Module Catalogues, Xi'an Jiaotong-Liverpool University   
 
Module Code: MTH201
Module Title: Engineering Mathematics III
Module Level: Level 2
Module Credits: 2.50
Academic Year: 2019/20
Semester: SEM1
Originating Department: Mathematical Sciences
Pre-requisites: N/A
   
Aims
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 and results in field therory .

To be familiar with the partial differential 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 related to and the use of vector fields, Fourier series, and partial differential equations.

To solve problem by establishing appropriate mathematical models using the most relevant techniques

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.
Syllabus 
Revision of Vector Calculus

0.1 Scalar and vector fields, differentiation of a vector function with respect to a scalar quantity.

0.2 Concepts of gradient, divergence, curl.

Vector Integral Calculus. Integral Theorems

1.1 Linear integral, closed line integral, circulations, conservative field, and potential.

1.2 Surface integral, elementary area vector, flux of a vector field, closed surface integral.

1.3 Volume integral and Gauss’s law of electrical field.

1.4 Green’s theorem, Stoke’s theorem and Gauss theorem.

1.5 Applications and examples.

Partial Differential Equations

2.1 Fourier series; sine series, cosine series, full-range series for functions with arbitrary periods.

2.2 Second order linear partial differential equations; classification.

2.3 Wave equation, solution by separation of variables, Fourier series solution.

2.4 Laplace's equation, Diffusion equation and their applications, series solution of boundary value problems by the method of separation of variables.

2.5 First order partial differential equations, solution by method of characteristics.

2.6 Further examples of application
Delivery Hours  
Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total
Hours/Semester 26     13        39 

Assessment

Sequence Method % of Final Mark
1 Midterm Exam 20.00
2 Formal Examination 70.00
3 Quiz 5.00
4 Quiz 5.00

Module Catalogue generated from SITS CUT-OFF: 12/16/2019 7:37:50 AM