Calculus I

(in Polish) kształcenia ogólnego
(in Polish) podstawowe
obligatory courses

The main purpose of the subject is to acquaint the students with foundations of the analysis of one real variable function. Differential and Integral Calculus I is the base for learning physics for the whole course of study.

(in Polish) w sali

The Differential and Integral Calculus I comprises the first semester of the two semestral course of the infinitesimal and integral calculus. It includes 30 hours of the lecture and 30 hours of the discussion session.

The content is following: elementary functions and their properties, sequences and series, differential and integral calculus of functions of one real variable.

Educational profile : general academic

Type of studies: full-time

Block (unit): mandatory subject (Module 2: Mathematical subjects)

Field of knowledge and discipline of science: Natural sciences, physical sciences, mathematics

Specialty, level of education: medical physics, undergraduate studies

Year/semester: 1st year of studies/1st semester

Prerequisites: none.

Teaching hours: Lectures - 30 h, classes (practical exercises) - 30 h.

Teaching methods: lecture, practical exercises (solving of problems), homework, discussions, consultations, unassisted studying.

ECTS: 5

Balance sheet of the student's work: lectures (30 h), classes and discussion sessions (30 h), consultations (15 h), unassisted studying (50 h).

Quantitative indicators: student's wok under direct guidance of a teacher - 3.6 ECTS; practical (laboratory) exercises - 0.0 ECTS.

Content:

1. Sequences and numerical series.

2. Elementary functions and their properties.

3. Derivative and its properties.

4. Taylor series.

5. Propeties of real functions and graph sketching.

6. Indefinite and definite integrals.

Classes cover the same range of material as the lecture including computational exercises and discussions.

Mandatory literature:

1. W. Krysicki, Z. Włodarski: Analiza matematyczna w zadaniach", t. 1 (in Polish)

2. M. Gewert, Z. Skoczylas: Analiza matematyczna, przykłady i zadania (in Polish)

Supplementary literature:

1. M. Fichtenholz: Rachunek różniczkowy i całkowy, t. 1 (in Polish)

2. L. Górniewicz, R. S. Ingarden: Analiza matematyczna dla fizyków, t. 1 (in Polish)

3. R. Rudnicki: Wykłady z analizy matematycznej (in Polish)

4. W. Rudin: Podstawy analizy matematycznej (in Polish)

A student:

1. Has basic knowledge of chosen parts of the analysis and other branches of higher mathematics, needful to study physics.

2. Has computational proficiency of mathematics and ability to use the mathematical methods for defining and solving physical and related problems.

3. Is capable to perform and to present chosen mathematical argumentation of minor complexity.

4. Is able to use understandingly mathematical language for

description physical systems and phenomena.

5. Has computational proficiency of infinitesimal and integral calculus for function with one real argument.

6. Is oriented in the problems of higher mathematics, important for studying physics.

7. Is capable to use known mathematical tools to the problems of mathematical-natural and technical sciences.

Labels:

K_W06, K_W07, K_U03, K_U04, K_U05.

Students should be present on lectures and lessons of calculations. They are stimulated for asking the questions and initiating the discussion.

Written and oral examinations undergo after the end of the course of Differential and Integral Calculus I. They verify acquirement of knowledge.

Students get the series of questions, exercises and problems for individual and unassisted solving. Content of the series of questions is correlated with the lecture. During the courses, students present solutions of given problems. Lecturer is advised to pay close attention to understanding used concepts and clarity of presentations. He stimulates students group for asking the questions and discussions. Lecturer tries to create sense of responsibility for team inside the students group and he encourages the group to joint work.