Applied Mathematics
Code  Completion  Credits  Range  Language 

101APM  Z,ZK  3  1P+1C  Czech 
 Course guarantor:
 Petr Kučera, Zdeněk Skalák
 Lecturer:
 Petr Kučera
 Tutor:
 Petr Mayer
 Supervisor:
 Department of Mathematics
 Synopsis:

basic concepts of differential and integral calculus of functions of one and more real variables, basic concepts from linear algebra, solutions of systems of liner algebraic equations, boundary problems for ordinary and partial differential equations (ODE,PDE), concept of classical solution, weak formulations of boundary problems, weak solutions, LaxMilgram lemma, existence of weak solution, boundary problems for linear ODE of second order with mixed boundary conditions, relation between classial and weak solution, regularity of weak solutions, finite difference method, finite element method for solutions of boundary problems, solution of Laplace's and Poisson's equations by finite difference method, solution of heat equation by finite difference method, onedimensional case, solution of heat equation by finite difference method, twodimensional case, solution of heat equation by finite element method, onedimensional case.
 Requirements:
 Syllabus of lectures:

1) Repetition: differentiation and integration of functions of one real variable, functions of more variables, partial derivatives, multiple integrals.
2) Repetition: basic concepts from linear algebra, solutions of systems of liner algebraic equations.
3) ordinary differential equations (ODE), classical solution, examples.
4) boundary problems for ODE of second order with mixed boundary conditions, discussion of solvability.
5) weak formulation of boundary problems, weak solution, LaxMilgram lemma, existence of weak solution.
6) relation between classical and weak solution, regularity of weak solutions.
7) finite difference method for solutions of boundary problems.
8) finite element method for solutions of boundary problems.
9) partial differential equations (PDE), classical solutions, examples.
10) boundary problems for PDE solution of Laplace's and Poisson's equations by finite difference method.
11) solution of heat equation by finite difference method, onedimensional case.
12) solution of heat equation by finite difference method, twodimensional case.
13) solution of heat equation by finite element method, onedimensional case.
 Syllabus of tutorials:

corresponds with syllabus of lectures
 Study Objective:
 Study materials:

TBA
 Note:
 Further information:
 https://mat.fsv.cvut.cz/vyuka/magistri/zs/apm
 Timetable for winter semester 2024/2025:

06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon Tue Wed Thu Fri  Timetable for summer semester 2024/2025:
 Timetable is not available yet
 The course is a part of the following study plans:

 Budovy a prostředí, specializace Technická zařízení budov (compulsory course)
 Budovy a prostředí, specializace Stavební fyzika (compulsory course)