Limit, continuity, partial derivatives and differentiability of functions of multiple variables. Equation of the tangent plane. Local extrema of functions of two variables. Gradient and directional derivative. Divergence, rotation. Double and triple integrals and their applications. Polar coordinates. Substitution theorem for double integrals. Curves in the 3D space, tangent line, arc length. Line integral. 3D surfaces. Separable differential equations, first order linear differential equations. Algebraic form of complex numbers. Second order linear differential equations with constant coefficients. Taylor polynomial of exp(x), sin(x), cos(x). Eigenvalues and eigenvectors of matrices.

Differential calculus of functions of several variables: partial derivatives, differentiability, tangent plane. Derivatives of composite functions. Local and global maxima / minima. Inverse function, implicit function. Double and triple integrals. (5 weeks)
Numerical series, power series, Taylor series. (2 weeks)
Laplace and Fourier transform. (1 week)
Linear algebra. Vectors, applications in geometry. Systems oflinear equations. (3 weeks).
Differential equations (separable differential equations, first order linear differential equations, second order linear differential equations with constant coefficients). (3 weeks)

Solving systems of linear equations:elementary row operations, Gauss-Jordan- and Gaussian elimination. Homogeneous systems of linear equations. Arithmetic and rank of matrices. Determinant:geometric interpretation, expansion of determinants. Cramer's rule, interpolation, Vandermonde determinant. Linear space,subspace, generating system, basis, orthogonal and orthonormal basis. Linear maps, linear transformations and their matrices. Kernel, image, dimension theorem. Linear transformationsand systems of linear equations. Eigenvalues, eigenvectors, similarity, diagonalizability. Infinite series:convergence, divergence, absolute convergence. Sewuences and series of functions, convergence criteria, power series, Taylor series. Fourier series:axpansion, odd and even functions. Functions in several variables:continuity, differential and integral calculus, partial derivatives, Young's theorem. Local and global maxima / minima. Vector-vector functions, their derivatives, Jacobi matrix. Integrals: area and volume integrals.

Physical fundamentals of generating ionizing radiations: radioactivity, radioactive decay, operation of equipment for generating ionizing radiations. Definition of doses. Biological effects of ionizing radiations: deterministic and stochastic effects, somatic and genetic effects. Control of applications of ionizing radiations in connection with the explanation of generic principles of radiation  protection (justification, optimization, and individual limitations). Procedures and conditions of generating ionizing radiations: external and internal exposure situations, natural and artificial radioactivity. Practical implementation of radiation protection: workplace and environmental radiation protection, monitoring, management and disposal of radioactive wastes, applications of radiation shielding. management of nuclear and radiological emergencies. 
H. Cember, T.E. Johnson: Introduction to Health Physics 

Differential equations: Separable d.e., first order linear d.e., higher order linear d.e. of constant coefficients. Series: Tests for convergence of numerical series, power series, Taylor series.
Functions of several variables: Limits, continuity. Differentiability, directional derivatives, chain rule. Higher partial derivatives and higher differentials. Extreme value problems. Calculation of double and triple integrals. Transformations of integrals, Jacobi matrix.
Analysis of complex functions: Continuity, regularity, Cauchy - Riemann partial differential equations. Elementary functions of complex variable, computation of their values. Complex contour integral. Cauchy - Goursat basic theorem of integrals and its consequences. Integral representation of regular functions and their higher derivatives (Cauchy integral formulae).