Module Catalogues, Xi'an Jiaotong-Liverpool University   
 
Module Code: MFE105TC
Module Title: Engineering Mathematics
Module Level: Level 1
Module Credits: 2.50
Academic Year: 2020/21
Semester: SEM1
Originating Department: School of Intelligent Manufacturing Ecosystem
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 Analysis

1.1 Revision of complex numbers

1.2 Complex Functions

1.3 Limit derivative, definition of analytic function, Cauchy-Riemann equations

1.4 Rational function, exponential function, trigonometric and hyperbolic function, logarithmic function

1.5 Complex integral: line integral, Cauchy's integral theorem

1.6 Laurent series

1.7 Analyticity at infinity, zeros and singularities

1.8 Integration by the method of residues


2. Laplace Transforms

2.1 Definitions of Laplace transform and inverse transform, condition for existence.

2.2 Properties and Laplace transform pairs

2.3 Using residue theorem to obtain inverse Laplace transform

2.4 Convolution and correlation

2.5 Use of Laplace transform for the solution of ODE


3. Power Series Solutions of Ordinary Differential Equations

3.1 The power series methods and its theoretical basis

3.2 Legendre's equation and Legendre polynomials

3.3 Extended power series method and indicial equation

3.4 Bessel's equation and Bessel functions of first kind

3.5 Bessel functions of second kind

3.6 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: 8/22/2019 5:47:14 PM