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 Dr B Cheal
Physics
Bradley.Cheal@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2018-19 Level 4 FHEQ First Semester 15

Aims

To ensure all students possess a common level of knowledge and skills irrespective of background.

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
  • A good working knowledge of differential and integral calculus

    		•
  • Familiarity with some of the elementary functions common in applied mathematics and science 

    		•
    An introductory knowledge of functions of several variables
    Manipulation of complex numbers and use them to solve simple problems involving fractional powers
    An introductory knowledge of series
    A good rudimentary knowledge of simple problems involving statistics: binomial and Poisson distributions, mean, standard deviation, standard error of mean

    Syllabus
    1  Statistics
    Mean and standard deviation.
    Probability and probability density functions.
    Normal distribution, standard error, standard error on the mean, weighted mean.
    Binomial distribution.
    Poisson distribution.

    Vectors
    Simple vector equations in science.
    Scalar and vector products.
    Components of vectors.
    Differentiation of vectors.

    Differentiation
    First principles and a conceptual understanding.
    Stationary points, minima and maxima.
    Chain rule, product rule, quotient rule and combinations of these.
    Implicit differentiation.
    Logarithmic differentiation.
    Maclaurin series and Taylor series.

    Partial Differentiation 
    Extension of differentiation to functions of multiple independent variables.
    First order, second order and mixed partial derivatives.
    Minima, maxima and saddle points.
    Directional deri vatives.

    Integration
    As the area under a curve and as the reverse of differentiation.
    Integration by substitution.
    Integration by parts.
    Integration using partial fractions.

    Multidimensional Integration
    Extension to integration to functions of many variables.
    Non-constant limits of integration / integrating over non-rectangular regions.
    Average values of functions.

    Coor dinate Systems
    Polar coordinates for 2 dimensions.
    Cyclindrical polar coordinates.
    Spherical polar coordinates.
    Change of variables in multiple integrals.

    Complex Numbers
    Extending the number system to imaginary and complex numbers.
    Argand diagram, modulus, argument, complex conjugate.
    Polar form of complex numbers.
    de Moivre''s theorem.
    Expressing sine and cosine functions in exponential form.
    Using complex numbers to derive trigonometric identities.
    Finding the n nth roots of numbers.

    Teaching and Learning Strategies

    Lecture - Lecture

    = 11 x 3 lectures/week

    Workshops - = 11 x 3 hour workshop

    Teaching Schedule
      Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other TOTAL
    Study Hours 33
    Lecture
    		        33
    = 11 x 3 hour workshop
    		66
    Timetable (if known) = 11 x 3 lectures/week
          		           
    Private Study 84
    TOTAL HOURS 150

    Assessment
    EXAM Duration Timing
    (Semester)    		 % of
    final
    mark    		 Resit/resubmission
    opportunity    		 Penalty for late
    submission    		 Notes
    Unseen Written Exam  2 hours  1  70  Yes  Standard UoL penalty applies  Exam Notes (applying to all assessments) If any continuous assessment component is failed and a resit is required, the mark for the resit examination will subsume the marks for all the continuous assessment components.  
    CONTINUOUS Duration Timing
    (Semester)    		 % of
    final
    mark    		 Resit/resubmission
    opportunity    		 Penalty for late
    submission    		 Notes
    Coursework  Problem sheet comple  1  10  No reassessment opportunity  Standard UoL penalty applies  Problem sheet There is no reassessment opportunity, Subsumed by exam 
    Coursework  10 x 3 hours  1  20  No reassessment opportunity  Standard UoL penalty applies  Problem Classes There is no reassessment opportunity, Subsumed by resit exam 

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