Course details

# Mathematical Analysis 2

IMA2 Acad. year 2022/2023 Winter semester 4 credits

Series. The limit, continuity, partial derivatives and extrema of a function of several variables. Double and triple integrals. Differential equations. Analytical and numerical solutions of the initial problem.

Guarantor

Course coordinator

Language of instruction

Czech, English

Completion

Credit+Examination (written)

Time span

• 26 hrs lectures
• 26 hrs exercises

Assessment points

• 80 pts final exam
• 20 pts numeric exercises

Department

Lecturer

Instructor

Subject specific learning outcomes and competences

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

Learning objectives

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.

Why is the course taught

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.

Recommended prerequisites

Prerequisite knowledge and skills

The IMA1 course.

Study literature

• 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.

Syllabus of lectures

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.

Syllabus of numerical exercises

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

Progress assessment

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

Controlled instruction

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

Exam prerequisites

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

Course inclusion in study plans

• Programme BIT, 2nd year of study, Compulsory
• Programme BIT (in English), 2nd year of study, Compulsory
• Programme IT-BC-3, field BIT, 2nd year of study, Compulsory