Course: Mathematical Analysis 2

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Course title Mathematical Analysis 2
Course code KMA/MAF2
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study not specified
Semester Summer
Number of ECTS credits 7
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
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 non-negative numbers. 2. Absolute and non-absolute 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.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Nanotechnology (1) Special and interdisciplinary fields 1 Summer
Faculty of Science General Physics and Mathematical Physics (1) Physics courses 1 Summer
Faculty of Science Optics and Optoelectronics (1) Physics courses 1 Summer
Faculty of Science Biophysics (2015) Physics courses 1 Summer
Faculty of Science Computer Physics (1) Physics courses 1 Summer
Faculty of Science Molecular Biophysics (2015) Physics courses 1 Summer
Faculty of Science Applied Physics (1) Physics courses 1 Summer