## Appleid Mathematics A3Back JP / EN

Numbering Code Year/Term U-ENG29 32070 LJ55U-ENG29 32070 LJ10 2021 ・ First semester 2 Lecture Japanese Wed.1 YAGASAKI KAZUYUKI (Graduate School of Informatics Professor) Fourier analysis originated in Fourier's work on thermal conduction and now becomes very important not only in mathematics but also in engineering, including applications in measurement technology. This course provides its theories and applications along with Laplace analysis closely related to it. To understand the fundamental theories of Fourier and Laplace analysis and develop an ability to apply them to concrete problems. Fourier series,2-3times,The definition of Fourier series expansions are given and their fundamental properties such as computation of Fourier coefficients and convergence of Fourier series are discussed. Properties and applications of Fourier series,3-4times,Several properties of Fourier series and their applications to differential and difference equations and signal processing are discussed. One-dimensional Fourier transform,3-4times,The definition of one-dimensional Fourier transforms is given, and their fundamental properties such as the inversion formula and applications to partial differential equations are discussed. Multi-dimensional Fourier transform,2-3times,The definition of multi-dimensional Fourier transforms is given, and their fundamental properties and applications to partial differential equations are discussed. Laplace transforms,2-3times,Properties of Laplace transforms and their applications to differential equations are discussed. Summary and learning achievement evaluation,1time,A summary and supplements of this course are given and the learning achievement of students is evaluated. Evaluation depends mainly on marks of examination, but marks of exercises and homework are taken into account when needed. Calculus, Linear Algebra and Differential Eqautions S. Nakamura: Fourier analysis, Asakura shoten isbn{}{9784254115741} H.Fukawa: Mathematics of control and vibration, KORONA-SHA ibid{}{TW86010572}