National University of Ireland, Galway Science without Borders

This course introduces functions of several variables, parametric curves and vector valued functions. The material covered includes:

1. Functions of several variables: partial derivatives, gradient, level curves, tangent planes, local extrema, Hessian matrix, double integrals.

2. Parametric curves: parametrisation of line segments and ellipses, derivatives, curvature, normal vector, oculating plane.

3. Vector valued functions: examples of vector fields, Green's Theorem.

On successful completion of this module the learner should be able to:

1. Sketch or describe graphs of 2-variable functions.

2. Determine equations of tangent planes.

3. Find parameterisations of common curves.

4. Compute arc length and curvature of a curve.

5. Optimise certain functions; apply method of Lagrange multipliers.

6. Compute line integrals and double integrals over specified domains.

7. Know and be able to apply Green's Theorem.

Code	Module Title	Semester	ECTS	Examination Arrangements
CS304	Mathematical and Logical Aspects of Computing	1	5	Two hour examination

This module introduces the key concepts of mathematical and computational logic. The learner will gain an insight into the applications, uses and limitations of propositional logic, and the use of mathematical techniques for analysing logical statements to establish validity. Motivated by a knowledge of the limitations of propositional logic, the concepts of predicate calculus are introduced, along with methods for studying the validity of statements made in that frame-work.

On successful completion of this module the learner should be able to:

1. Represent mathematical statements in propositional and predicate logic.

2. Establish if given compound propositions are equivalent.

3. Derive the disjunctive and conjunctive normal forms of a proposition.

4. Apply semantic and syntactic techniques to check logical consequence.

5. Parse and analyse statements formulated in predicate logic.

6. Demonstrate knowledge of mathematical and logical reasoning.

This calculus course builds on earlier basic calculus knowledge. Topics covered include: convergence of sequences & series, Taylor's & the Maclaurin series, multiple integrals using Cartesian, polar and elliptical coordinates, Fourier series, computation of line integrals directly and by using Green's theorem. This course builds on earlier basic calculus.

1. Sequences & series: Sequence definition/description, terms used to describe sequences e.g. upper bound, limits, convergence of a sequence, definition of a series, convergence of a series, absolute/conditional convergence, geometric series, telescopic series, analysis of the harmonic series, the integral test, p series, comparison test, ratio test, root test.

2. Power series: Definition of a general power series, centre of convergence, radius of convergence, interval of convergence including end points, coefficients of the power series, Taylor series, Maclaurin series, approximate evaluation of functions at various points using power series, definition of a Fourier series, odd and even functions, period of a function, computation of the Fourier series coefficients.

3. Double integration: comparison with single variable integration, double integral as a volume under a surface, evaluation of double integrals using known volumes under surfaces, evaluation of double integrals using integration techniques over rectangular and non-rectangular domains of integration.

4. Polar and elliptical coordinates: definition of polar and elliptical co-ordinates, Jacobean determinant, evaluation of volumes under surfaces over full/partial elliptical and circular domains, double integrals used to compute areas of domains.

5. Line integrals: parameterisation of curves in Euclidean 2 space, chain rule, integration techniques, Green's theorem, evaluation of a line integral using Green's theorem.

On successful completion of this module the learner should be able to:

1. Define and describe a sequence and establish if a sequence converges.

2. Define a series and establish if a series converges/diverges, converges absolutely/ conditionally. Define a geometric, telescopic and the harmonic series. Use the integral test and in particular use it to find which values of p for which the p series converges. Apply the comparison test, ratio test and root test.

3. Define a general Taylor and Maclaurin series. Compute the coefficients of the power series and establish the centre, radius and interval of convergence. Evaluate approximately a function at various points using power series.

4. Define a Fourier series, even and odd functions and compute Fourier coefficients.

5. Compute volumes under surfaces using double integrals over rectangle and non-rectangle domains.

6. Use polar and elliptical coordinates to compute volumes over full/segments of circular/elliptical domains.

7. Compute line integrals over curves in the Euclidian 2 space directly and by using Green's theorem.

Topics covered include:

1. Vector Spaces and Linear Subspaces. Axioms and examples, linear combinations, spanning sets.

2. Linear Independence and Rank. Dependent and independent sets, bases, dimension, rank of a matrix.

3. Linear Transformations. Kernel, image, rank-nullity theorem, matrix representations.

4. Inner Product Spaces. Bilinear forms. Cauchy-Schwarz Inequality, Orthogonal sets, Gram-Schmidt process, function spaces and Fourier Series (some examples only), least squares approximation.

