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 INTRODUCTION TO THE METHODS OF APPLIED MATHEMATICS Code MATH224 Coordinator Professor JA Gracey Mathematical Sciences Gracey@liverpool.ac.uk Year CATS Level Semester CATS Value Session 2021-22 Level 5 FHEQ Second Semester 15

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.

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.

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.

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

Assessment

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 hour    50
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  around 60-90 minutes    50