Mathematics for Electrical and Electronic Engineering 1
| Numbering Code | U-ENG26 26102 LE72 | Year/Term | 2022 ・ Second semester | |
|---|---|---|---|---|
| Number of Credits | 2 | Course Type | Lecture | |
| Target Year | Target Student | |||
| Language | English | Day/Period | Fri.1 | |
| Instructor name |
OOMURA YOSHIHARU (Research Institute for Sustainable Humanosphere Professor) DOI SHINJI (Graduate School of Engineering Professor) |
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| Outline and Purpose of the Course | We study properties of eigenfunctions, such as trigonometric functions, Bessel functions, Legendre functions as solutions of linear differential equations, which appear in various subjects of electric and electronic engineering such as electromagnetics, plasma physics, and quantum mechanics. As applications of these eigenfunctions, we also study Fourier series, Fourier transform, and Laplace transform. | |||
| Course Goals | We learn mathematical methods to describe spatial and temporal evolutions of various physical phenomena. | |||
| Schedule and Contents |
Classification of Partial Differential Equations,2times,Partial Differential Equations (PDE) : Laplace, Helmholtz, and diffusion equations; elliptic, hyperbolic, and parabolic types of 2nd order PDE.; derivation of Ordinary Differential Equations (ODE) from PDE by separation of variables Ordinary Differential Equations,2times,Series solutions by Frobenius' method; trigonometric, Bessel, and Legendre functions. Singular points for ODE; Wronskian; linear independence of solutions; second solution Sturn-Liouville Theory,1time,Self-ajoint ODE; Hermitian operator; Sturm-Liouville theory Green's Function Method,1time,Green's function method to solve nonhomogeneous equations. Bessel Functions,2times,MATLAB Demonstration (vibrating membrane, EM wave radiation), generating function, Bessel series; application to frequency modulation. Hankel functions; 3D Helmholtz equation in spherical coordinates, spherical Bessel functions Legendre Functions,1time,Legendre functions; generating functions; boundary value problems; associated Legendre polynomials. Fourier Series,1time,Properties of Fourier Series, Gibbs Phenomenon Fourier Transform,2times,Fourier integral, Fourier transforms of Gausian and derivatives, Dirac delta function, Solutions of wave equation and diffusion equation Laplace Transform,2times,Laplace transform, inverse Laplace transform, initial value problems of ODE Confirmatin of Understanding,1time,The level of understanding on all topics covered by this lecture will be confirmed through by the term examination. |
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| Evaluation Methods and Policy | The grade will be given by adding all points of reports (5points x 13times) and a term examination(100points). A grade grater than or equal to 60 is successful. If the total point exceeds 100, the grade is given as 100. | |||
| Course Requirements | Calculus, Vector Analysis, Functions of Complex Variable, and English comprehension of the level of VOA Special English | |||
| Study outside of Class (preparation and review) | Try to read chapters of the textbook based on the lecture notes. | |||
| Textbooks | Textbooks/References | Mathematical Methods for Physicists: A Comprehensive Guide, Seventh Edition, Arfken, Weber, and Harris isbn{}{9780123846549} (Kindle version is available.) | ||
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