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 III
Code PHYS207
Coordinator Dr J Alaria
Physics
Jonathan.Alaria@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2021-22 Level 5 FHEQ First Semester 15

Aims

To re-inforce students' prior knowledge of mathematical techniques To introduce new mathematical techniques for physics modules To enhance students' problem-solving abilities through structured application of these techniques in physics


Learning Outcomes

(LO1) At the end of the module the student should be able to: Have knowledge of a range of mathematical techniques necessary for physics and astrophysics programmes Be able to apply these mathematical techniques in a range of physics and astrophysics programmes

(S1) Numeracy/computational skills - Reason with numbers/mathematical concepts

(S2) Numeracy/computational skills - Problem solving


Syllabus

 

Overview Integral and differential vector calculus: Scalar and vector fields Scalar and vector field functions Polar coordinate systems Derivation of the gradient, divergence and curl functions Examples of these operations including their physical significance Vector operations in polar coordinate systems Stoke’s theorem with examples Gauss’ theorem with examples Line, surface and volume elements in circular, spherical and cylindrical polar coordinates Line, surface and volume integrals in different coordinate systems - applications  Vectors and Matrices Real and complex vectors, linear independence, basis, scalar product, orthonormal basis. Revision of matrices. Sum, product, transposition. Symmetric and antisymmetric matrices.  Trace and determinant of square matrices. Laplace expansion theorem. Row echelon form of a matrix. Rank of a matrix. Application to vectors (coplanarity, collinearity). Systems of linear equations, Gaussian elimination. Inversion o f matrices using row operations. E igenvalues and eigenvectors of matrices. Complex and degenerate eigenvalues. Real symmetric matrices and diagonalisation. Orthogonal transformations and orthogonal matrices. Applications: rotational motion, inertia tensor. Applications Application: rotational motion, inertia tensor Hermitian scalar product of complex vectors. Hermitian matrices and diagonalization. Unitary transformations and unitary matrices. Application: quantum mechanics. Revision of Taylor's theorem, Taylor's theorem with remainder. Revision of infinite sums and series. Ratio test. Radius of convergences of power series. Revision of Taylor series. Generating Taylor series from known Taylor series by substitution and differentiation.


Teaching and Learning Strategies

Teaching Method 1 – Lectures delivered online.
Description: Lecture to entire cohort on all course topics over VLE.
Attendance Recorded: No
Notes: = Nominal 2 x 1-hour lectures/week.

Teaching Method 2 - Workshops delivered online.
Description: Weekly problem-solving classes to learn together with guidance from staff and receive feedback.
Attendance Recorded: Yes
Notes: = 12 x 1-hour workshops.


Teaching Schedule

  Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other TOTAL
Study Hours 24

        12

36
Timetable (if known)              
Private Study 114
TOTAL HOURS 150

Assessment

EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Timed, online, open book examination  2 hours    60       
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
problem set submitted online  2 hours    20       
problem set submitted online  2 hours    20       

Recommended Texts

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