Module Details

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.
Title FURTHER METHODS OF APPLIED MATHEMATICS
Code MATH323
Coordinator Prof DI Jack
Mathematical Sciences
Dij@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2016-17 Level 6 FHEQ First Semester 15

Aims

To give an insight into some specific methods for solving important types of ordinary differential equations.

To provide a basic understanding of the Calculus of Variations and to illustrate the techniques using simple examples in a variety of areas in mathematics and physics.

To build on the students'' existing knowledge of partial differential equations of first and second order.


Learning Outcomes

After completing the module students should be able to:

-     use the method of "Variation of Arbitrary Parameters" to find the solutions of some inhomogeneous ordinary differential equations.

-     solve simple integral extremal problems including cases with constraints;

-     classify a system of simultaneous 1st-order linear partial differential equations, and to find the Riemann invariants and general or specific solutions in appropriate cases;

-     classify 2nd-order linear partial differential equations and, in appropriate cases, find general or specific solutions.   [This might involve a practical understanding of a variety of mathematics tools; e.g. conformal mapping and Fourier transforms.]


Syllabus

1

Ordinary differential equations; some methods, including the variation of arbitrary constants, for solving certain types of equations.

Introduction to the Calculus of Variations for problems without and with constraints.

Simultaneous first-order linear partial differential equations;  Riemann invariants.

Second-order linear partial differential equations; classification, reduction to standard forms, conformal mappings. Fourier transforms.


Recommended Texts

Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.
Explanation of Reading List:

Pre-requisites before taking this module (other modules and/or general educational/academic requirements):

MATH101; MATH224; MATH102; MATH103  

Co-requisite modules:

 

Modules for which this module is a pre-requisite:

 

Programme(s) (including Year of Study) to which this module is available on a required basis:

Programme:FGH1 Year:3,4

Programme(s) (including Year of Study) to which this module is available on an optional basis:

Programme:F344 Year:3,4 Programme:G100 Year:3 Programme:G101 Year:3,4 Programme:NG31 Year:3 Programme:G110 Year:3 Programme:GG14 Year:3 Programme:G1F7 Year:3 Programme:G1N2 Year:3 Programme:G1N3 Year:3 Programme:G1R9 Year:4 Programme:G1X3 Year:3 Programme:GG13 Year:3 Programme:GN11 Year:3 Programme:FG31 Year:3 Programme:GL11 Year:3 Programme:GR11 Year:4 Programme:GV15 Year:3 Programme:BCG0 Year:3 Programme:L000 Year:3 Programme:Y001 Year:3 Programme:MMAS Year:1

Assessment

EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Written Exam  2.5 hours  First semester  100  Standard University Policy    Assessment 1 Notes (applying to all assessments) Exam rubric: "Full marks can be obtained for complete answers to FIVE questions. Only the best five answers will be taken into account."  
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes