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 I
Code PHYS107
Coordinator Professor B Cheal
Physics
Bradley.Cheal@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2024-25 Level 4 FHEQ First Semester 15

Aims

To provide a foundation for the mathematics required by physical scientists. To assist students in acquiring the skills necessary to use the mathematics developed in the module.

Learning Outcomes

(LO1) A good working knowledge of differential and integral calculus

(LO2) Familiarity with some of the elementary functions common in applied mathematics and science

(LO3) An introductory knowledge of functions of several variables

(LO4) Manipulation of complex numbers and use them to solve simple problems involving fractional powers

(LO5) An introductory knowledge of series

(LO6) Ability to manipulate matrices with confidence and use matrix methods to solve simultaneous linear equations.

(LO7) Basic familiarity with the gradient vector operator.

(S1) Problem solving skills

(S2) Collaborative Learning

Syllabus
 

Vectors
Scalar and vector products. Simple vector equations. Applications of vectors to solving physics problems.

Matrices
Addition, multiplication, determinant, inverse, solution of systems of linear equations, eigenvalues, and eigenvectors

Single variable differentiation
From first principles. Product, chain and quotient rules. Application to physical systems.

Introduction to Series. Arithmetic Series, Geometric Series. Taylor and Maclaurin Series.

Partial Differentiation.
Minima, maxima. Grad operator, directional derivative.

Integration.
Integration by substitution. Trigonometric integration. Integration by parts. Integration by partial fractions. Volumes of a revolution.

Multi-dimensional integration.
Integrating scalar functions of two or three variables.

Polar coordinate systems.
Spherical polar coordinates. Cylindrical polar coordinates. Multivariable integration of scalar functions expressed in these coordinates.

Complex Numbers.
Basic manipulation. Polar and exponential forms. Applications.

Teaching and Learning Strategies

Teaching Method 1 - Lectures
Description: 3 x 1 hour Lecture to entire cohort on all course topics incorporating active learning sessions

Teaching Method 2 - Workshops
Description: = 12 x 3 hour workshop
In each workshop, students complete a problem sheet, supported by staff and peers.

Teaching Schedule
  Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other TOTAL
Study Hours 33

         36

 69
Timetable (if known)              
Private Study 81
TOTAL HOURS 150

Assessment
EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Examination  150    80       
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Coursework First 5 problem sets  2    10       
Coursework - Second 5 problem sets  2    10       

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