﻿ Ho LEE

## Topics in Analysis

### Department of Mathematics Kyung Hee University

26 Kyungheedae-ro, Dongdaemun-gu, Seoul, 02447, Korea
email: holee@khu.ac.kr

### Notices

• 교재: Applied Partial Differential Equations (by J. D. Logan)
• 수업시간: 월, 수 12:00~13:15, 스페이스21 B103호.
• 한글날 10/9 수요일 수업합니다.
• 한글날 10/9 (수요일) 수업 계획 취소합니다.
• 중간고사: 10/23 수요일, 12:00~13:20, 시험 장소 추후 공지.
• 중간고사 범위: 아래 [Sources and Duhamel's principle] 까지.

### Topics

• [PDE models] Heat flow; heat equation; boundary and initial conditions; evolution and steady state models; linear and non-linear equations; homogeneous and non-homoneneous equations; Examples 1.2, 1.3, 1.4, 1.5; Exercises 1, 2, 5, 6; 연습문제 12, 13, 14 제외.
• [Conservation Laws] conservation law; flux and source; constitutive relations (or equations of state); method of characteristics; advection equation; advection and decay; Examples 1.8, 1.9, 1.10, 1.11; characteristic coordinates and characteristic curves (뒤쪽 nonlinear advection 파트에 나옴); nonlinear advection 제외; 연습문제 2, 3, 4, 5; 연습문제 9 번 이후 제외.
• [Diffusion] Fick's law; diffusion equation; Fourier's law; heat equation; advection-diffusion and advection-diffusion-decay equations; Dirichlet, Neumann, and Robin condisions; steady-state solution; Exercises 2, 3, 4, 5, 6; 연습문제 8 번 이후 제외.
• [Cauchy Problem for the Heat Equation] Cauchy problem; erf function; heat kernel; fundamental solution; point source; Exercises 1, 2, 3, 6, 7.
• [Vibrations and Acoustics] vibrations of a string; derivation of the wave equation; right-traveling and left-traveling wave solutions; Exercises 3, 4, 5; you may skip the Exercises 6-9.
• [Cauchy Problem for the Wave Equation] characteristic coordinates; d'Alembert's formula; domain of dependence; region of influence; Exercises 1, 3, 7, 9.
• [Semi-infinite domains] odd extension for the heat and the wave equations; Exercises 1, 4.
• [Sources and Duhamel's principle] derivation using the characteristic coordinates; Duhamel's principle for the heat and the wave equations; Example 2.6; Exercises 3, 5.
• 여기까지 중간고사를 봅니다.
• 중간고사 성적 확인
• [Ch. 3. Orthogonal expansion]에서 풀어볼 문제: 3.1 Exercises 없음; 3.2 Exercises 1, 2, 3, 6, 7, 8, 9, 11, 13, 14, 15; 3.3 Exercises 3, 4, 8, 9.
• [Ch. 3]에서 풀어볼 연습문제들을 바탕으로 11월 13일 수요일 수업시간에 퀴즈를 봅니다.