Physics with Mathematics II, classes

Classes directed to students of the Faculty of Physics enrolled to the programme "Applications of Physics in Biology and Medicine: Molecular Biophysics and Molecular Design and Bioinformatics".

Classroom

Classes accompanying the lecture "Physics with mathematics II", focused practical methods of solving simple problems in linear algebra, complex analysis, differential equations, thermodynamics and statistical physics.

The classes are devoted to solving problems related to subjects considered on the accompanying lectures.

Program:

1. Analysis of convergence of sequences and series of functions, determination of limiting functions or sums of series, development into Taylor series, computation of aproximate values of functions;

2. Algebraic and exponential forms of complex numbers, geometric interpretation of expressions involving complex numbers, derivation of trigonometric identities, complex solution of algebraic equations;

3. Solutions of systems of linear equations, matrix operations, determination of matrix representation of linear operations, determination of eigen values and vectors of matricesp;

4. Classification of differential equations, solutions of differential equations of order one and two, writting differential equations for physical problems;

5. Determination of equilibrium states of composed systems after realising internal constraints, determination for work and heat effects in different processes, determination of state equations from fundamental relation, determination of thermodynamic parameters from the partition function.

Description by Jan Antosiewicz, November 2010.

Required acctivity of students:

Classes 6 h a week = 90 h

Self studiec on problems considered during classes 4 h a week = 60 h

Preparation for tests: 60 h

Together 210 h

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.

Knowledge:

1. elementary methods of solving problems from calculus and linear algebra

2. elementary methods of solving problems from thermodynamics and statistical physics

Skills:

1. using Taylor series and Euler eguation, solving systems of linear algebraic equations,

2. solving selected types of differential equations of first and second order

3. finding equilibrium state of composed system, determination of thermodynamic effects of processes, determination of thermodynamic parameters based on statistical considerations

There are four written tests composed of solution of 4 problems each. Total number point for the tests is 72.

Admission for the Classes requires passing the first part of the Lecture and Classes presented during winter semester. The Classes require regular and intensiv self work of students during whole semester. Each participation of a student in solution of given problem at the blackboard in noted by the assistant. This activity can bing up to 10% of the points possible to achieve for the tests. Succesful completion of the Classes requires passing two out of four tests.

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