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 W Maciejewski
Physics
W.Maciejewski@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2024-25 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) Knowledge of a range of mathematical techniques necessary for physics and astrophysics programmes

(LO2) 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

(S3) Collaborative learning

Syllabus
 

Review of Integral vector calculus and introduction of differential vector calculus: Scalar and vector fields, Scalar and vector field functions, Polar coordinate systems, Derivation of the gradient, divergence and curl functions, Vector operations in polar coordinate systems, Stoke’s theorem with examples Gauss’ theorem with examples. Vectors and Matrices: Real and complex vectors, linear independence, basis, scalar product, orthonormal basis. Review of matrices, Laplace expansion theorem. Row echelon form of a matrix. Rank of a matrix. Application to vectors (coplanarity, collinearity). Gaussian elimination. Complex and degenerate eigenvalues. Real symmetric matrices and diagonalisation. Orthogonal transformations and orthogonal matrices. Applications: rotational motion, inertia tensor.

Teaching and Learning Strategies

Teaching Method 1 –Lectures delivered. Description: Lecture to entire cohort on all course topics on campus. Attendance Recorded: Yes. Teaching

Method 2 -Workshops delivered in person on campus. 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,in person, closed book examination.  150    80       
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Problem sheets 1-5  0    10       
Problem sheets 6-10  0    10       

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