Calculus II

obligatory courses

Calculus I 0900-FM1-1RRC1

The aim of the course is to acquaint students with the basics of mathematical analysis of functions of many variables and the basic methods of solving ordinary differential equations. These methods play a key role in physics. The subject is a necessary basis for teaching the majority of physics subjects throughout the course of studies.

(in Polish) w sali

Differential and Integral calculus II is the second part of a two-semester course of differential and integral calculus and includes two hours of lecture and two hours of class exercises. c

The subject consists of differential and integral calculus of functions of many variables, including vector analysis, and the introduction to the theory of ordinary differential equations (with an emphasis on equations of the first order and linear equations of constant coefficients).

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/2nd semester

Prerequisites: Differential and Integral Calculus I.

Teaching hours: Lectures - 30 h, classes (practical exercises) - 45 h.

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

ECTS: 6

Balance sheet of the student's work: lectures (30 h), classes and discussion sessions (30 h), consultations (15 h), unassisted studying (75 h).

Quantitative indicators: student's wok under direct guidance of a teacher - 4.2 ECTS; practical (laboratory) exercises - 0.0 ECTS.

Content:

1. Differentiation of inverse and implicit functions. Chain rule.

2. Local and global extremes of functions of two variables.

3. Change of variables. Jacobian.

4. Double integrals, triple integrals and their applications.

5. Gradient, curl and divergence.

6. Calculation of curvilinear integrals (work, circulation along the curve) and surface integrals (flux). Stokes' theorem.

7. Approximate solution of algebraic equations.

8. Ordinary differential equations of the first order (equations with separated variables, substitution method).

9. Solution of linear equations with constant coefficients. The variation

of constants method for non-homogeneous equations.

10. Applications of differential equations in physics.

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

1. W.Krysicki, L.Włodarski: Analiza matematyczna w zadaniach, PWN, Warszawa 1998 (in Polish).

2. R.Rudnicki: Wykłady z analizy matematycznej, PWN, Warszawa 2001 (in Polish)..

3. M.Gewert, Z.Skoczylas, Analiza matematyczna II, GiS, Wrocław 2004 (in Polish).

4. M.Gewert, Z.Skoczylas, Równania różniczkowe zwyczajne, GiS, Wrocław 2003 (in Polish).

5. M.Gewert, Z.Skoczylas, Elementy analizy wektorowej, GiS, Wrocław 2000 (in Polish).

Student:

1. Learns the basic mathematical apparatus of mathematical analysis and other branches of higher mathematics, necessary for further study of physics.

2. Acquires computational skills and the ability to use mathematical tools to pose and solve problems of physics and related disciplines.

3. Is able to conduct and present selected mathematical reasoning with a low degree of complexity

4. Uses mathematical language to describe the physical reality.

5. Has computational skills in differential and integral calculus of functions of many variables and is able to solve simple ordinary differential equations.

6. Is familiar with the issues of higher mathematics which are important for further study of physics.

7. Is able to apply methods of higher mathematics to some issues natural and technical sciences.

Labels:

K_W06, K_W07, K_U03, K_U04.

Students solve computational problems during classes and receive homework tasks, including those related to the subject of lectures. The emphasis is on the acquisition of several skills, described as the main learning outcomes. The results are checked through written tests (colloquia). Activity during classes and creativity in approaching solved problems are also assessed.

After completion of education in the subject Differential and Integral Calculus II there is a written and oral examination which verifies the acquired knowledge.