Mathematics 3

Grading of the course requires grading of the following courses:

Mathematics 2 (101MAT2)

Lecturer:

Josef Jirásko (gar.)

Tutor:

Josef Jirásko (gar.), Martin Hála

Supervisor:

Department of Mathematics

Synopsis:

The course has been designed to give an integrated view of integral calculus of functions of several variables, line integrals and includes aspects of

fundamental and advanced properties of initial and boundary-value problems, eigenvalues, eigenfunctions and differential operators. The use of computers is a focus throughout the course.

Requirements:

101MAT2

Syllabus of lectures:

1. Linear differential equation of the 2nd order.

2. Variation of constants. Trial functions.

3. Boundary-value problems. Eigenvalues.

4. Differential operators and their properties.

5. Energy functionals. Variational principle.

6. Double integral. Definition and properties. Fubini theorem. Exchange of variables.

7. Test.

8. Application of double integrals.

9. Triple integral. Definition and properties. Fubini theorem. Exchange of variables.

10. Applications of triple integrals.

11. Line integral of a function.

12. Line integral of a vector field. Independence of the path. Green's theorem.

13. Potential fields.

14. Applications of line integrals.

Syllabus of tutorials:

Study Objective:

Students are able to solve fundamental problems based on multiple integrals and line integrals in scalar and vector fields. Students can solve boundary value problems and selected problems used in building practice.

Study materials:

Bubeník F.: Mathematics for Engineers, Vydavatelství ČVUT, 1997. Bubeník F.: Problems to Mathematics for Engineers, Vydavatelství ČVUT, 1999. Rektorys K. et al.: Applied Mathematics, Praha, Prometheus 2000.

Note:

Time-table for winter semester 2011/2012:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
Fri	roomTH:A-s134 Jirásko J. 11:00–12:50 (lecture parallel1) Thákurova 7 (FSv-budova A) A34
Thu	roomTH:A-334 Jirásko J. 16:00–17:50 (lecture parallel1 parallel nr.259) Thákurova 7 (FSv-budova A) A334
Fri

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans: