Mathematical Analysis 2

• 26 hrs lectures
• 26 hrs exercises

• 80 pts final exam
• 20 pts numeric exercises

The ability to understand the basic problems of higher calculus and use derivatives, integrals and differential equations for solving specific problems.

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.

The IMA2 course follows on the IMA1 course and complements the necessary knowledge of the concepts of calculus needed to understand and master advanced technical and physical subjects.

• Mathematical Analysis 1 (IMA1)

• Discrete Mathematics (IDM)

The IMA1 course.

• Fong, Y., Wang, Y., Calculus, Springer, 2000.
• Ross, K. A., Elementary analysis: The Theory of Calculus, Springer, 2000.
• Small, D. B., Hosack, J. M., Calculus (An Integrated Approach), McGraw-Hill Publ. Comp., 1990.
• Thomas, G. B., Finney, R. L., Calculus and Analytic Geometry, Addison-Wesley Publ. Comp., 1994.
• Zill, D. G., A First Course in Differential Equations, PWS-Kent Publ. Comp., 1992.

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.

Written tests during semester (five 4-point tests).

Classes are compulsory (presence at lectures, however, will not be controlled), absence at numerical classes has to be excused.

The condition for receiving the credit is obtaining at least 8 of points from the tests during the semester.