5. Applications.

On successful completion of this module the learner should be able to:

1. Identify and categorize examples of linear and nonlinear spaces.

2. Decide whether or not a given set is a spanning set for a given vector space.

3. Decide whether or not a given subset of Rn is linearly independent.

4. Compute the rank of a matrix.

5. Find a basis for the image and kernel of a linear transformation.

6. Compute the matrix representation of a linear transformation on finite dimensional vector spaces.

7. Use the Gram-Schmidt process to find an orthonormal basis for an inner product space.

8. Prove the Cauchy-Schwarz inequality

9. Compute the Fourier coefficients of some simple periodic functions.

10. Find the linear least squares fit to a given data set

1. Motivation, leading to

2. Definition of a metric space; examples and non-examples. Make your own!

3. New metric spaces (= subspaces) and new concepts (= continuous functions, convergent sequences) from old.

4. Open sets, limit points, completeness, compactness.

5. Application: Banach's Fixed point theorem (aka Contraction Mapping Theorem).

6. Special subsets of the reals, including the Cantor set.

On successful completion of this module the learner should be able to:

1. Write down, explain and use definitions of key concepts encountered throughout the module.

2. Demonstrate how key definitions emerge naturally from the parent example given by the real line.

3. Establish that each example from a given list forms a metric space and illustrate other properties which such examples may have.

4. Construct proofs which connect and relate metric concepts.

5. Produce examples which illustrate and distinguish definitions such as limit point of a set, complete metric space, closed set etc.

6. Write down all mathematical work with rigour and precision.

7. Create new or other lines of mathematical enquiry on the basis of mathematical ideas encountered in this module.

Code	Module Title	Semester	ECTS	Examination Arrangements
MA343	Groups 1	1	5	Two hour examination

Introduction to Group Theory. Topics covered include the group axioms, symmetries, permutations, cyclic groups, dihedral groups, small groups of matrices, homeomorphisms, normal subgroups, Isomorphism Theorems, automorphism groups, free groups, relators and presentations. The material covered includes:

1. Group Axioms: the group axioms as abstraction of properties of the symmetries of an object, permutations, rotations, reflections, translations, cyclic groups, the integers, groups of matrices.

2. Basic notions: subgroup, order, cosets, Lagrange's Theorem, generators, many examples.

3. Homeomorphisms: structure preserving maps, quotient structures, kernels, normal subgroups, regular representation, conjugation representation.

4. Theory: Isomorphism Theorems, simplicity of alternating groups, universal property of free groups, direct products, presentations, centre and commutator subgroup.

On successful completion of this module the learner should be able to:

1. Carry out calculations in abstract algebraic structures given by axioms.

2. Work with homeomorphisms, quotient structures and free groups.

3. Determine the structure of small groups given by generators and relations or by generating matrices or by generating permutations.

4. Describe symmetries of geometric objects in terms of permutations or matrices.

5. Find and write proofs for abstract group theoretic facts at scholarly standard.

6. Search, read, understand and make use of more advanced literature in the field.

Most mathematical problems arising in engineering and the physical sciences are expressed as nonlinear equations, differential equations, or systems of linear equations. This module provides the mathematical understanding of the methods that can be applied to solve these problems, and the knowledge of how to determine which algorithm is most appropriate in which setting. In addition, the students learn how to program these methods in Matlab - the industry standard software tool for numerical prototyping.

On successful completion of this module the learner should be able to:

1. Derive Newton's (and related) methods for solving nonlinear equations.

2. Give a mathematical analysis of the convergence properties of iterative methods for nonlinear equations.

3. Provide a derivation and analysis of Euler's method based on Taylor's series.

4. Motivate and apply Runge-Kutta methods for solving initial value problems.

5. Construct a matrix factorisation method for solving systems of linear equations.

6. Analyse the stability of linear solvers based on condition numbers.

7. Estimate the eigenvalues of large symmetric matrices.

8. Implement the numerical algorithms described above in Matlab.

Code	Module Title	Semester	ECTS	Examination Arrangements
MA416	Rings	1	5	Two hour examination

An introduction to Ring Theory. The material covered includes:

1. Basic definitions: rings, units, zero divisors, fields and integral domains. The group of units of a ring. Fundamental examples of rings: integers, rationales, reals, polynomials, integers modulo n

2. Ring homeomorphisms: definitions, examples, kernels, images and isomorphisms.

3. Ideals and quotient rings: definition of left, right and two-sided ideals, construction of the quotient ring, the first isomorphism theorem.

