Bachelor of Engineering (Civil): Year 1

Limits and graphs of a continuous function of one real variable. Continuity and derivative of a function. Engineering applications of the Intermediate Value Theorem. Determining derivatives from first principles. Techniques of differentiation. Finding tangents, maxima/minima, points of inflection of functions. Accurate curve sketching. Applications to engineering problems on rates of change (acceleration, inflation) and maxima/minima. Definition of an integral. Numerical approximations of integrals. Applications of the Fundamental Theorem of Calculus. Techniques of integration. Computation of lengths of curves, areas of planar regions, and volumes of revolution. Power series representation of functions, including Taylor’s Theorem. Engineering Algebra: Engineering problems modelled by systems of linear equations. Solving systems (with a unique solution) by gaussian elimination. Computer demonstrations. Vectors, planes and intersections of planes in n-dimensional euclidean space. Finding the general solution of a system of m linear equations in n unknowns. Inconsistent/consistent systems. Matrix algebra. Inverse, transpose and adjoint matrices. Linear transformations of the plane. Computer applications to engineering problems such as: Kirchoff’s Laws, computer graphics. Definition and properties of a determinant. Efficient computation of determinants using row operations. Volumes of parallelograms/parallelopipeds. Theoretical formula for the inverse of a matrix. Complex numbers: argument, modulus, Argand diagram, de Moivre’s Theorem. Applications to trigonometric functions. Complex roots of polynomials. Roots of unity. Factorization of real polynomials. Characteristic polynomials, eigenvalues, eigenvectors and diagonalization of matrices. Classification of conic sections. Orthogonal transformations of the plane, and an application to finding standard forms for conic sections. Differential Equations and Probability Introduction to Data and Probability. Ordinary differential equations, with emphasis on modelling and applications in Engineering, including harmonic oscillators and projectile motion. Vectors in two and three dimensions, Kinematics, Relative velocity, Newton’s Laws of motion, Conservation of momentum, Work, power and energy, Circular motion and angular momentum, Systems of particles and centres of mass. The aim of this module is to equip the learner with basic knowledge, skills and competences associated with the fundamentals of a range of topics in engineering chemistry. Indicative content is as follows: Atomic structure, chemical arithmetic: calculations involving industrially and biologically important chemical processes. Bonding. Gases: Working model of a gas; gas laws; kinetic theory. Phase changes. Solutions: Concentration units; solubility; detergents, separation techniques: Distillation. Properties of solids and materials: Model of a solid; simple crystal structures; metals; Band Theory; relationship between structure and macroscopic properties. Superconductors; Semiconductors. Acids and bases: Basic definitions; strong and weak acids and bases, pH calculations. Buffers. Redox processes: Electrochemistry; cells and electrode processes; corrosion and its prevention Thermodynamics: Basic concepts and laws; enthalpy; calorific value of fuels; entropy; free-energy and spontaneity of chemical reactions; bond dissociation concept. Thermodynamics of biological processes. Kinetics/equilibria: Determination of rate and order of reactions; factors affecting rates of reactions; catalysis, including enzyme catalysis. Le Chatelier’s Principle; calculation of equilibrium constants. Organic chemistry: Historical introduction. Chemical reactions of important functional groups including aromatic systems. Isomerism including chirality. Polymerisation. Wave nature of light, refraction, geometrical optics, mirrors, prisms, lenses, optical instruments, principle of linear superposition, interference, Young's slits, diffraction, resolving power. (~9 hrs) Kinematics in one dimension, force, Newton's Laws, work, energy, circular motion, gravity, conservation of momentum and energy, (~9 hrs) Electric charge, Coulombs Law, electric field and potential, basic electrical circuit laws, magnetism, magnetic induction, (~9 hrs) Photoelectric effect, line spectra, Bohr model of the atom, x-rays, lasers, the nucleus, nuclear energy, radioactive decay, radiological safety. (~9 hrs) Laboratory work. This module gives students an historical perspective and an appreciation of the role of engineers in society across several engineering disciplines. In addition, it presents some fundamental engineering theories and introduces topics such as material behaviour/choice and the design of engineering components and systems. Student learning will be framed in the context of sustainable and responsible engineering practice, while independent thinking and teamwork skills critical for subsequent years will be fostered. Engineering Graphics introduces the students to Engineering Graphics as a language and to Engineering Drawings. The students will acquire familiarity with AutoCAD and the necessary skills to complete Engineering Drawings. The skills and knowledge acquired in this module will enable the students to apply AutoCAD to engineering design problems. The module combines lecture time with laboratory/design office assignments. Semester 1 of this module will provide an introduction to Engineering Computation, beginning with a general overview of computer systems, operating systems and applications. Students will store data and operate on it using a spreadsheet program, and then learn how to move such data into a numerical computing package and develop basic programs to perform more sophisticated data visualisation and processing. Semester 2 will introduce students to the basics of software development and programming in a modern procedural programming language. By tackling specific Engineering problems, students will gain experience of designing, developing, testing, and evaluating computer programs. They will develop software for both desktop and embedded computing platforms.