電気電子数学1

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 科目ナンバリング U-ENG26 26102 LE72 開講年度・開講期 2020・後期 単位数 2 単位 授業形態 講義 対象学生 学部生 使用言語 英語 曜時限 金1 教員 大村　善治（生存圏研究所 教授） 土居　伸二（工学研究科 教授） 授業の概要・目的 We study solutions of partial and ordinary differential equations, such as trigonometric functions, Bessel functions, Legendre functions. As applications of these eigen functions, we study Fourier series, Fourier and Laplace transforms, which are mathematical bases of electrical engineering and electronics, plasma physics, and quantum mechanics. 到達目標 Understanding mathematical methods for discription of physical phenomena evolving in space and time. 授業計画と内容 1st and 2nd lectures:Classification of partial differential euqaions(PDE). Derivation of ordinary differential equations (ODE) frmo typical PDE in Catesian coordinates, polar cyclindrical coordinates, and circular spherical coordinates.3rd and 4th lectures:Series solutions by Frobenius' method; trigonometric, Bessel, and Legendre functions. Singular points for ODE; Wronskian; linear indepedence of solutions; second solutionSturn-Liouville Theory5th and 6th lectures: Self-ajoint ODE; Hermitian operator; Sturm-Liouville theory Green's Function Method, Green's function method to solve nonhomogeneous equation, Bessel Functions7th and 8th lectures: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 9th and 10th lectures:Legendre functions; generating functions; boundary value problems; associated Legendre polynomials, Fourier Series11th and 12th lectures:Properties of Fourier Series, Gibbs PhenomenonFourier Transform, Fourier integral, Fourier transforms of Gausian and derivatives, Dirac delta function, Solutions of wave equation and diffusion equation13th and 14th lectures:Laplace Transform, inverse Laplace transform, initial value problems of ODE 成績評価の方法・観点 The grade is determined by adding the scores of report assignments (5 points x 12 times) and a term test (100 points). If the total socre exceeds 100 points, the score is given as 100. 履修要件 Calculus, Vector Analysis, Complex Variables, and English listening comprehention at the level of VOS special english. 授業外学習（予習・復習）等 Reprot assignments are announced at every lecture, and the report should be submitted at the beginning of the next lecture. 教科書 Mathematical Methods for Physicists, Arfken, Weber, qand Harris, (Elsevier), ISBN:978-0-12-384654-9