 Pravděpodobně máte vypnutý JavaScript. Některé funkce portálu nebudou funkční.
Course detail
Mathematics for Applications
Course unit code:  FSI9MPA  

Academic year:  2016/2017  
Year of study:  Not applicable.  
Semester:  summer  
Number of ECTS credits:  1  



























Type of course unit:
Lecture:  20 hours, optionally 

Teacher / Lecturer:  doc. Mgr. Jaroslav Hrdina, Ph.D. 
Syllabus:  (the choice will issue from specializations of of individual students) Differential and integral calculus of functions of one variable  Derivative, its geometrical and physical meaning  Investigation of a function  Taylor´s series  Primitive function  Evaluation of integrals by a substitution and by parts  Riemann´s definite integral  geometrical and physical meaning  Lebesgue´s integral  Delta function and theory of distributuions Differential and inegral calculus of functions of more variables  Partial derivatives  Total differential  applications in physics  Extremes and saddle points  Differential operators: gradient, divergence, curl, and Laplacian  applications in physics  Geometrical and physical meaning of double and triple integral  Transformation of coordinates  Jacobian  Line integral  independence of the path of integration  Surface integral  Green´s, Gauss´, and Stokes´ theorems  applications in physics Series  Numerical series  Functional series  Fourier series Analysis in complex domain  Holomorphic functions  Integral in complex domain, Cauchy´s theorem  Taylor´s and Laurent´s series, theory of residues  Hilbert transform Differential equations  Ordinary linear differential equations  Systems of ordinary linear differential equations with constant coefficients  Partial differential equations (Fourier method, method of characteristics) Algebra  Systems of linear equations  Matrices and determinants  Polynomials and solution of algebraic equations in complex domain  Groups Elements of functional analysis  Metric, vector, unitary, and Hilbert spaces  Spaces of functions  Orthogonal systems, orthogonal (Fourier) transform Elements of calculus of variations 