Applied Functional Analysis

Academic year

2025Year

Term

Second Semester

Course title

Applied Functional Analysis

Class type

Lecture

Course title (ENG)

Applied Functional Analysis

Class code・Class name・Teaching forms

Z1500006 Applied Functional Analysis

Instructor

SAITO Seiken

Credits

2.0Credits

Day and Time

Thu.3Period

Campus

Hachioji Remote

Location

Relationship between diploma policies and this course

A) A high degree of specialized expertise　100%
B) The skills to use science and technology　0%
C) The ability to conduct research independently, knowledge pertaining to society and occupations, and sense of ethics required of engineers and researchers　0%
D) Creative skills in specific areas of specialization　0%

Goals and objectives

If an indefinite integral of a function f(x) is not presented by closed form, we need use
approximate value of the definite integral of f(x). So the theory of numerical integration
are important. We study in the lectures theory of numerical integration of
Gauss type. Especially Gauss-Legendre type is detailed explanation.

Prerequisites

Understanding Linea Algebra （linear independance,inner product,orthogonalbasis)

Method Using AL・ICT

Not used

Class schedule

1 Linear space
2 Linear independance and orthonormal basis
3 Gram–Schmidt orthonormalization
4 Orthogonal polynomial
5 Christoffel–Darboux formula
6 Function Approximation and Interpolation
7 Interpolation with orthogonal polynomials
8 Gaussian Quadrature
9 Legendre-Gauss Quadrature
10 Laguerre-Gauss Quadrature
11 Hermite-Gauss Quadrature
12 Recurrence formula for Legendre polynomial
13 Differencial equation for Legendre polynomial
14 Introduction to Finite Element Method
15 Reflection on class content (on demand)

Evaluation

Students must submit a report some problem given in lecture.

Feedback for students

I respond to your inquiries about submissions and exams via KU-LMS and email.

Textbooks

No particular specification.

Reference materials

Masatake Mori, "Numerical Analysis," Kyoritsu Shuppan.

Office hours and How to contact teachers for questions

Thursday 14:10〜15:10 (Laboratory Hachioji 1E-314)

Message for students

Thoroughly review (prepare) Linear Algebra of Undergraduate Lectures.
Please check KU-LMS as it may notify you of homeworks etc.
PC may be used in class.

Course by professor with work experience

Not applicable

Work experience and relevance to the course content if applicable

Teaching profession course

Electrical Engineering and Electronics Program

Syllabus data