Integration and Measure

Theorethical hours: 20 h.
Exercises hours: 20 h.
Personal working hours: 70 h.

PRERREQUISITES AND RECOMMENDED PREVIOUS KNOWLEDGE

Linear Algebra, Differential Calculus, Integral Calculus, Vector Calculus.

 

GENERAL DESCRIPTION OF THE COURSE

An introductory course to the mathematical Measure Theory and to the modern integration methods. The course ends with some applications to Transforms Theory and to solving linear differential equations.

OBJECTIVES: KNOWLEDGE AND SKILLS

• To introduce the student in the study of modern integration methods, in particular the Lebesgue integral. 
• To know the convergence theorems on integration and the functional L^p spaces. 
• To apply these results to the differentiation of parametric integrals and in particular to the Fourier and Laplace transforms.

TEACHING MATERIAL

The students receive a course notes including the mathematical concepts and the theorems needed to solve the exercises. They also receive a list of exercises, with hints for the more difficult ones, and the list of solutions  of the exercises in a separate file.

They also have basic reference texts to facilitate the understanding of the concepts. A list of complementary bibliography completes the reference texts. A list of exercises is provided with some hints for the more difficult problems. Finally, the students have the complete solutions of all problems in a separate list.

 PRACTICAL ASSIGMENTS AND ASSESSMENT ACTIVITIES

The students have several assessment tests with its solutions in order to check that they have acquired the necessary capabilities.