| Course title | Mathematical Analysis 2 |
|---|---|
| Course code | KMA/PAN2 |
| Organizational form of instruction | Lecture + Lesson |
| Level of course | Bachelor |
| Year of study | not specified |
| Semester | Summer |
| Number of ECTS credits | 5 |
| Language of instruction | Czech |
| Status of course | Compulsory |
| Form of instruction | Face-to-face |
| Work placements | Course does not contain work placement |
| Recommended optional programme components | None |
| Course availability | The course is available to visiting students |
| Lecturer(s) |
|---|
|
| Course content |
|
Course Description The content of the course focuses on mastering transcendental functions in the real domain, the fundamentals of integral calculus for a function of one real variable, and the theory of numerical series in the real domain, including proofs of the most important properties. Transcendental Functions Definitions of trigonometric, inverse trigonometric (cyclometric), exponential, and logarithmic functions and their basic properties. Integral Calculus: Antiderivatives and Methods The concept of an antiderivative (primitive function) and its determination. Basic methods of calculating antiderivatives and their connection to differentiation. The integration by parts method and recurrence relations. The substitution method and its application. More complex examples utilizing both methods. Basic substitutions for conversion to the integration of a rational function. Integral Calculus: Newton and Riemann Integrals Definition of the Newton integral. Integration by parts and substitution applied to the Newton integral. Linearity of the integral and additivity with respect to the domain of integration. Uniform continuity. Definition of the Riemann integral and its fundamental properties. Linearity of the integral and additivity with respect to the domain of integration. Existence of the Riemann integral for continuous and monotonic functions. Differentiation with respect to the upper limit. Existence of an antiderivative for a continuous function. Theorem regarding the relationship between the Newton and Riemann integrals. Basic geometric applications of the Riemann integral: areas of plane regions. Length of a function's graph, length of a plane curve, volume of a solid of revolution, and the surface area of a surface of revolution. Series Series, basic concepts and definitions, along with convergence and divergence. Series with non-negative terms and convergence criteria. Geometric and harmonic series, and the integral test (criterion). Absolute and non-absolute (conditional) convergence of series. Leibniz's test (criterion) for alternating series. Convergence estimates and the calculation of Euler's number with a specified precision.
|
| Learning activities and teaching methods |
Monological explanation (lecture, presentation,briefing)
|
| Learning outcomes |
|
Elementary theory of the integral calculus of a real fuction of one real variable and a theory of number series and series of functions in the set of real numbers.
Integral calculus, series, transcendent functions of real variable. |
| Prerequisites |
|
Analytic thinking. AN1.
KMA/KAN1 ----- or ----- KMA/PAN1 |
| Assessment methods and criteria |
|
Oral exam, Written exam
Credit - see syllabus. |
| Recommended literature |
|
| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester |
|---|