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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) [email protected] 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. 2. 3. 4. 5. 6. 7. 8. 9. 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