Mathematical Analysis 2

• 26 hrs lectures
• 26 hrs exercises

• 100 pts final exam

The main goal of the course is to enhance the knowledge of calculus from the previous semester and explain the basic principles and methods of higher calculus. The emphasis is put on handling the practical use of these methods for solving specific problems and the ability to understand the basic problems of higher calculus and use derivatives, integrals and differential equations for solving specific problems.

• Mathematical Analysis 1 (IMA1)

• Discrete Mathematics (IDM)

The IMA1 course.

• Serge Lang, Calculus of Several Variables, 2012, Springer, ISBN-13: 978-14-612-7001-0
• Dineen, Sean (University College of Dublin, Irela), Functions of Two Variables 2 000, Taylor & Francis Inc,, ISBN/EAN 978-15-848-8190-2 / 978-15-848-8190-2

1. Number series.
2. Power series.
3. Fourier series.
4. Differential calculus of functions of several variables I: limit, continuity, partial derivatives, Schwarz theorem.
5. Differential calculus of functions of several variables II: differential, tangent plane, Taylor polynomial.
6. Differential calculus of functions of more variables III: local extrema, Hess matrix, Sylvester criterion.
7. Integral calculus of functions of several variables I (particularly in 2 and 3 dimensions): definitions and basic concepts.
8. Integral calculus of functions of several variables II: multidimensional and multiple integrals, Fubini theorem.
9. Integral calculus of functions of several variables III: evaluation and applications of double and triple integrals.
10. Introduction to differential equations. Initial problem. Existence and uniqueness of a solution. Separable and linear equations.
11. Numerical solution of differential equations of the first order.

Problems discussed at numerical classes are chosen so as to complement suitably the lectures.

Requirements for awarding credit:

Passing control tests and achieving at least 55% of points or completing a comprehensive written paper and achieving at least 55% of points.
Awarding credit is a necessary condition for taking the exam.

Exam requirements:

The exam is written.

For all tasks in the written part, a calculation must be written, or the procedure must be described, or the result must be justified verbally. The examples are divided into thematic groups. If the student does not achieve at least 50% of the total number of achievable points in each thematic group of examples, the written part and the entire exam are evaluated with a grade of "F" (unsatisfactory) and the student does not proceed to the oral part.

If the student does not achieve at least 50% of the total number of achievable points in the written paper, the written part and the entire exam are evaluated with a grade of "F" (unsatisfactory).

Completion of the course for students with individual study:
Passing the comprehensive control test and achieving at least 55% of points.
Awarding credit is a necessary condition for taking the exam.
The exam is written.
For all tasks in the written part, a calculation must be written, or the procedure described, or the result must be justified verbally. The examples are divided into thematic groups. If the student does not achieve at least 50% of the total number of achievable points in each thematic group of examples, the written part and the entire exam are graded "F" (unsatisfactory).
If the student does not achieve at least 50% of the total number of achievable points in the written work, the written part and the entire exam are graded "F".

Participation in seminars is checked.