1. to PHY226 Mathematical Methods for Physics and Astronomy to PHY226 Mathematical Methods for Physics and Astronomy Phil Lightfoot, E47, (24533) p.k.lightfoot@shef.ac.uk Purpose of the course: To provide the further mathematical knowledge and skills needed to fully complete future physics courses

2. 2 nd 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 2 nd year – will give full information at 2pm in 2 nd Year Lab today

3. Assessment for PHY226 Final Course Grades based on: 70% Final Examination 10% 1 st assessed homework 10% 2 nd assessed homework 10% Marks from 2 problems classes You must hand work in by deadlines

4. Books and Course Pack Recommended Recommended Mary L. Boas ‘Mathematical Methods in the Physical Sciences’ (Wiley) Physical Sciences’ (Wiley) Erwin Kreyszig – ‘Advanced Engineering Mathematics’ (Academic Press) Mathematics’ (Academic Press) Course pack (£7 from physics office or just borrow one of three copies from me) three copies from me) Jordan & Smith ‘Mathematical Techniques’ Data Sheet – keep a copy at hand!

5. Phil’s Problems Your notes contain gaps for worked examples which we will fill in as we go through the course. With maths, more than any other module, the only way to understand it is to do it!!!! 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.

6. Outline Syllabus 1. Brief revision of basic algebra 2. Complex numbers 3. Ordinary differential equations (ODEs) 4. Fourier series 5. Fourier integrals 6. Convolution theorem 7. Intro to PDEs: Wave equation in 1D 8. Diffusion equation 9. PDEs in 3D 10. Spherical co-ordinates & harmonics

7. Lecture course Differential equationsFourier analysis OpticsQuantum mechanics Thermal physics

8. Lecture course 1 st order ordinary Differential equationsFourier analysis e.g. radio decay OpticsQuantum mechanics Thermal physics

9. Lecture course 1 st order ordinary Differential equationsFourier analysis 2 nd order ordinary e.g. radio decay e.g. LHO/SHM OpticsQuantum mechanics Thermal physics

10. Lecture course 1 st order ordinary Differential equationsFourier analysis 2 nd order ordinary 2 nd order ordinary damped e.g. radio decay e.g. LHO/SHM e.g. suspension OpticsQuantum mechanics Thermal physics

11. Lecture course 1 st order ordinary Differential equationsFourier analysis 2 nd order ordinary 2 nd order ordinary damped 2 nd order ordinary damped forced e.g. radio decay e.g. LHO/SHM e.g. suspension e.g. heated lattice OpticsQuantum mechanics Thermal physics

12. Lecture course 1 st order ordinary Differential equationsFourier analysis 2 nd order ordinary 2 nd order ordinary damped 2 nd order partial Cartesian 2 nd order ordinary damped forced e.g. radio decay e.g. LHO/SHM e.g. suspension e.g. sea waves e.g. heated lattice OpticsQuantum mechanics Thermal physics

13. Lecture course 2 nd order partial 3D Cart/Polar

14. Lecture course 1 st order ordinary Differential equationsFourier analysis 2 nd order ordinary 2 nd order ordinary damped 2 nd order partial Cartesian 2 nd order ordinary damped forced 2 nd order partial 3D Cart/Polar e.g. radio decay e.g. LHO/SHM e.g. suspension e.g. sea waves e.g. heated lattice e.g. sound waves OpticsQuantum mechanics Thermal physics

15. Lecture course 1 st order ordinary Differential equationsFourier analysis 2 nd order ordinary 2 nd order ordinary damped 2 nd order partial Cartesian 2 nd order ordinary damped forced 2 nd order partial 3D Cart/Polar e.g. radio decay e.g. LHO/SHM e.g. suspension e.g. sea waves e.g. heated lattice e.g. sound waves Fourier series Fourier Transforms OpticsQuantum mechanics Thermal physics

16. Lecture course 1 st order ordinary Differential equationsFourier analysis 2 nd order ordinary 2 nd order ordinary damped 2 nd order partial Cartesian 2 nd order ordinary damped forced 2 nd order partial 3D Cart/Polar e.g. radio decay e.g. LHO/SHM e.g. suspension e.g. sea waves e.g. heated lattice e.g. sound waves e.g. Wave equatione.g. Schrodingere.g. Diffusion equation Fourier series Fourier Transforms OpticsQuantum mechanics Thermal physics