic/plastic materials.
Prerequisite: BIOMENG 321 or ENGSCI 343
Restriction: ENGSCI 344
Computational Techniques in Mechanics and Bioengineering
Theoretical and applied finite element and boundary element methods for static and time dependent problems of heat flow, bioelectricity, linear elasticity and non-linear mechanics.
Prerequisite: ENGGEN 131 or equivalent, and 15 points from ENGSCI 311, 313, 314
Decision Making in Engineering
Introduction to techniques for decision making in engineering systems including decision heuristics, simple prioritisation, outranking approaches, analytic hierarchy process, application to group decision making.
Prerequisite: ENGSCI 211 or MATHS 250
Algorithms for Optimisation
Meta-heuristics and local search techniques such as Genetic Algorithms, Simulated Annealing, Tabu Search and Ant Colony Optimisation for practical optimisation. Introduction to optimisation under uncertainty, including discrete event simulation, decision analysis, Markov chains and Markov decision processes and dynamic programming.
Prerequisite: 15 points from COMPSCI 101, ENGGEN 131, MATHS 162, 199, and 15 points from COMPSCI 120, ENGSCI 111, STATS 125
Integer and Multi-objective Optimisation
Computational methods for solving optimisation problems. Algorithms for integer programming including branching, bounding, cutting and pricing strategies. Algorithms for linear and integer programmes with multiple objective functions.
Prerequisite: ENGSCI 391 or 765
Scheduling and Optimisation in Decision Making
A course of advanced topics arising in the practical application of optimisation models for machine and resource scheduling, routing applications, staff rostering and performance measurement.
Prerequisite: ENGSCI 391 or 765
Advanced Simulation and Stochastic Optimisation
Advanced simulation topics with an emphasis on optimisation under uncertainty. Uniform and non-uniform random variate generation, input distribution selection, output analysis, variance reduction. Simulation-based optimisation and stochastic programming. Two-stage and multi-stage programs with recourse. Modelling risk. Decomposition algorithms. Scenario construction and solution validation.
Prerequisite: ENGSCI 391 or 765
Advanced Optimisation in Operations Research
Linear programming, the revised simplex method and its computational aspects, duality and the dual simplex method, sensitivity and post-optimal analysis. Network optimisation models and maximum flow algorithms. Transportation, assignment and transhipment models, and the network simplex method. Integer programming. The implementation and solution of optimisation models for practical applications.
Prerequisite: 15 points from ENGGEN 150, ENGSCI 111, MATHS 208, 250, 253, and 15 points from COMPSCI 101, ENGGEN 131, MATHS 162, STATS 220
Restriction: ENGSCI 391
Advanced Operations Research and Analytics
Advanced Operations Research and Analytics topics including selected theory, algorithms and applications for non-linear programming, smooth and non-smooth optimisation, equilibrium programming and game theory.
Prerequisite: ENGSCI 391 or 765
Whole Organ Modelling
Advanced computational modelling of whole organs with an emphasis on integrative physiology and coupled field problems in bioengineering. Finite deformation elasticity theory and computational aspects. Current flow in excitable tissue. Finite element collocation techniques. Coupled finite element – boundary element problems.
Prerequisite: BIOMENG 321 or ENGSCI 343
Capstone Project
Group based projects involving the application and integration of knowledge in computational engineering, data analytics and operations research for design, prototyping and performance testing of a new product. Topics include social and Te Tiriti considerations, engineering design practice, optimisation methods in robust design, material selection and structural analysis, risk management, communication skills, prototype manufacturing and design validation.
Prerequisite: 60 points from courses listed in Part III of the BE(Hons) Schedule for Engineering Science
Restriction: ENGSCI 363
Project X - Level 9
Students are required to submit a report on a topic assigned by the appropriate Head of Department.
Prerequisite: Departmental approval
Project Y - Level 9
Students are required to submit a report on a topic assigned by the appropriate Head of Department.
Prerequisite: Departmental approval
To complete this course students must enrol in ENGSCI 788 A and B
Project Z - Level 9
Students are required to submit a report on a topic assigned by the appropriate Head of Department.
Prerequisite: Departmental approval
Thesis (Operations Research and Analytics) - Level 9
Prerequisite: Departmental approval
To complete this course students must enrol in ENGSCI 793 A and B
Thesis (Operations Research and Analytics) - Level 9
Prerequisite: Departmental approval
To complete this course students must enrol in ENGSCI 794 A and B
Research Project - Level 9
Prerequisite: Departmental approval
To complete this course students must enrol in ENGSCI 795 A and B, or ENGSCI 795