Mathematics I.
Code  Completion  Credits  Range  Language 

2011091  Z,ZK  7  4P+4C+0L  Czech 
 Garant předmětu:
 Lecturer:
 Tutor:
 Supervisor:
 Department of Technical Mathematics
 Synopsis:

In the course, greater emphasis is placed on the theoretical basis of the concepts discussed and on the derivation of basic relationships and connections between concepts. Students will also get to know the procedures for solving problems with parametric input. In addition, students will gain extended knowledge in some thematic areas: eigennumbers and eigenvectors of a matrix, Taylor polynomial, integral as a limit function, integration of some special functions.
 Requirements:

Knowledge of high school mathematics in the range of a real gymnasium.
 Syllabus of lectures:

1. Basics of linear algebra – vectors, vector spaces, linear independence of vectors, dimensions, bases.
2. Matrix, operation, rank. Determinant. Regular and singular matrices, inverse matrices.
3. Systems of linear equations, Frobenian theorem, Gaussian elimination method.
4. Eigennumbers and eigenvectors of a matrix.
5. Differential calculus of real functions of one variable. Sequence, monotony, limit.
6. Limit and continuity of a function. Derivation, geometric and physical meaning.
7. Monotonicity of a function, local and absolute extrema, convexity, inflection point. Asymptotes, graph of the function.
8. Taylor polynomial, remainder after nth power. Approximate solution of the equation f(x)=0.
9. Integral calculus of real functions of one variable – indefinite integral, integration by parts, integration by substitution.
10. Definite integral, its calculation.
11. Application of a definite integral: surface area, volume of a rotating body, length of a curve, application in mechanics.
12. Numerical calculation of the integral.
13. Improper integral.
 Syllabus of tutorials:

The same as in lectures.
 Study Objective:

Gain an understanding of basic mathematical concepts and methods and be able to apply them in other engineering subjects.
 Study materials:

Neustupa, J.: Mathematics I, CTU Publishing House, Prague, 1996,
Finney, R. L., Thomas, G.B.: Calculus, AddisonWesley, New York, Ontario, Sydney, 1994
 Note:
 Further information:
 https://mat.nipax.cz/mati
 No timetable has been prepared for this course
 The course is a part of the following study plans: