Module Catalogues, Xi'an Jiaotong-Liverpool University   
Module Code: MTH101
Module Title: Engineering Mathematics I
Module Level: Level 1
Module Credits: 5.00
Academic Year: 2021/22
Semester: SEM1
Originating Department: Department of Pure Mathematics
Pre-requisites: N/A
The aims of this module are to:

To give students advanced mathematical tools common to engineering applications.

To demonstrate the physical origin of applied mathematics.

To understand the basic concepts in vector analysis, complex functions and Laplace transforms

To be familiar with the equations of importance to engineering and science and their properties.

To train the students' ability to think logically and independently and to acquire the skills of problem solving.
Learning outcomes 
On successful completion of the module, the student is expected to have:

A good understanding of the basics concepts of:

A. Complex functions and their integrals.

B. Laplace transforms.

C. Series solutions of ODEs.

D. Be able to solve problem 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 classes, case studies and revision seminars.
Complex Analysis (18 h)

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

Laplace Transforms (9 h.)

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

Power Series Solutions Of Ordinary Differential Equations (10 h)

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.

2 hours Revision

Delivery Hours  
Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total
Hours/Semester 39    13      98  150 


Sequence Method % of Final Mark
1 Formal Examination 80.00
2 Midterm 20.00

Module Catalogue generated from SITS CUT-OFF: 12/5/2020 1:16:56 PM