Physics with Mathematics II, lecture 1100-1BB21w
The course is focused on presentation of basic notions and statements of classical (and in limited extent quantum) physics related to matter and its molecular nature. We will consider electric and magnetic properties of matter, properties of electromagnetic radiation and electromagnetic interactions, thermodynamic and statistical description of matter and processes occuring in material media. Simultaneously we will discuss mathematical tools used in solving practical problems encountered in these areas of physics.
Program:
1. Sequences and series of functions (criteria of convergence, differentiation and integration of function series, Taylor series).
2. Complex numbers (functions of complex variables, elementary complex analysis, Euler equation, representation of elementary functions).
3. Systems of linear equations and linear transformations, (matrices, permutations, determinants, matrix representation of linear transformation, inversion of matrices, vector space of functions, functions as vectors, change of base, Hermit matrices, eigenvalue, eigenvector, eigenfunction, tensor of moments of inertia).
4. Ordinary and partial differential equations, linear differential equations, systems of differential equations.
5. Calculus of probability (basic notions, conditional probability).
6. Electricity and magnetism (electrostatic field, Coulomb law, Gauss law, Poisson and Laplace equations, electric fields in matter, electric currents, magnetic fields, Lorentz force, Ampere law, Biot-Savart law, magnetic fields in matter, electromagnetic induction, Faraday laws, Maxwell equations).
7. Wave Motion (wave equation, free and dumped oscilations, reflection and diffraction of Waves)..
8. Electromagnetic radiation (relflection and diffraction, interferention, interactions with matter, geometric and wave optics).
9. Elements of thermodynamics and statistical physics (thermodynamic description of macroscopic matter, thermodynamic equilibrium, relaxation processes, thermodynamic potentials, statistical ensembles, partition functions and their relations to thermodynamic potentials).
Description by Jan Antosiewicz, November 2010.
Required acctivity of students:
Lectures 4 h a week = 60 h
Self studiec on the Lectures 4 h a week = 60 h
Preparation for exam: 30 h
Together 150 h
Mode
Prerequisites (description)
Learning outcomes
Knowledge:
1. basic calculus and linear algebra
2. basic electricity and magnetism
3. thermodynamic description of matter and statistical origins of thermodynamic properties of matter.
Skills:
1. Application of Taylor series and Euler equation
2. Application of linear equations in physical problems
3. Finding electric and magnetic fields from different sources
4. Analysis of thermodynamic properties of physical systems
Assessment criteria
Final exam consists of solution of 3 problems in mathematics and 3 problems in physics and complection of a test composed of 10 closed questions. Admission for exam requires succesfull completion of classes accompanying the lecture.
Admission for the Lecture requires passing the first part of the Lecture presented during winter semester. The Lecture requires regular and intensiv self work of students during whole semester.
Practical placement
none
Bibliography
1. E. Shilov, Elementary real and complex analysis, Dover Publications Inc., New York.
2. J. W. Dettman, Introduction to linear algebra and differential equations, Dover Publications Inc., New York.
3. M. Tenenbaum, H. Pollard, Ordinary differential equations, Dover Publications Inc., New York.
4. G. E. Hay, Vector and tensor analysis, Dover Publications Inc., New York.
5. D. Halliday, R. Resnick, J. Walker, Fundamentals of Physics (vol. 1-5), Wiley
6. F. Bueche, E. Hecht, Schaum's outline of college physics, Dover Publications Inc., New York.
7. A. Halpern, 3000 Solved problems in physics, Dover Publications Inc., New York.
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: