Mathematics for Electrical and Electronic Engineering 2

Numbering Code U-ENG26 36103 LJ72 Year/Term 2021 ・ First semester
Number of Credits 2 Course Type Lecture
Target Year Target Student
Language Japanese Day/Period Wed.3
Instructor name DOI SHINJI (Graduate School of Engineering Professor)
Outline and Purpose of the Course Transformation and approximation of data (signals) are basic tasks of any science or technology. Also, conceptions of linear space and linear mapping are the basis of not only such signal processing but of a number of engineering theories. Thus, this course discusses mainly signal theory and function approximation problems, explaining linear algebraic and functional analytic concepts and their engineering applications. Students learn the mathematical techniques needed in electrical and electronic engineering, specifically the concepts of linear space, functional analysis, and signal theory. Through this course, students not only learn the foundations of numerous subjects such as basic communications theory, control engineering, and signal/image processing, they also gain an expanded perspective from which they can look out on a number of different subjects.
Course Goals Learn the mathematical techniques needed for electrical and electronic engineering, specifically the concepts of linear space, functional analysis, and signal theory.
Schedule and Contents Linear space and linear mapping, 3-4 classes: Review linear algebra, explaining not only linear space in terms of matrix calculation but also describing the concepts of linear space and linear mapping. Describe expression on the basis of data (vectors) and its relation to eigenvalue problems, as well as the relationship between eigenvalue problems, on the one hand, and variation problems (minimax problems) and least squares approximation problems on the other, and explain the importance of linear algebraic concepts.
Abstract space/signal space, 2-4 classes: Explain not only finite dimensional vectors, but also functional spaces with elements (vectors) of infinite dimensional signals/functions. Introduce metric spaces, and describe convergence, Cauchy sequences, and completeness within them. Also, introduce norms in linear space, norm spaces, and inner product spaces, and describe the properties of these spaces. Introduce examples of functional spaces, and describe convergence and completeness. Also, describe mapping (operators), projection, orthogonality, and orthogonalization in functional spaces, and again explain the importance of linear algebraic concepts.
From abstract space to continuous/discrete signals, 2-3 classes: Introduce specific function systems as the bases of functional spaces. Explain the functional systems used frequently in analog and digital signal processing such as trigonometric functional systems and Haar functional systems. Also, describe how the polynomial systems of Legendre, Laguerre, and Hermite seen in Electrical and Electronic Mathematics 1 and Quantum Mechanics are produced by the orthogonalization of functions.
Continuous/discrete signal transformation (basic), 2-3 classes: Discuss function expansion in terms of system and signal notation methods. Explain general Fourier series as an expansion upon trigonometric functional systems, and discuss application of continuous and discrete signals to least squares approximation problems.
Continuous/discrete signal transformation (applied), 2-4 classes: Explain the various application methods used in system engineering and signal processing. Describe the discrete Fourier transform, wavelet expansion, and the finite element method in terms of the functional expansion by non-orthogonal (and a finite number of) functions.
Confirmation of learning attainment, 1 class: Confirm the degree of learning attained with respect to the above subjects.
Evaluation Methods and Policy Final examination + report assignments
Course Requirements Linear algebra, calculus
Study outside of Class (preparation and review) Review handouts and example solutions of problems provided in the class.
References, etc. Principles of Applied Mathematics, J.P.Keener, (Westview Press), Japanase translation: キーナー応用数学, 上下,日本評論社
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