4. Fields of fractions: construction.

5. Polynomial rings: irreducibility, primitivity, unique factorisation, Gauss' lemma, and Eisenstein's irreducibility criterion.

6. Euclidean rings: definitions, basic properties and case studies of e.g. the Gaussian integers, and Laurent polynomial rings.

On successful completion of this module the learner should be able to:

1. Determine whether a given algebraic structure is a ring or not.

2. Determine the group of units and the set of zero divisors in a ring.

3. Explain the concepts of homomorphisms, ideals, kernels and quotient rings and relate them to each other.

4. Calculate the field of fractions of an integral domain.

5. Determine whether a given polynomial is irreducible or not.

6. Prove Gauss lemma and Eisenstein's criterion.

7. Find the maximal and prime ideals of a given commutative ring.

8. Decide whether a given domain is a Euclidean ring.

A "measure" on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size. Measure is a generalization of the concepts of length, area, and volume. An important example is Lebesgue measure, which assigns the conventional length, area and volume of Euclidean geometry to suitable subsets of n-dimensional space. Measure Theory is the basis for Integration and it is the foundation for an understanding of Probability Theory.

On successful completion of this module the learner should be able to:

1. Carry out basic operations on sequences of sets.

2. Decide whether a given set function is a measure and execute basic operation with measures.

3. Apply the theory of integration in a wide range of settings, including the real numbers and probability spaces. Decide when term by term integration of a sequence or series of functions is permissible.

4. Give an account of the basic facts about measure spaces and integration.

5. Compose and write proofs of theorems about measures and integrals.

Topics covered include:

1. Partial differentiation.

2. Critical points in the plane and Lagrange multipliers.

3. Optimisation with the Lagrange multiplier method.

4. Fourier Series

5. Double and line integrals in the plane.

6. Green’s theorem in the plane.

Topics covered include:

1. 
   Dimensional analysis: fundamental units, derived units, dimensionless quantities, the Buckingham pi theorem, analysing systems using dimensional analysis, similarity, scale models.
   
2. 
   Calculus of variations: some examples of variational problems - shortest distance between two points, minimal surface area of revolution, Fermat's principle. Derivation of the Euler-Lagrange equation, some first integrals of the Euler-Lagrange equation, solution of some problems, the Euler-Lagrange equations for several functions.
   
3. 
   The Lagrangian formulation of mechanics: coordinate systems, degrees of freedom, generalised coordinates, holonomic systems, constraint forces, the action integral and Hamilton's principle, derivation of the Lagrange equations of motion for a holonomic system, examples of solving mechanics problems using Lagrange's equations.
   
4. 
   Rigid body motion: the motion of the centre of mass of a system of particles, angular momentum and torque, motion about the centre of mass of a rigid body, angular velocity, the moment of inertia tensor, kinetic energy of a rigid body, the solution of some problems for rigid bodies.
   

The topics covered include:

1. 
   Network flow models.
   
2. 
   Activity networks.
   
3. 
   Traffic flow.
   
4. 
   Game theory.
   

This is a course on classical mathematical methods of applied mathematics. Topics covered include:

1. 
   Solution methods for second order linear differential equations with constant coefficients and special ODEs;
   
2. 
   Power series and Frobenius series solutions of second order linear ordinary differential equations with variable coefficients;
   
3. 
   Orthogonality relations for trigonometric functions, Legendre functions, and Bessel functions;
   
4. 
   The calculation of some real integrals using complex contour integration;
   
5. 
   Complex analytic functions.
   

Topics include: algebra of events, probability spaces, conditional probability, independence of events; conbinatorics and random sampling; concept of a random variable (rv); discrete and continuous probability distributions (mass, density and cumulative distribution functions); functions of rv-s; properties of expectation and variance; conditional and joint rv-s and probability distributions; probability and moment generating functions; Markov and Chebyshev inequalities; Weak law of large numbers; Central limit theorem.

1. Sources of data, sampling, experiments, random variation.

2. Exploring data - graphical and numerical summaries.

3. Basic notions of probability - sample spaces, events, combination of events, counting.

4. Conditional probability and independence, Bayes' Theorem.

5. Random variables and probability distributions.

6. Binomial and related probability distributions.

7. Poisson distribution for counts, events over time.

8. Expectation - mean and variance.

9. Bivariate distributions - marginal and conditional probabilities, correlation and independence.

10. Normal distribution - properties, use of tables, central limit theorem and approximations.

11. Use of Minitab for data exploration and probability model calculations.

Various non-parametric hypothesis tests are demonstrated and a comparison of suitability of applying non-parametric and parametric methods is discussed. The module also builds on regression modelling, where topics covered include model estimation, model checking and inference for simple linear regression and multiple linear regression models, and procedures in variable selection. Models discussed are applicable for a single quantitative response with quantitative and/or qualitative predictors.

The topics covered include:

1. Populations and samples, correlation and association, response and explanatory variables.

2. Simple linear regression: estimation using least-squares, properties of estimators, inference on parameter estimates, construction and use of ANOVA table, confidence and prediction intervals, residuals and model diagnostics.

3. Multiple regression: matrix formulation of general linear model, least-squares estimation, properties of estimators, inference on parameter estimates, ANOVA table, fitted values, residuals, the hat-matrix, predictions, diagnostics and model checking.

4. Model choice and variable selection: testing of nested models, variable selection criteria, stepwise and best subsets variable selection methods.

5. Categorical explanatory variables: use of indicator variables for categorical variables, test of overall significance, analysis of covariance, interaction.

6. Practical computer lab sessions: Use of Minitab statistical software to fit regression models, statistical report writing, including a group project and presentation.

The course is design to provide hands-on experience on biomaterials design; fabrication; and in vitro and in vivo assessment.

This module entails the study of fundamental biomechanics concepts ranging from bio-solid mechanics to bio-fluid mechanics. Topics covered include from mechanics of joints in the human body, biomechanics of soft tissue, bone biomechanics, cardiac biomechanics, biomechanics of blood flow and biomechanics of muscle.

This module provides a comprehensive presentation of the finite element (FE) method and computational fluid dynamics (CFD), both of which form critically important parts of modern engineering analysis and design methods. Details of theoretical formulations, numerical implementations and case study applications are presented. The descriptive and analytical content in the lectures is supported by computer laboratory practicals using commercial analysis code (both FE and CFD).

This course integrates the principles and methods of engineering and life sciences towards the fundamental understanding of structure-function relationships in normal and pathological mammalian tissues especially as they relate to the development of biological tissues to restore, maintain, or improve tissue/organ function.

This module covers the biomaterials aspects of biocompatibility, tissue engineering and drug delivery. Molecular and cellular interactions with biomaterials are analyzed in terms of cellular biology and regenerative medicine.

This module entails the study of advanced concepts in the areas of biomechanics and mechanobiology. During semester I students will study tissue biomechanics, with topics including non-linear viscoelasticity, anisotropic hyperelasticity of arteries, and constitutive laws for muscle contractility. During semester II cell mechanobiology is studied with topics including cell mechanics, mechanosenors, tissue differentiation and adaptive remodelling theories. 

This module examines both computer aided drawing and surveying. The work on CAD represents an extension of the material that is covered in Engineering Graphics in the first year. The surveying portion includes both coursework and practical assignments. In the latter, the students, working in teams, produce a drawing of an area that they surveyed.

This component consists of integrated lectures and laboratories that include:

• Tape and offset surveying

• Adjustments of the level and theodolite

• Levelling. Traverse surveying

• Electronic Distance Measurement

• Field work

AutoCAD

This module will cover fundamental areas of engineering hydraulics; theorical content will be augmented by a detailed group design project.

• Pipe flow

• Pipe flow with friction

• Reservoir hydraulics

• Pumps

• Water distribution systems

• Culvert design

This module covers: characterisation and measurement of water parameters, regulations, septic tank design and on-line resources used in the planning applications, 'passive' wastewater treatment using constructed wetlands and sand filters and issues of public acceptance; wastewater and water treatment at municipal-scale, including growth and food utilisation kinetics, attached and suspended culture systems; agricultural wastewater treatment, and greenhouse gas emissions measurement.

