Course Catalogue

LJMU Partner Taught

To develop skills in advanced engineering mathematics for application to the solution of Civil and Building Services Engineering problems.

Outline Syllabus:Error arithmetic: significant figures and estimation techniques, error arithmetic operations, systematic and random errors, application to experimentation and general laboratory work Number systems: natural, integer, rational, reals, dinary, binary, octal and hexadecimal number systems. Complex numbers: real and imaginary parts of complex numbers, complex number notation. Cartesian and polar forms, Argand diagrams, powers and roots and the use of de Moivre’s theorem, use of phasor and Argand diagrams Numerical integral: determine the integral of functions using mid-ordinate, trapezoidal and Simpson’s rules Numerical estimation methods: method of bisection, Newton-Raphson iteration method, estimates of scientific functions Vector notation and operations: Cartesian co-ordinates and unit vectors, types of vector and vector representation, addition and subtraction, multiplication by a scalar, graphical methods Matrix operations and vectors: carry out a range of matrix operations, e.g. vectors in matrix form, square and rectangular matrices, row and column vectors, significance of the determinant, determinant for 2x2 matrix, the inverse of a 2x2 matrix, Gaussian elimination to solve systems of linear equations (up to 3x3), Vector geometry: determine scalar product, vector product, angle between two vectors, equation of a line, norm of a vector, dot and cross products First order differential equations: engineering use, separation of variables, integrating factor method, complementary function and particular integral Numerical methods for first order differential equations: need for numerical solution, Euler’s method, improved Euler method, Taylor series method Application of second order differential equations: Engineering situations: applications, e mechanical systems, fluid systems, etc. Finite Difference and finite element methods