Module Catalogues, Xi'an Jiaotong-Liverpool University

Module Code: MFE105TC
Module Title: Engineering Mathematics
Module Level: Level 1
Module Credits: 2.50
Semester: SEM1
Originating Department: School of Intelligent Manufacturing Ecosystem, Taicang
Pre-requisites: N/A

 Aims This module aims to equip students with advanced mathematical tools common to engineering applications; specifically, this module demonstrates to students the physical origin of applied mathematics and enables them to understand the basic concepts in vector analysis, complex functions and Laplace transforms. This module thereby trains students to think logically and independently of given problems in practice and solve them with advanced mathematical tools.
 Method of teaching and learning A Acquire the basic concepts in complex functions and their integrals.B Understand Laplace transforms and their properties and apply them for the solutions of ordinary differential equations.C Understand power series methods and their theoretical basis and apply them for the solutions of ordinary differential equations.D Be able to solve problems by establishing appropriate mathematical models using the most relevant techniques.E Have an appreciation of the importance of mathematics to engineering and science.
 Method of teaching and learning This module will be delivered by a combination of formal lectures, problem-solving tutorials and a revision seminar.
 Syllabus 1. Complex Analysis1.1 Revision of complex numbers1.2 Complex Functions1.3 Limit derivative, definition of analytic function, Cauchy-Riemann equations1.4 Rational function, exponential function, trigonometric and hyperbolic function, logarithmic function1.5 Complex integral: line integral, Cauchy's integral theorem1.6 Laurent series1.7 Analyticity at infinity, zeros and singularities1.8 Integration by the method of residues2. Laplace Transforms2.1 Definitions of Laplace transform and inverse transform, condition for existence.2.2 Properties and Laplace transform pairs2.3 Using residue theorem to obtain inverse Laplace transform2.4 Convolution and correlation2.5 Use of Laplace transform for the solution of ODE3. Power Series Solutions of Ordinary Differential Equations3.1 The power series methods and its theoretical basis3.2 Legendre's equation and Legendre polynomials3.3 Extended power series method and indicial equation3.4 Bessel's equation and Bessel functions of first kind3.5 Bessel functions of second kind3.6 Orthogonal functions, orthogonality of Legendre's polynomials and Bessel function.4. 2-Hour Revision
Delivery Hours
 Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total Hours/Semester 28 2 14 31 75

## Assessment

 Sequence Method % of Final Mark 1 Midterm Exam 20.00 2 Final Exam 80.00
 Module Catalogue generated from SITS CUT-OFF: 12/16/2019 7:23:50 AM