to PHY226
Mathematical Methods for
Physics and Astronomy
Purpose of the course:
To provide the further mathematical
knowledge and skills needed to fully
complete future physics courses
Phil Lightfoot, E47, (24533) p.k.lightfoot@shef.ac.uk
2nd Year Structure Autumn Semester:
2 lectures per week in each of the following modules:
PHY202 - Quantum Mechanics
PHY203 - Thermal Physics
PHY225 - Programming in C
PHY226 - Mathematical Methods for Physics and Astronomy
PHY221 - Topics in Classical Physics
Lab on Mon and Fri 2-5pm (called PHY230 - Expt Physics I)
Problem classes (1 per wk on either Tues or Wed) marks taken
Tutorials (1 per wk) – you must attend but no marks taken
Vitaly Kudryavtsev – head of 2nd year – will give full information
at 2pm in 2nd Year Lab today
Assessment for PHY226
Final Course Grades based on:
70% Final Examination
10% 1st assessed homework
10% 2nd assessed homework
10% Marks from 2 problems classes
You must hand work in by deadlines
Books and Course Pack
Recommended
Mary L. Boas ‘Mathematical Methods in the
Physical Sciences’ (Wiley)
Erwin Kreyszig – ‘Advanced Engineering
Mathematics’ (Academic Press)
Course pack (£7 from physics office or just borrow one of
three copies from me)
Jordan & Smith ‘Mathematical Techniques’
Data Sheet – keep a copy at hand!
Phil’s Problems
With maths, more than any other module, the only way to
understand it is to do it!!!!
Your notes contain gaps for worked examples which we will fill
in as we go through the course.
I’ve put questions and model answers relevant to each lecture
at:- http://www.hep.shef.ac.uk/Phil/PHY226.htm
If you understand the lectures, and can do these questions, you
will do very well in the final examination.
Outline Syllabus
1.
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10.
Brief revision of basic algebra
Complex numbers
Ordinary differential equations (ODEs)
Fourier series
Fourier integrals
Convolution theorem
Intro to PDEs: Wave equation in 1D
Diffusion equation
PDEs in 3D
Spherical co-ordinates & harmonics
Lecture course
Differential equations
Quantum mechanics
Fourier analysis
Optics
Thermal physics
Lecture course
Differential equations
1st order ordinary
Quantum mechanics
Fourier analysis
e.g. radio decay
Optics
Thermal physics
Lecture course
Differential equations
Fourier analysis
1st order ordinary
e.g. radio decay
2nd order ordinary
e.g. LHO/SHM
Quantum mechanics
Optics
Thermal physics
Lecture course
Differential equations
Fourier analysis
1st order ordinary
e.g. radio decay
2nd order ordinary
e.g. LHO/SHM
2nd order ordinary damped
e.g. suspension
Quantum mechanics
Optics
Thermal physics
Lecture course
Differential equations
Fourier analysis
1st order ordinary
e.g. radio decay
2nd order ordinary
e.g. LHO/SHM
2nd order ordinary damped
e.g. suspension
2nd order ordinary damped forced e.g. heated lattice
Quantum mechanics
Optics
Thermal physics
Lecture course
Differential equations
Fourier analysis
1st order ordinary
e.g. radio decay
2nd order ordinary
e.g. LHO/SHM
2nd order ordinary damped
e.g. suspension
2nd order ordinary damped forced e.g. heated lattice
2nd order partial Cartesian
Quantum mechanics
e.g. sea waves
Optics
Thermal physics
Lecture course
2nd order partial 3D Cart/Polar
Lecture course
Differential equations
Fourier analysis
1st order ordinary
e.g. radio decay
2nd order ordinary
e.g. LHO/SHM
2nd order ordinary damped
e.g. suspension
2nd order ordinary damped forced e.g. heated lattice
2nd order partial Cartesian
e.g. sea waves
2nd order partial 3D Cart/Polar
e.g. sound waves
Quantum mechanics
Optics
Thermal physics
Lecture course
Differential equations
Fourier analysis
1st order ordinary
e.g. radio decay
2nd order ordinary
e.g. LHO/SHM
2nd order ordinary damped
e.g. suspension
Fourier series
Fourier Transforms
2nd order ordinary damped forced e.g. heated lattice
2nd order partial Cartesian
e.g. sea waves
2nd order partial 3D Cart/Polar
e.g. sound waves
Quantum mechanics
Optics
Thermal physics
Lecture course
Differential equations
Fourier analysis
1st order ordinary
e.g. radio decay
2nd order ordinary
e.g. LHO/SHM
2nd order ordinary damped
e.g. suspension
Fourier series
Fourier Transforms
2nd order ordinary damped forced e.g. heated lattice
2nd order partial Cartesian
e.g. sea waves
2nd order partial 3D Cart/Polar
e.g. sound waves
e.g. Schrodinger
Quantum mechanics
e.g. Wave equation
Optics
e.g. Diffusion equation
Thermal physics