SylabUZ
| Course name | Mathematical analysis II |
| Course ID | 11.1-WF-FizP-MA-II-S17 |
| Faculty | Faculty of Physics and Astronomy |
| Field of study | Physics |
| Education profile | academic |
| Level of studies | First-cycle studies leading to Bachelor's degree |
| Beginning semester | winter term 2020/2021 |
| Semester | 2 |
| ECTS credits to win | 5 |
| Course type | obligatory |
| Teaching language | english |
| Author of syllabus |
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| The class form | Hours per semester (full-time) | Hours per week (full-time) | Hours per semester (part-time) | Hours per week (part-time) | Form of assignment |
| Lecture | 30 | 2 | - | - | Exam |
| Class | 45 | 3 | - | - | Credit with grade |
Familiarize students with the advanced methods and potential abilities of classical analysis essential in further education.
Mathematical analysis I, Algebraic and geometrical methods in physics
- Partial Derivatives. Differentials in applications. Chain Rules for Functions of Several Variables. Directional Derivatives and Gradients. Tangent Planes and Normal Lines.
- Extreme values of functions of several Variables. Extreme values of functions defined on restricted domains. Implicit functions. Conditional extrema problems and the method of Lagrange multipliers. Applications in geometry and physics.
- Double integrals. Volume and surface area. Double integrals in polar coordinates. Moments and center of mass.
- Triple Integrals and its applications. Triple integrals in cylindrical and spherical coordinates. Change of variables and the Jabionan of a transformation.
- Line integrals and their applications. Conservative fields and independence of path. Geen’s theorem.
- Surface integrals and their applications. Gradients, divergence, curl as differential operators. Gauss’ divergence theorem and Stokes’ theorem.
The problem-solving lecture, a seminar lecture, the use of multimedia, demonstrating method. The discussion method classes, the problem-classical method, solving exercises illustrating the content of the lecture
| Outcome description | Outcome symbols | Methods of verification | The class form |
Class:
The grade consists of two criteria: the scores in four tests organized during classes (70%) and degree of active participation in classes and suitable preparation (30%). A student is required to obtain at least 50% of maximal score. The student with the lowest passing grade of 10% of maximal score may write a correction test before the exam class.
Lecture:
The final exam is composed of written part. To be admitted to the exam a student must receive a credit for the class.
The course credit consists of the class grade (50%) and the exam grade (50%). The course credit is attained by positive passing both class and exam.
[1] G. M. Fichtenholz, Rachunek różniczkowy i całkowy, tom I i II, PWN, Warszawa 1995.
[2] M. Gewert, Z. Skoczylas, Analiza matematyczna 2, Definicje, twierdzenia, wzory, Oficyna Wydawnicza GIS, Wrocław 2005.
[3] M. Gewert, Z. Skoczylas, Analiza matematyczna 2, Przykłady i zadania, Oficyna GIS, Wrocław 2005.
[4] M. Gewert, Z. Skoczylas, Elementy analizy wektorowej, Teoria, przykłady i zadania, Oficyna GIS, Wrocław 1998.
[5] W. Kołodziej, Analiza matematyczna w zadaniach, PWN, Warszawa 1978.
[6] W. Kołodziej, Podstawy analizy matematycznej w zadaniach, Oficyna Wydawnicza Politechniki Warszawskiej, Warszawa 1995.
[7] W. Krysicki, L. Włodarski, Analiza matematyczna w zadaniach, cz. 2, Warszawa 1992.
[8] H. i J. Musielakowie, Analiza matematyczna, tom I cz. 1 i 2, Wydawnictwo Naukowe UAM, Poznań 1993.
[9] G. I. Zaporożec, Metody rozwiązywania zadań z analizy matematyczne, WNT, Warszawa 1976.
[1] F. Leja: Rachunek różniczkowy i całkowy, PWN, Warszawa 1972.
[2] R. Adams, C. Essex, Calculus - A Complete Course 7th ed - (Pearson Canada, 2010)
[3] Earl W. Swokowski, Calculus with Analytic Geometry Alternate Edition –PWS Publisher 1983.
Modified by dr hab. Piotr Lubiński, prof. UZ (last modification: 03-06-2020 16:15)