General introduction to concepts (characteristics, measurement of parameters, regulations); Septic tank design (internet resources, percolation test, processes, planning applications); Constructed wetlands; Filtration (design criteria, P adsorption isotherms); Natural purification processes (physical, biochemical); Dissolved oxygen model; Wastewater treatment (population equivalents; grit removal, sedimentation tanks; growth and food utilisation, kinetics, suspended culture system, attached culture systems); Water treatment (coagulation, sedimentation, filtration, disinfection); Agricultural engineering (soil quality vs. spreading, volumes produced, legalisation, loading rates); Greenhouse gas emissions (measurement, importance).

Laboratories

1. Nutrient removal

2. Determination of the oxygen transfer coefficient

3. BOD test,

4. Suspended solids test

5. COD test

This module builds on previous module(s) of building and organising project plans for execution of projects using commercial software

In this module the students consider more advanced topics on structural behaviour and use a variety of methods to solve for bending moments and shear forces in different structures. The analytical methods are supplemented by a number of computational analysis laboratories. Solid mechanics topics such as torsion, bending, shear and buckling are also considered in addition to dynamics. Some of the theoretical concepts are also illustrated through laboratory experiments.

Structural Form; Qualitative Structural Analysis; Computer-based Structural Analysis; Moment Distribution Method; Principle of Virtual Work;

Approximate methods of analysis applied to frames. Analysis of multi-storey frames by division into free bodies and use of the inflection points, from where analysis by equilibrium can proceed; Analysis of statically indeterminate trusses by approximate methods; Defining the duality of structural analysis: structural approach and flexibility approach. Study of a propped cantilever to enable the flexibility and stiffness methods to be compared. Implementation of the flexibility method and application to frames and trusses to calculate internal forces and deflections; Construction of influence lines for beams, parabolic arches and trusses; Proof of several theorems on influence lines. Application of moment distribution to a variety of frames.
Mechanics of Solids

Properties of Area: moment of inertia, parallel axis theorem, product of inertia; Torsion: basic equations, varying cross section, rectangular shafts, thin tubular sections, open sections; Beam Bending: basic equations, combined bending and direct stress, unsymmetrical bending, bending of composite beams

Deflection of Beams: deflection equations, differential equation solution, moment area method; Transverse Shear in Beams: shear stress expression, different cross section configurations, shear centre; Stress-Strain Transformation: analysis of stress and strain, Mohr circle of stress/strain, principal moments of inertia, strain gauges; Energy Considerations: strain energy, axial, bending, shear, torsion; Inelastic Problems: fundamentals of plastic behaviour, torsion beyond the yield point, plastic hinge; Elastic Instability: Various end conditions; Eigen value Problems; Beam-Column behaviour; Vibrations: Single degree of freedom structures; Vibrations of beams and shafts;
Computational Analysis

Use of a structural analysis package to analyse a number of continuous beam and frame problems

Students work in groups to carry out three experiments on both model and full scale structures. These experiments are:

- Plastic collapse of portal frames.

- Vibrations of a simply supported beam.

- Tests on reinforced concrete model beams.

Discipline	Module Code	Module Title	ECTS	Taught/Examined in Semester	Examination Arrangements
Civil Engineering	CE342	Structures I	5	1	2 x 2 hour exams

This module represents a continuation of the Strength of Materials module from 2nd year. The students are exposed to a number of structural analysis techniques for common Civil Engineering structures. They will also use a structural analysis package to analyse relevant structures.

Approximate methods of analysis applied to frames. Analysis of multi-storey frames by division into free bodies and use of the inflection points, from where analysis by equilibrium can proceed; Analysis of statically indeterminate trusses by approximate methods; Defining the duality of structural analysis: structural approach and flexibility approach. Study of a propped cantilever to enable the flexibility and stiffness methods to be compared. Implementation of the flexibility method and application to frames and trusses to calculate internal forces and deflections; Construction of influence lines for beams, parabolic arches and trusses; Proof of several theorems on influence lines. Application of moment distribution to a variety of frames.

