Lecturer(s)


Burkotová Jana, Mgr. Ph.D.

Fürst Tomáš, RNDr. Ph.D.

Tomeček Jan, doc. RNDr. Ph.D.

Kouřilová Pavla, Mgr. Ph.D.

Course content

A. Differential Equations. 1. An invitation to differential equations: Decay of radioactive material, population models. 2. A detour: Spaces of infinite dimension, Hilbert and Banach spaces, fixed point theorems. 3. Existence and uniqueness of the solution to an ordinary differential equation. 4. Separable equations and other solution techniques. 5. A revision of linear algebra, linear differential equations. 6. Linear differential equations of higher order, solution techniques. 7. Application: Damped and forced oscillations. B: Functions of several variables. 1. The notion of functions of several variables, continuity and limits. 2. A second visit to spaces of higher dimension. 3. Differentiation. 4. Taylor polynomial. 5. Potential, vector fields, gradient, divergence, curl and application. 6. Implicit functions. 7. Minima and maxima of functions of several variables: Lagrange multipliers. C: Bonus. How differential equations relate to extrema of functions of several variables. An introduction to the calculus of variations. D: Series. 1. Series of nonnegative numbers. 2. Absolute and nonabsolute convergence. 3. Function series: Fourier analysis.

Learning activities and teaching methods

Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
 Attendace
 78 hours per semester
 Preparation for the Course Credit
 40 hours per semester
 Homework for Teaching
 30 hours per semester
 Preparation for the Exam
 60 hours per semester

Learning outcomes

Understand differential equations and differential calculus of functions of several variables
Comprehension Understand basic ODEs and differential calculus of functions of several variables.

Prerequisites

Differential calculus of functions of a single variable.
KMA/MAF1

Assessment methods and criteria

Oral exam, Written exam
Credit: the student has to pass two written tests (i.e. to obtain at least half of the possible points in each test).

Recommended literature


J. Kopáček. (2001). Matematická analýza pro fyziky II. Matfyzpress.

J. Veselý. (2001). Matematická analýza pro učitele II. Matfyzpress.
