Physics with Mathematics, Part I 1100-1BB01

The aim of the lecture, together with exercises and demonstrations (II semester), is to present concepts and theorems of classical and quantum mechanics. Parallel to physics, all necessary tools of mathematics will be provided.

Programme:
Mathematics: mathematical analysis (calculus) and elements of linear algebra.
a. linear vector space, basis and dimension, scalar product, metric space, coordination systems
b. functions and their graphs, coordination systems , sequences and their limits, limit of a function, continuity
c. first and second derivatives, their graphical interpretations, differentiation of a function, finding minima and maxima
d. functions of many variables, partial derivatives, finding minima and maxima
e. scalar and vector fields
f. antiderivative, definite and indefinite integrals, double and triple integrals, line and surface integrals
h. complex numbers and functions
i. linear operators, eigenvalues and eigenfunctions
Physics:
a. Description of location and path of material points
b. Newtonian law of dynamics, inertial frames
c. Conservation laws: mechanical energy, momentum and angular momentum, conservation and central forces, potential forces and potential energy, work
d. Noninertial frames:
e. Elements of dynamics of rigid body
f. Fundamentals of quantum mechanics
Quantum descriptions: free particle, particle in a box, particle and a barrier, harmonic oscillator, rigid rotator, hydrogen atom

Written by Maciej Geller, June 2009