### 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 MATHEMATICS FOR PHYSICISTS II Code PHYS108 Coordinator Professor RN McGrath Physics R.McGrath@liverpool.ac.uk Year CATS Level Semester CATS Value Session 2021-22 Level 4 FHEQ Second Semester 15

### Aims

To consolidate and extend the understanding of mathematics required for the physical sciences. To develop the student’s ability to apply the mathematical techniques developed in the module to the understanding of physical problems.

### Learning Outcomes

(LO1) Ability to manipulate matrices with confidence and use matrix methods to solve simultaneous linear equations.

(LO2) Familiarity with methods for solving first and second order differential equations in one variable.

(LO3) A basic knowledge of vector algebra.

(LO4) A basic understanding of Fourier series and transforms.

(LO5) A basic understanding of series methods for the solution of differential equations

(S1) Numeracy

(S2) Problem solving skills

(S3) Teamwork

### Syllabus

* Matrices- addition, multiplication, determinant, inverse, solution of systems of linear equations.

* Differential equations – first and second order Diff. Eqn.s in one variable, separation of variables, integrating factors, homogenous (and inhomogeneous) equations.

Vector calculus – differentiation and integration of vectors, vector and scalar fields, Grad, Div, Curl and Laplace in Cartesian Co-ords.

Mention Laplace’s and Poisson’s equations and different coordinate systems. Series solutions, Legendre polynomials, mention spherical harmonics and Schrödinger’s equation.

Fourier series, periodic functions, even and odd expansions. Fourier integrals and transforms. Convolution theorem.

### Teaching and Learning Strategies

Teaching Method 1 - Lecture [online]
Description: 12 x 3 lectures/week
Attendance Recorded: No

Teaching Method 2 - Problems Class
Description: 12 x 2-hour problems classes. Students attempt a range of problems associated with the course material, under supervision of the lecturer and demonstrators
Attendance Recorded: No

The module will be delivered remotely in 2021. Asynchronous learning materials (notes/videos/exercises etc) will be made available to students through the VLE. The module will have regular synchronous sessions in active learning mode.
We are planning no changes to module content compared to previous years, and expect students to spend a similar amount of time-on-task compared to previous years. These changes will mainly constitute a rebalancing of hours from scheduled directed learning hours to unscheduled directed learning hours as students will have some flexibility as to when they access asynchronous materials.

### Teaching Schedule

 Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other TOTAL Study Hours 24 36 60 Timetable (if known) Private Study 90 TOTAL HOURS 150

### Assessment

EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
online time-controlled examination  2 hours    60
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Problems Classes Standard UoL penalty applies for late submission. This is not an anonymous assessment. Assessment Schedule (When) :2  10 x 2 hours    40