Module Catalogues, Xi'an Jiaotong-Liverpool University   
 
Module Code: MTH106
Module Title: Introduction to the Methods of Applied Mathematics
Module Level: Level 1
Module Credits: 5.00
Academic Year: 2019/20
Semester: SEM2
Originating Department: Mathematical Sciences
Pre-requisites: N/A
   
Aims
To recognise and solve equations in the common classes of soluble ordinary differential equations.

To provide a grounding in elementary approaches to solution of some of the standard partial differential equations encountered in the applications of mathematics.

To introduce some of the basic tools,for example,fourier series and matrix methods, used in the solution of differential equations and other applications of mathematics.
Learning outcomes 
A. Solve basic ordinary differential equations, including systems of first order equations.

B. Be familiar with the concept of Fourier series and their potential application to the solution of partial differential equations.

C. Solve simple first order partial differential equations.

D. Solve basic boundary value problems for second order linear partial differential equations using the method of separation of variables.
Method of teaching and learning 
Students will be expected to attend about three hours of formal lectures and about one hours of supervised tutorials (problem classes)in a typical week.


Lectures and tutorials will introduce students to the academic content and practical skills which are the subject of the module, while tutorials, problem classes and computer practicals will allow students to practice those skills.


In addition, students will be expected to devote two hours of unsupervised time to private study.


Private study will provide time for reflection and consideration of lecture material and background reading.

This module is assessed by course work, a midterm and a written examination at the end of the module.

Syllabus 
Solution of separable, homogeneous, and linear first order ordinary differential equations.


Revision of first and second order ordinary linear differential equations, Euler's differential equation.


Systems of first order linear equations, revision of eigenvalues and eigenvectors for small matrices.


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


- First order partial differential equations solved using the method of characteristic.


- Second order linear partial differential equations; wave equation, Laplace's equation, Diffusion equation and their applications, series solution of boundary value problems by the method of separation of variables
Delivery Hours  
Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total
Hours/Semester 39    13      98  150 

Assessment

Sequence Method % of Final Mark
1 Midterm Exam 15.00
2 Course Work 15.00
3 Final Exam 70.00

Module Catalogue generated from SITS CUT-OFF: 8/20/2019 6:18:23 PM