### 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 2021-22 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) A good rudimentary knowledge of simple problems involving statistics: binomial and Poisson distributions, mean, standard deviation, standard error of mean

(S1) Problem solving skills

### Syllabus

Introduction to statistics. Binomial and Poisson distributions, mean, standard deviation, standard error on mean, chi-squared, application to experimental analysis.

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

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. Applications of partial differentiation to finding solutions to physics problems.

Definite integrals. Volumes of rotation. Integration. Integration by substitution. Trigonometric integration. Integration by parts. Integration by partial fractions.

Multi-dimensional integration.

Polar coordinate systems. Spherical polar coordinates. Cylindrical polar coordinates. Using polar coordinates to find simple solutions to physical problems.

Complex Numbers

### Teaching and Learning Strategies

Teaching Method 1 - Lectures delivered online
Description: Lecture to entire cohort on all course topics incorporating active learning sessions

Teaching Method 2 - Workshops
Description: = 12 x 2 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 36 24 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
Examination  150 minutes    70
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Coursework - 5 problem sets  5 x2 hours (10 hours    15
Coursework 5 problem sets  5x 2hours (10 hours     15

### Recommended Texts

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