Mathematics BSc
Course description
2013.
Course description
2013.
Analysis 4
Hours lect+pc |
Credits lect+pc |
Assessment | Specialization | Course code lect/pc |
Semester | Status |
---|---|---|---|---|---|---|
2 + 2 | 2 + 3 | exam + term grade |
applied math. | mm1c1an4a mm1c2an4a |
4 | compulsory |
Course coordinator
- Péter Simon
Strong | Weak | Prerequisites | |
---|---|---|---|
Practice class | |||
Strong:
| |||
Lecture | |||
Weak:
practice class
| |||
Weak:
|
Remarks
Syllabus designed by:
- Péter Simon, Department of Numerical Analysis, Faculty of Informatics.
Literature
- A. C. Zaanen: Integration. North Holland Publ. Co., Amsterdam 1967.
Syllabus
- Surfaces and their area, curves on surfaces.
- Integration on surfaces. Poincare-Stokes, Gauss-Ostrogradski theorems.
- Measure theory: measures on sigma-algebras, Lebesgue- and Lebesgue-Stieltjes measure, Borel sets.
- Integration on measure spaces, Lebesgue integral. Convergence theorems.
- Lp spaces, their basic properties and completeness.
- Absolute continuity, Radon-Nikodym theorem.
- Fubini's theorem.
- Signed measures, Hahn- and Jordan decomposition.