Teaching Responsibility

LJMU Schools involved in Delivery:

LJMU Partner Taught

Learning Methods

Lecture
Seminar
Tutorial

Module Offerings

4500ICBTCE-APR-PAR
4500ICBTCE-JAN-PAR
4500ICBTCE-SEP-PAR

Aims

This unit will provide the analytical knowledge and techniques needed to carry out a range of engineering tasks and will provide a base for further study of engineering mathematics.

Learning Outcomes

1.
Identify the use of basic algebraic manipulations and mathematical functions in the solution of engineering problems and apply trigonometric methods to solve engineering problems.
2.
Demonstrate the knowledge of calculus and apply techniques in differentiation and integration to the solution of engineering problems.
3.
Demonstrate the knowledge statistics and probability and apply to solve engineering problems.
4.
Use and apply mathematical software to the solution of engineering mathematics problems such as Mini Tab, excel etc;

Module Content

Outline Syllabus:Algebraic methods: Substitution, simplification, factorization, indices, evaluation and transposition of formulae, fractions and partial fractions. Linear and quadratic equations, linear simultaneous equations. Functions: Notation, types of function, composite and inverse, graphs. polynomial division, quotients and remainders, use of factor and remainder theorem, rules of order for partial fractions (including linear, repeated and quadratic factors), reduction of algebraic fractions to partial fractions. Revision of elementary coordinate geometry: Distance between two points, the straight line, simple polynomial curves. Cartesian and polar co-ordinate systems, properties of the circle. Arithmetic and geometric: notation for sequences, arithmetic and geometric progressions, the limit of a sequence, sigma notation, the sum of a series, arithmetic and geometric series, Pascal’s triangle and the binomial theorem. Trigonometric :Introduction, Trigonometric ratios of acute angles, evaluating trigonometric ratios, solution of right angled triangles, Angles of elevation and depression, sine and cosine rules, area of any triangle, solving engineering applications. Calculus: the concept of the limit and continuity, definition of the derivative, derivatives of standard functions, notion of the derivative and rates of change, differentiation of functions using the product, quotient and function of a function rules, integral calculus as the calculation of area and the inverse of differentiation, the indefinite integral and the constant of integration, standard integrals and the application of algebraic and trigonometric functions for their solution, the definite integral and area under curves. Further differentiation: second order and higher derivatives, logarithmic differentiation, differentiation of inverse trigonometric functions, differential coefficients of inverse hyperbolic functions. Further integration: integration by parts, integration by substitution, integration using partial fractions. Applications of the calculus: e.g. maxima and minima, points of inflexion, rates of change of temperature, distance and time, electrical capacitance, rms values,electricalcircuitanalysis,ACtheory,electromagneticfields,velocityandaccelerationproblems,complex stress and strain, engineering structures, simple harmonic motion, centroids, volumes of solids of revolution, second moments of area, moments of inertia, rules of Pappas, radius of gyration, thermodynamic work and heat energy. Tabular and graphical form: data collection methods, histograms, bar charts, line diagrams, cumulative frequency diagrams, catter plots. Central tendency and dispersion: the concept of central tendency and variance measurement, mean, median, mode, standard deviation, variance and interquartile range, application to engineering production. Regression, linear correlation: determine linear correlation coefficients and regression lines and apply linear regression and product moment correlation to a variety of engineering situations. Probability: Introduction, Laws of probability, engineering applications of probability.

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