Properties of Area: moment of inertia, parallel axis theorem, product of inertia; Torsion: basic equations, varying cross section, rectangular shafts, thin tubular sections, open sections; Beam Bending: basic equations, combined bending and direct stress, unsymmetrical bending, bending of composite beams

Deflection of Beams: deflection equations, differential equation solution, moment area method; Transverse Shear in Beams: shear stress expression, different cross section configurations, shear centre; Stress-Strain Transformation: analysis of stress and strain, Mohr circle of stress/strain, principal moments of inertia, strain gauges; Energy Considerations: strain energy, axial, bending, shear, torsion; Inelastic Problems: fundamentals of plastic behaviour, torsion beyond the yield point, plastic hinge; Elastic Instability: Various end conditions; Eigen value Problems; Beam-Column behaviour; Vibrations: Single degree of freedom structures; Vibrations of beams and shafts;
Computational Analysis

Use of a structural analysis package to analyse a number of continuous beam and frame problems

This module introduces the theory supporting, design, maintenance and operation of waste and wastewater treatment systems. Topics covered will include wastewater and waste composition and characteristics, design of treatment facilities, energy efficiency and production, control and monitoring techniques that are used in these systems and current state of the art. The module discusses the engineers’ responsibility to the public and the environment when designing and operating such facilities.

The module content includes: Project and project management characteristics; Stakeholders; Management and organisational concepts; Project life-cycle and its characteristics; Project financing, mechanisms for project financing and measures of project profitability; Project planning; Project delivery/procurement systems; Networks, planning, scheduling and resource allocation; Computer based network analysis; Estimating; Project monitoring and control; Project changes, claims & disputes; Quality.

•Project stakeholders;

• Management and organisational concepts;

• Project life-cycle and its characteristics;

• Project financing, mechanisms for project financing and measures of project profitability;

• Project planning;

•Project delivery/procurement systems;

• Organisation structure diagrams;

• Networks, planning, scheduling and resource allocation;

• Computer based network analysis;

• Estimating;

• Project monitoring and control;

• Project changes, claims and disputes;

• Classification and distribution of costs;

• Quality.

Discipline	Module Code	Module Title	ECTS	Taught/Examined in Semester	Examination Arrangements
Civil Engineering	CE472	Structural Analysis	5	1	2 x 2 hour exams

This module follows on from the structures modules in 3rd year and the students receive additional lectures on moment distribution in addition to the stiffness method, the concepts associated with shear walls and a brief introduction to the finite element method.  Students will also be required to carry out a number of laboratory assignments that are used to illustrate the theoretical concepts from the coursework

Design of Concrete and Steel Structures. Design of class 1-4 beams, laterally supported and unsupported. Design of laterally-supported compound and plate girders. Web panels with intermediate transverse stiffeners. Code moment and shear interaction curves. Beam-columns. Use of Microsoft EXCEL spreadsheet design templates incorporating VBA coding for design tasks, e.g., column stacks. Design and detail reinforced concrete slabs, beams, columns, foundations and retaining walls

The Advanced Structures module builds on structural engineering topics that students would have taken at undergraduate level. Advanced topics include 3-D structures, theory of elasticity, structural dynamics and inelastic/plastic analysis.

This module introduces students to computer-based methods used in the solution of engineering problems. It provides the level of knowledge required to successfully apply these methods to a broad range of applications including structures, heat transfer, fluids flow etc. Students get hands-on experience in using commercial finite element software.

This module deals with transport systems and infrastructure. Highway engineering topics include bituminous materials and advanced pavement management strategies. A focus is placed on road safety engineering. The design of public transport systems, along with the engineering solutions necessary to improve the sustainability of transport in the 21st century are described. Urban mobility is discussed with particular focus on non-motorised transport. Assessment is both project and exam based.

This module will focus on design of Concrete and Steel Structures by studying the following: Introduction to allowable stress design and limit states design philosophies. Overview of modern LSD steel and concrete codes, principally Eurocodes 2 and 3. Design simple steel structural members including ties, struts, beams, connections, truss roofing systems.Design one-way reinforced concrete spanning slabs, singly and doubly reinforced concrete beams, columns and pad foundations.

This module covers the fundamentals of computer architectures, and embedded systems design. The students learn to program an embedded system and learn how to interface to analogue and digital peripherals. The students work in groups on a project involving an embedded system for a practical application

Review of systems. Circuit analysis and theorems. Measurement and instrumentation. Sensors, actuators, transducers. Sensed quantities. Passive, active sensors. Resistors, capacitors, inductors as sensing elements. Practical sensor applications. Sensor characteristics. Frequency response. Noise and errors in measurements. Signal conditioning and filtering. Analogue and digital sensors. Analogue-digital conversion. Display of sensed values. Data acquisition and instrument control using a computer.