### 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 FIELD THEORY AND PARTIAL DIFFERENTIAL EQUATIONS Code MATH283 Coordinator Professor JA Gracey Mathematical Sciences Gracey@liverpool.ac.uk Year CATS Level Semester CATS Value Session 2023-24 Level 5 FHEQ First Semester 7.5

### Aims

To introduce students to the concepts of scalar and vector fields. To develop techniques for evaluating line, surface and volume integrals.

To introduce students to some of the basic methods for solving partial differential equations

### Learning Outcomes

(LO1) Evaluate Grad, Div, Curl and Laplace operators in Cartesian and polar coordinates.

(LO2) Evaluate line, double and volume integrals.

(LO3) Understand of the physical meaning of flux and circulation.

(LO4) Solve simple boundary value problems for the wave equation, diffusion equation and Laplace's equation.

### Syllabus

Vector Calculus:
Revision of partial differentiation;
scalar and vector fields;
field operators Grad, Div, Curl, and the Laplacian;
Line, double, surface and volume integrals (spheres and cuboids only);
flux and circulation of vector field, theorems of Gauss and Stokes;
potential functions;
applications to electromagnetism.

Partial Differential Equations:
Basic equations of mathematical physics, wave equation, diffusion equation, Laplace's equation;
solution by method of separation of variables;
calculation of eigenfunctions for simple initial and boundary value problems.

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

MATH101 Calculus I 2022-23; MATH102 CALCULUS II 2022-23; MATH103 Introduction to Linear Algebra 2022-23

### Assessment

EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Final Assessment.  60    50
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Class Test  60    20
Homework 1 online in Moebius    10
Homework 2 online in Moebius    10
Homework 3 online in Moebius    10