Mathematical Analysis 1

• 26 hrs lectures
• 26 hrs exercises

• 80 pts final exam
• 20 pts numeric exercises

The main goal of the course is to explain the basic principles and methods of calculus. The emphasis ismput on handling the practical use of these methods for solving specific tasks and the ability to understand the basic problems of calculus and use derivatives and integrals for solving specific problems.

Fundamentals of calculus are a necessary part of a study at a technical university because virtually all technical and physical subjects employ the concepts of a derivative and integral.

• Discrete Mathematics (IDM)

Secondary school mathematics.

• 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.

1. The concept of a function of a real variable, properties of functions and basic operations with functions.
2. Elementary functions of a real variable.
3. Limit and continuity of a function. Limit of a sequence.
4. Derivative and a differential of a function.
5. Higher-order derivatives. Taylor polynomial. Extrema of a function.
6. Graph properties.
7. Indefinite integral, basic methods of integration.
8. Definite Riemann integral, its applications.
9. Improper integral.
10. Numerical integration.
11. Numerical solutions of equations.
12. Interpolation and approximation.

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

Written tests during the semester (maximum 20 points). Classes are compulsory. Presence at lectures will not be controlled, absence at numerical classes has to be excused.

The condition for receiving the credit is obtaining at least 8 points from the tests during the semester and active work at classes.