Module Specification
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
1. Module Title INTRODUCTION TO THE METHODS OF APPLIED MATHEMATICS
2. Module Code MATH224
3. Year Session 2023-24
4. Originating Department Mathematical Sciences
5. Faculty Fac of Science & Engineering
6. Semester Second Semester
7. CATS Level Level 5 FHEQ
8. CATS Value 15
9. Member of staff with responsibility for the module
Professor JA Gracey Mathematical Sciences Gracey@liverpool.ac.uk
10. Module Moderator
11. Other Contributing Departments  
12. Other Staff Teaching on this Module
Mr AP Smithson School of Electrical Engineering, Electronics and Computer Science Alan.Smithson@liverpool.ac.uk
Professor T Teubner Mathematical Sciences Thomas.Teubner@liverpool.ac.uk
Dr SA Fairfax Mathematical Sciences Simon.Fairfax@liverpool.ac.uk
13. Board of Studies
14. Mode of Delivery
15. Location Main Liverpool City Campus
    Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other TOTAL
16. Study Hours           36

 36
17.

Private Study

 102
18.

TOTAL HOURS

 138
 
    Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other
19. Timetable (if known)            
 
20. Pre-requisites before taking this module (other modules and/or general educational/academic requirements):

 
21. Modules for which this module is a pre-requisite:

 
22. Co-requisite modules:

 
23. Linked Modules:

 
24. Programme(s) (including Year of Study) to which this module is available on a mandatory basis:
25. Programme(s) (including Year of Study) to which this module is available on a required basis:
26. Programme(s) (including Year of Study) to which this module is available on an optional basis:
27. Aims
 

•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 (Fourier Series) used in the solution of differential equations and other applications of mathematics.
 
28. Learning Outcomes
 

(LO1) After completing the module students should: - be fluent in the solution of basic ordinary differential equations, including systems of first order equations:- be familiar with the concept of Fourier series and their potential application to the solution of both ordinary and partial differential equations:- be familiar with the concept of Laplace transforms and their potential application to the solution of both ordinary and partial differential equations: - be able to solve simple first order partial differential equations: - be able to solve the basic boundary value problems for second order linear partial differential equations using the method of separation of variables.
 
29. Teaching and Learning Strategies
 

The module will not be taught in 21/22 and will assessment will run for external repeaters
 
30. Syllabus
   

- Revision of first and second order ordinary differential equations, Euler''s differential equation, systems of inear equations.

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

- Second order linear partial differential equations; classification, Wave equation, Laplace''s equation, Diffusion equation and their applications, series solution of boundary value problems by the method of separation of variables.

- First order partial differential equations; solution by method of characteristics.
 
31. Recommended Texts
  Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.
 

Assessment
32. EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
  Final Assessment Open book and remote Assessment Schedule (When) :Second semester 1 50
33. CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
  Class Test 1 Open book and remote Assessment Schedule (When) :Second semester 0 50