Applied Mathematics II - NCHF072
Title: Aplikovaná matematika II
Guaranteed by: Department of Condensed Matter Physics (32-KFKL)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:3/3, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: RNDr. Artem Ryabov, Ph.D.
doc. RNDr. Viktor Holubec, Ph.D.
Teacher(s): doc. RNDr. Viktor Holubec, Ph.D.
doc. RNDr. Ivo Křivka, CSc.
RNDr. Artem Ryabov, Ph.D.
doc. RNDr. Pavel Solař, Ph.D.
RNDr. Julie Šťastná, Ph.D.
In complex pre-requisite: MC260P01C, MC260P01M, MC260P02C
Is complex co-requisite for: MC260P112, MC260P28
Opinion survey results   Examination dates   Noticeboard   
Annotation -
The second semester of the four-semester course on Applied Mathematics. Basics of linear algebra and matrix calculus. Differential and integral calculus of functions of several variables. Ordinary differential equations.
Last update: Houfek Karel, doc. RNDr., Ph.D. (02.05.2023)
Course completion requirements -

The course credit is awarded at practicals after passing three brief (60 min.) tests. The test on topic 1) from the Syllabus will be written during practicals on 18.3.2025; the test on topic 2) at practicals on 22.4.2025, and the third test [topics 3) and 4)] will be written on 20.5.2025. Passing each test means gaining at least 50% of points from it.

After getting the course credit at practicals, students can attend final exams. These exams consist of written and oral parts and they take place during the examination period. The written part (60 min.) comprises solving 2 practical examples from topics 1)-4). The oral part (60 min.) is a discussion of theoretical concepts (definitions and theorems from lectures) related to the examples in the written part.

Last update: Ryabov Artem, RNDr., Ph.D. (18.02.2025)
Literature -
  • Lecture notes and materials for practicals.

  • G. Strang, Introduction to Linear Algebra, Fifth Edition (2016).

  • J. Callahan, K. Hoffman, D. Cox, D. O’Shea, H. Pollatsek, L. Senechal: Calculus in Context, Five Colleges, Inc., 2008.

  • The most suitable literature for preparing yourself efficiently for exams and tests are notes taken at lectures and practicals. In addition, there exists a course page on Moodle:

https://dl1.cuni.cz/course/view.php?id=16205

Here, after logging in with your SIS/CAS credentials, you can read/download supporting study materials: PDF documents with lecture notes and examples from practicals. The documents will be regularly updated during the semester.

Last update: Ryabov Artem, RNDr., Ph.D. (28.02.2024)
Requirements to the exam -

The requirements for the exam correspond to the course syllabus to the extent that was given in the lectures and exercises.

Last update: Houfek Karel, doc. RNDr., Ph.D. (02.05.2023)
Syllabus -

The course covers four topics:

1) Linear algebra: Linear vector spaces. Matrices and determinants, systems of linear equations, Gaussian elimination. Bilinear and quadratic forms, positive and negative definiteness.

2) Basic theory of functions of several variables: metric, limits, continuity. Partial derivatives and total differential, operators grad, div, rot. Multidimensional integral. Exchange of limits and integrals, derivatives and integrals.

3) Series: Number series, convergence and divergence, absolute and non-absolute convergence, Taylor series.

4) Ordinary differential equations and their systems: basic methods, Bernoulli and Euler equations, equations in the form of total differential, solving equations using series.

Last update: Ryabov Artem, RNDr., Ph.D. (28.02.2024)