Mathematical analysis 2
Some basic information about the module
The aim of studying and bibliography
The main aim of study:
The aim of the course is to familiarize students with such topics of mathematical analysis, such as: partial derivatives, extrema of functions of two variables, double and triple integrals, curve integrals, surface integrals, their applications and use of CAS Maxima software.
The general information about the module:
The module consists of 30 hours of lectures, 30 hours of classes and 15 hours of laboratories. It ends with an exam.
Bibliography required to complete the module
| 1 | F. Leja | Rachunek różniczkowy i całkowy | PWN, Warszawa. | 2008. |
| 2 | W. Żakowski, W. Kołodziej | Matematyka cz.2. Analiza matematyczna | WNT, Warszawa. | 2013. |
| 3 | M. Gewert, Z. Skoczylas | Analiza matematyczna 2. Definicje, twierdzenia, wzory | GiS, Wrocław. | 2016. |
| 4 | W. Krysicki, L. Włodarski | Analiza matematyczna w zadaniach cz.2 | PWN, Warszwa. | 2011. |
| 5 | M. Gewert, Z. Skoczylas | Analiza matematyczna 2. Przykłady i zadania | GiS, Wrocław. | 2016. |
| 6 | P.N. de Souza, R.J. Fateman, J. Moses, C. Yapp | The Maxima Book | http://maxima.sourceforge.net. | - |
| 7 | G. Berman | Zbiór zadań z analizy matematycznej | Pracownia Komputerowa Jacka Skalmierskiego, Gliwice. | 2000. |
Basic requirements in category knowledge/skills/social competences
Formal requirements:
The student satisfies the formal requirements set out in the study regulations.
Basic requirements in category knowledge:
Knowledge of the basics of the differential and integral calculus of one variable function.
Basic requirements in category skills:
Ability to calculate limits and derivatives of functions and basic indefinite and definite integrals.
Basic requirements in category social competences:
Preparation for taking substantively justified mathematical actions to solve the posed problem.
Module outcomes
| MEK | The student who completed the module | Types of classes / teaching methods leading to achieving a given outcome of teaching | Methods of verifying every mentioned outcome of teaching | Relationships with KEK | Relationships with PRK |
|---|---|---|---|---|---|
| MEK01 | Can calculate partial derivatives and extrema of functions of two variables. | lecture, solving classes, laboratory | test, written exam |
K-W01+ K-U01+ |
P6S-UW P6S-WG |
| MEK02 | Can calculate the double integrals and the triple integrals. | lecture, solving classes, laboratory | test, written exam |
K-W01+ K-U01+ |
P6S-UW P6S-WG |
| MEK03 | Can calculate curve integrals | lecture, solving classes, laboratory | test, written exam |
K-W01+ K-U01+ |
P6S-UW P6S-WG |
| MEK04 | Can calculate surface integral. | lecture, solving classes, laboratory | test, written exam |
K-W01+ K-U01+ K-K01+ |
P6S-KK P6S-UW P6S-WG |
| MEK05 | Can calculate derivatives of multiple variables and multiple integrals in the CAS Maxima and perform graphs of functions in 2D and 3D. | laboratory | project at the computer |
K-W02+ K-K02+ |
P6S-KK P6S-KO P6S-WG |
The syllabus of the module
| Sem. | TK | The content | realized in | MEK |
|---|---|---|---|---|
| 2 | TK01 | W1-W12, C1-C12, L1-L5 | MEK01 MEK05 | |
| 2 | TK02 | W13-W20, C13-C20, L6-L10 | MEK02 MEK05 | |
| 2 | TK03 | W21-W26, C21-C26, L11-L13 | MEK03 MEK05 | |
| 2 | TK04 | W27-W30, C27-C30, L14-L15 | MEK04 MEK05 |
The student's effort
| The type of classes | The work before classes | The participation in classes | The work after classes |
|---|---|---|---|
| Lecture (sem. 2) | contact hours:
30.00 hours/sem. |
complementing/reading through notes:
3.00 hours/sem. Studying the recommended bibliography: 2.00 hours/sem. |
|
| Class (sem. 2) | The preparation for a Class:
5.00 hours/sem. The preparation for a test: 8.00 hours/sem. |
contact hours:
30.00 hours/sem. |
Finishing/Studying tasks:
3.00 hours/sem. |
| Laboratory (sem. 2) | The preparation for a Laboratory:
5.00 hours/sem. The preparation for a test: 5.00 hours/sem. |
contact hours:
15.00 hours/sem. |
Finishing/Making the report:
5.00 hours/sem. |
| Advice (sem. 2) | The preparation for Advice:
1.00 hours/sem. |
The participation in Advice:
1.00 hours/sem. |
|
| Exam (sem. 2) | The preparation for an Exam:
10.00 hours/sem. |
The written exam:
2.00 hours/sem. |
The way of giving the component module grades and the final grade
| The type of classes | The way of giving the final grade |
|---|---|
| Lecture | Written exam. The obvious exercises and the extra exercises. The obvious exercises must be solved. Only the obvious exercises - 3.0. |
| Class | Written tests. The obvious exercises and the extra exercises. The obvious exercises must be solved. |
| Laboratory | Project at the computer (obligatory). |
| The final grade |
Sample problems
Required during the exam/when receiving the credit
(-)
Realized during classes/laboratories/projects
(-)
Others
(-)
Can a student use any teaching aids during the exam/when receiving the credit : yes
Available materials : undersigned the leaf of format what the highest A4, double-recorded, with any content