Credits: 5

Schedule: 24.02.2020 - 01.04.2020

Teaching Period (valid 01.08.2018-31.07.2020): 

Not lectured (2018-2019)

IV Spring (2019-2020)

Lectured every other year

 

Learning Outcomes (valid 01.08.2018-31.07.2020): 

After this course you will know how to apply real analysis methods in research.

 

Content (valid 01.08.2018-31.07.2020): 

Lebesgue spaces (Hölder's and Minkowski's inequalities, Riesz-Fischer theorem, dual spaces and weak convergence), Hardy-Littlewood maximal function (Vitali covering theorem, Marcinkiewicz interpolation theorem, maximal function theorem, Lebesgue's differentiation theorem), convolution approximations, differentiation of Radon measures (Besicovitch covering theorem, Lebesgue points), Radon-Nikodym theorem, Riesz representation theorem, weak convergence and compactness for Radon measures, Sobolev spaces (Poincare and Sobolev inequalities).

 

Assessment Methods and Criteria (valid 01.08.2018-31.07.2020): 

Teaching methods: lectures and exercises

Assessment methods: homework assignments and attendance (100%)

 

Workload (valid 01.08.2018-31.07.2020): 

Contact hours 36 h

Self-study ca 100h

 

Study Material (valid 01.08.2018-31.07.2020): 

All material is available at the course homepage.

Substitutes for Courses (valid 01.08.2018-31.07.2020): 

Mat-1.3283 

 

Course Homepage (valid 01.08.2018-31.07.2020): 

https://mycourses.aalto.fi/course/search.php?search=MS-E1281

Prerequisites (valid 01.08.2018-31.07.2020): 

MS-A00XX, MS-A01XX, MS-A02XX, MS-A03XX, MS-A050X, MS-C1350, MS-C1540, MS-E1280

 

Grading Scale (valid 01.08.2018-31.07.2020): 

0-5

 

Description

Registration and further information