Mathematics III
prof. RNDr. Jan Slovák, DrSc.
Mathematics III
prof. RNDr. Jan Slovák, DrSc.
Mathematics III
Info
Course
Term
Spring 2025

This is the third continuation of the main Maths courses in the programme.

We shall shape the individual weeks together. The work will be based on individually solved tasks and discussions, covering the following schedule:  topology in the context of metric spaces (2 weeks); calculus in more variables (constraint extrema, integration, general Stokes theorem - 4 weeks); ordinary differential equations (intro to qualitative approach, geometry of ODEs - 3 weeks); elements of partial differential equations (elementary classical methods, Cauchy-Kowalevska, etc. - 2 weeks); comments towards variational calculus and complex analysis (1 week);
comments towards complex analysis (1 week).

Everything is covered in the text (Chapters 7-9) available at www.math.muni.cz/~slovak/BG.pdf.
1. Metrics - abstract concept, practical use
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Teacher recommends to study from 17/2/2025 to 23/2/2025.
2. Metrics - topology, general principles and results
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Teacher recommends to study from 24/2/2025 to 2/3/2025.
3. Differential Calculus as direct applications of linear algebra in geometric analysis
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Teacher recommends to study from 3/3/2025 to 9/3/2025.
4. Integral Calculus as direct applications of linear algebra in geometric analysis
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Teacher recommends to study from 10/3/2025 to 16/3/2025.
5. Vector fields and differential forms, implicit function theorem
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Teacher recommends to study from 17/3/2025 to 23/3/2025.
6. Integration revisited, Stokes theorem and classical vector calculus
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Teacher recommends to study from 24/3/2025 to 30/3/2025.
7. Ordinary differential equations, basic principles and numerical approach
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Teacher recommends to study from 31/3/2025 to 6/4/2025.
8. Ordinary differential equations as flows of vector fields, qualitative approach
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Teacher recommends to study from 7/4/2025 to 13/4/2025.
9. Ordinary differential equations in modelling
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Teacher recommends to study from 14/4/2025 to 20/4/2025.
10. Gentle introduction to general differential equations, integrability issue, first and second order equations
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Teacher recommends to study from 21/4/2025 to 27/4/2025.
11. Gentle survey of most important second order equations, Cauchy-Kowalevski approach
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Teacher recommends to study from 28/4/2025 to 4/5/2025.
12. Remarks on Variational Calculus, general concepts
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Teacher recommends to study from 5/5/2025 to 11/5/2025.
13. Remarks on Variational Calculus, gradient descent applications
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Teacher recommends to study from 12/5/2025 to 18/5/2025.
14. A few glimpses towards the concepts of holomorphy
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Teacher recommends to study from 19/5/2025 to 25/5/2025.
MUNI 3.2.1 DataAnalytics
Předmět vznikl za finanční podpory projektu Data Analytics NPO MUNI 3.2.1 DataAnalytics NPO_MUNI_MSMT-16606/2022

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