Bachelor of Engineering (Civil): Year 2

Planning and development acts; bye laws and building regulations; foundations methods; wall construction; roofing systems; floors and floor finishes. Thermal properties; heat and sound insulations. External and internal finishes. General properties of building materials. Masonry materials. Concrete Technology: Properties and testing of cement and aggregates. Design of concrete mixes. Principal properties and testing of fresh and hardened concrete. Timber as an engineering material. Properties and behaviour of metals, plastics and composites. Concepts of stress and strain, equilibrium, compatibility, pin jointed structures, statically indeterminate members. Principal stresses, Mohr circle. Pressure vessels and flexible cables. Torsion of uniform and non-uniform circular shafts. Connection, bolted and welded, methods of failure, strength characteristics. Beams, shear force and bending moment diagrams, bending stresses, shear stresses, deflections, buckling of columns.

• Laboratory work in strength of materials
• Surveying Field Work
• Concrete Technology
• Further Applications of AutoCAD
• Communications
• Computational Analysis of Simple Structures
• Hydraulics laboratory

Fluid properties, pressure in a fluid; hydrostatics, forces and moments on submerged surfaces; buoyancy and stability of floating bodies; theorems on conservation of mass, momentum and energy (Bernoulli’s theorem); measurement of fluid pressure, pressure difference and kinetic energy; flow measurement by Venturi, orifice and Pitot devices and by notches and weirs; forces exerted by a jet and application to rotors and turbines; energy losses caused by frictional resistance to flow and form losses, ie energy losses due to enlargements and bends, etc.; flow in pipes; uniform flow in open channels; transmission of power by pipeline; viscosity and oiled bearings; elements of pneumatics. Introduction to geology; the rock forming minerals; the classification, nature and engineering aspects of igneous, sedimentary and metamorphic rocks; global processes and geologic time; surface processes, including erosion and deposition in coastal, fluvial and glacial environments, stress and strain in the Earth’s crust, folds and faults. The weekly timetable comprises of three classes focusing on grammar, reading, writing skills, and conversation. A fourth class takes place in the language laboratory and focuses on pronunciation exercises, listening comprehensions and dictation work. The course includes an introduction to modern German society. Relevant video material will be screened in class and made available on Blackboard. Rn as a vector space: subspaces, linear independence, bases, dimension; Linear transformations, the natural matrix and the matrix with respect to a given basis; Eigenvectors, eigenvalues and diagonalisation; Gerschgorin discs; methods for finding eigenvalues, e.g. Jacobi method; Orthogonality and projections; Overdetermined systems of linear equations; the least-squares method; Orthogonal reduction of a symmetric matrix; Inner products, orthonormal bases and the Gram-Schmidt process.

• Sequences and series: series of positive terms, the Ratio and Comparison Tests for convergence, alternating series Power series: functions defined by power series, their integrals and derivatives, Abel’s Theorem
• Functions of 2 and 3 variables: limits and continuity, partial differentiation, total derivatives
• Scalar functions, vector functions, vector fields
• The Chain Rule, the Jacobian matrix
• Equations of tangent planes and normal lines, extrema of scalar functions, maxima and minima of constrained functions, Lagrange multipliers
• Arc lengths, line integrals, polar curves
• Multiple integration: areas and volumes, Jacobians, change of variables
• Functions of a complex variable: analytic functions, the Cauchy-Riemann equations, harmonic functions and applications to fluid flow and heat flow
• Complex contour integrals: Cauchy’s Integral Theorem and Cauchy’s Integral Formula, the calculus of residues.

Scientific programming in Matlab; Root finding: iterative methods, convergence, order, Newton’s method, the secant method; Interpolation: Lagrange form and error, Newton’s divided difference interpolation, cubic splines; Numerical integration: some Newton-Cotes formulae with error (Trapezoid rule, Simpson’s rule); Some numerical methods in linear algebra: Gauss elimination, solutions by iteration, Gauss-Seidel iteration, Jacobi iteration, eigenvalues by iteration; Some numerical methods for ordinary differential equations: the Euler method, the improved Euler method, Runge-Kutta methods. Core

• Revision of simple summary statistics, basic probability ideas
• Continuous probability distributions – models for variability: Poisson, uniform, normal, exponential
• Expectation, means, variance
• Combinations of variables, central limit theorem, transformations Joint distributions, correlation
• Estimation – point and interval estimates; means, variances, proportions
• Hypothesis testing – comparing means, proportions
• Simple linear regression – model, estimation, inference, diagnostics multiple regression – least-squares, model fitting, model selection

Special Topics

• Design and analysis of experiments – analysis of variance, simple designs, fractional factorials
• Introduction to statistical modelling – maximum likelihood, application to reliability Stochastic processes – Poisson process, queues

Practical Work

• Introduction to Matlab, looking at data, transformations
• Probability distributions, probability plotting, normal distribution and central limit theorem
• Simple linear regression – fitting, inference, diagnostics Multiple regression – model selection. Analysis of variance.

• Force systems: the resultant of a distributed system of forces and couples at a point, mechanical equivalence of force systems, wrench systems
• Rigid body statics: equations of equilibrium, free body diagrams, supports and hinges, solved problems
• Rigid body kinematics and dynamics: the equations of motion for a rigid body, motion of the centre of mass, motion about the centre of mass, angular velocity, moments of inertia, solved problems in two and three dimensions
• Laplace transforms: definition and examples, Laplace transform of a derivative, solution of initial value problems for ODEs using the transform, modelling simple electrical circuits, the Heaviside function
• Coordinate systems: definition of cylindrical and spherical coordinate systems, the Jacobian matrix and area/volume elements, coordinate bases and changing vectors from one coordinate system to another, scale factors.

• Dimensional analysis: dimensionless variables and parameters, the Buckingham Pi theorem and its utility in analyzing simple engineering system, dynamic similarity and building scale models
• Stability: analyzing the stability of mechanical systems in equilibrium, some worked examples
• Fourier series: definition, sine series, cosine series, some examples, applications
• Vector calculus: scalar fields, vector fields, geometry of curves, tangent vectors, directional derivatives, div, grad, curl, normal to a surface, integration in 2 and 3 dimensions (areas, volumes), the line integral, surface integrals, integral theorems
• Partial Differential Equations (PDEs): three important examples - the heat equation, the wave equation, and Laplace’s equation. Modelling simple engineering systems using PDEs: heat flow, solid-state diffusion, acoustic waves, fluid flow. Solution of PDEs via the method of separation of variables and using Laplace transforms. Interpreting the solutions in engineering contexts.

Chain surveying. Level and theodolite adjustments. Levelling. Traverse surveying. Tacheometry. Contouring. Hydrographic surveying. Areas and volumes. Mass haul diagrams. Geodimeter. Setting out engineering works. Photogrammetry. Theory of Errors. Geographic information systems. GPS. Field work.