Module Details

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.

Module Title

FURTHER METHODS OF APPLIED MATHEMATICS

Module Code

MATH323

Year

Session 2023-24

Originating Department

Mathematical Sciences

Faculty

Fac of Science & Engineering

Semester

First Semester

CATS Level

Level 6 FHEQ

CATS Value

Member of staff with responsibility for the module

Dr GT Piliposyan

Mathematical Sciences

G.Piliposyan@liverpool.ac.uk

10.

Module Moderator

11.

Other Contributing Departments

12.

Other Staff Teaching on this Module

Professor N Movchan

Mathematical Sciences

Nvm@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	24		24				48
17.	Private Study							102
18.	TOTAL HOURS							150

		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): MATH102 CALCULUS II; MATH101 Calculus I; MATH103 Introduction to Linear Algebra; MATH221 Differential Equations

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 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.

28.

Learning Outcomes

(LO1) 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.]

29.

Teaching and Learning Strategies

Material is presented during lectures (3 hours per week). Tutorials (1 hour per week) are used for consolidation and practice, and for help with individual questions.

30.

Syllabus

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.

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 on campus	100		70

33.	CONTINUOUS	Duration	Timing (Semester)	% of final mark	Resit/resubmission opportunity	Penalty for late submission	Notes
	Class test	75		30