Mathematics I

Course guarantor:

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 n-th 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 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, Addison-Wesley, New York, Ontario, Sydney, 1994

Note:

Further information:

https://mat.nipax.cz/mati

No time-table has been prepared for this course

The course is a part of the following study plans:

• 10 62 67 00 BTZI 2012 P základ (compulsory course in the program)
• 11 68 73 00 BTZI 2012 K základ (compulsory course in the program)
• 02 26 31 34 BSTR EPT 2012 P základ (compulsory course in the program)
• 03 26 31 36 BSTR IAT 2012 P základ (compulsory course in the program)
• 04 26 31 38 BSTR KPP 2012 P základ (compulsory course in the program)
• 06 40 45 48 BSTR EPT 2012 K základ (compulsory course in the program)
• 07 40 45 50 BSTR IAT 2012 K základ (compulsory course in the program)
• 08 40 45 52 BSTR KPP 2012 K základ (compulsory course in the program)
• 05 40 45 46 BSTR TZP 2012 K základ (compulsory course in the program)
• 16 80 85 00 BVES TVA 2012 P základ (compulsory course in the program)
• 14 80 85 00 BVES MAT 2012 P základ (compulsory course in the program)
• 15 80 85 00 BVES OBR 2012 P základ (compulsory course in the program)
• 13 80 85 00 BVES EKO 2012 P základ (compulsory course in the program)
• 18 86 90 00 BVES MAT 2012 K základ (compulsory course in the program)
• 20 86 90 00 BVES TVA 2012 K základ (compulsory course in the program)
• 19 86 90 00 BVES OBR 2012 K základ (compulsory course in the program)
• 17 86 90 00 BVES EKO 2012 K základ (compulsory course in the program)
• 05 40 45 46 DSTR TZP 2012 K základ (compulsory course in the program)
• 06 40 45 48 DSTR EPT 2012 K základ (compulsory course in the program)
• 07 40 45 50 DSTR IAT 2012 K základ (compulsory course in the program)
• 08 40 45 52 DSTR KPP 2012 K základ (compulsory course in the program)
• 10 62 67 00 DTZI 2012 P základ (compulsory course in the program)
• 11 68 73 00 DTZI 2012 K základ (compulsory course in the program)
• 13 80 85 00 DVES 2012 P úvodní studijní plán (compulsory course in the program)
• 13 80 85 00 DVES EKO 2012 P (compulsory course in the program)
• 14 80 85 00 DVES MAT 2012 P (compulsory course in the program)
• 15 80 85 00 DVES OBR 2012 P (compulsory course in the program)
• 16 80 85 00 DVES TVA 2012 P (compulsory course in the program)
• 17 86 90 00 DVES 2012 K úvodní studijní plán (compulsory course in the program)
• Scénické technologie (compulsory course in the program)