# Mathematical Analysis ΙΙ

• Course Code DS-002 Type of Course
• Theory/Lab Sessions 4 hours / 1 hours ECTS Credits 7
• Semester Faculty

### Learning Outcomes

This course attempts to enhance the knowledge gained in the course Mathematical Analysis and to provide an appropriate mathematical background that enables the students to study the fields of computers and computers networks. After successfully completing this course, students are expected to have acquired the basic knowledge of Analysis regarding Gamma and Beta functions, Laplace Transform, Sequence and Series of Functions, Functions of two or more variables (differentiation, integration), as well as Fourier series, integrals and transform, which are necessary in Computer Science. The course directly supports most of the curriculum subjects and lessons: Note that during the lesson, specific examples of application are discussed in some of the above curricular subjects such as applications in telecommunication systems, cryptography, digital services such as e- learning, e-health. In conclusion, the students through the course process develop mathematical thinking and analyze, adapt their acquired knowledge to apply them to a variety of subjects in the field of study or the field of study, as well as to acquire new knowledge. In addition, they learn to solve complex or new problems in their scientific field of study by developing integrated as well as creative or innovative solutions and approaches while supporting their solutions and views in a methodical and scientific way. Finally, they learn to analyze and critically and responsibly choose ideas and information about those elements that concern them.

### Course Contents

• Improper Integrals, Improper Integrals Depending on a Parameter. Gamma and Beta Functions.
• Laplace transformations.
• Vectors in the level and in the space.
• Vector interrelations. Applications: laws of Kepler.
• Functions of Two Variables. Differentiation of Functions of Two Variables. Interrelations of multiple variables (definition, graphic representation, limits, constantly, certain derivative, derivative as for direction, total differential gear, very little – biggest).
• Precise differential equations.
• Double and triple integrals, change of coordinates – applications.
• Sequences and Series of Functions
• Fourier Series and Integrals. Fourier transformations.
• Completion of vector fields (bent – divergence – turn, curve integrals, surface integrals, theorems green, gauss, stokes).
• M. Filippakis, Applied Analysis and Fourier Theory, Tsotras Publications, Athens 2017, 2nd Edition.
• Zygmund A. (2003): Trigonometric Series, 3rd Edition, Cambridge University Press.
• Teaching Notes.