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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
Teaching methods:	full-time

Guarantor:	RNDr. Artem Ryabov, Ph.D. RNDr. Viktor Holubec, Ph.D.
In complex pre-requisite:	MC260P01M, MZ370P19
Is complex co-requisite for:	MC260P112, MC260P28

Opinion survey results Examination dates SS schedule Noticeboard

Annotation -

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

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.

Course completion requirements -

Last update: RNDr. Artem Ryabov, Ph.D. (27.02.2024)

The course credit (Z) 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 13.3.2024; the test on topic 2) at practicals on 24.4.2024, and the test on topic 4) will be written within the first week of the examination period. Passing each test means gaining at least 50% of points from it.

After getting the course credit at practicals, students can attend the 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.

Literature -

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

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.

Requirements to the exam -

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

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

Syllabus -

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

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.