KOW Pu Zhao (邱普照)

General Information

• Begins ~ ends: February 19, 2024 ~ June 21, 2024
• Instructor: Pu-Zhao Kow
• Email: pzkow [at] g.nccu.edu.tw
• Office hour: Thursday (16:10 ~ 17:00)
• Teaching Language: Chinese and English
• Lecture Note: Pu-Zhao Kow, An introduction to partial differential equations and functional analysis. Note: The lecture note may update during the course.

References

Note. See my lecture note for some more advance monographs.

• H. Brezis, Functional analysis, Sobolev spaces and partial differential equations, Universitext, Springer, New York, 2011. MR2759829, Zbl:1220.46002, doi:10.1007/978-0-387-70914-7
• L. C. Evans, Partial differential equations, volume 19 of Grad. Stud. Math. AMS, Providence, RI, second edition, 2010. MR2597943, Zbl:1194.35001, doi:10.1090/gsm/019
• D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order (reprint of the 1998 edition), volume 224 of Classics in Mathematics, Springer-Verlag Berlin Heidelberg, 2001. MR1814364, Zbl:1042.35002, doi:10.1007/978-3-642-61798-0
• P.-F. Hsieh and Y. Sibuya, Basic theory of ordinary differential equations Universitext, Springer-Verlag, New York, 1999 MR1697415, doi:10.1007/978-1-4612-1506-6
• F. John, Partial differential equations, volume 1 of Appl. Math. Sci., Springer-Verlag, New York-Berlin, third edition, 1978. MR0514404, Zbl:0426.35002

Prerequisite

• Calculus

Homeworks

• Homework 1: Return by March 7, 2024 (Thursday) 16:00
• Homework 2: Return by March 14, 2024 (Thursday) 16:00
• Homework 3: Return by March 21, 2024 (Thursday) 16:00
• Homework 4: Return by March 28, 2024 (Thursday) 16:00
• Homework 5: Return by April 11, 2024 (Thursday) 16:00
• Homework 6: Return by April 11, 2024 (Thursday) 16:00
• Homework 7: Return by May 16, 2024 (Thursday) 16:00
• Homework 8: Return by May 23, 2024 (Thursday) 16:00
• Homework 9: Return by June 6, 2024 (Thursday) 16:00
• Homework 10: Return by June 6, 2024 (Thursday) 16:00

Schedule

• The lectures are on Thursday (13:10-16:00) at 志希070221.

Time	Room	Activities
22.02.2024 13:10-16:00	志希070221	Week 1 - Lecture (Thursday): Preliminaries; what is partial differential equations
29.02.2024 13:10-16:00	志希070221	Week 2 - Lecture (Thursday): First order PDE (Transport equation)
07.03.2024 13:10-16:00	志希070221	Week 3 - Lecture (Thursday): Transport equation with variable coefficients; 1D wave equation on real line (d'Alembert formula) [Return Homework 1]
14.03.2024 13:10-16:00	志希070221	Week 4 - Lecture (Thursday): 1D wave equation on real line, half-line and bounded interval; Duhamel's principle; n-dimensional wave equation [Return Homework 2]
21.03.2024 13:10-16:00	志希070221	Week 5 - Lecture (Thursday): n-dimensional wave equation; Kirschhoff's formula; Hadamard's method of descent; weak derivatives [Return Homework 3]
28.03.2024 13:10-16:00	志希070221	Week 6 - Lecture (Thursday): Weak derivatives and distribution derivatives [Return Homework 4]
04.04.2024 13:10-16:00	志希070221	Week 7 - Public holiday (Thursday): No class
11.04.2024 13:10-16:00	志希070221	Week 8 - Lecture (Thursday): [Return Homework 5 and Homework 6]
18.04.2024 13:10-16:00	志希070221	Week 9 - Lecture (Thursday)
25.04.2024 13:10-16:00	志希070221	Week 10 - Midterm exam (Thursday)
02.05.2024 13:10-16:00	志希070221	Week 11 - Lecture (Thursday): Review midterm exam; Weak formulation of Poisson/Helmoltz equation
09.05.2024 13:10-16:00	志希070221	Week 12 - Lecture (Thursday): Lax-Milgram theorem for Hilbert spaces [Return Homework (midterm exam)]
16.05.2024 13:10-16:00	志希070221	Week 13 - Lecture (Thursday): Maximum principle, solving elliptic PDE (Eigenvalue problem and Fredholm alternative) [Return Homework 7]
23.05.2024 13:10-16:00	志希070221	Week 14 - Lecture (Thursday): Fourier series [Return Homework 8]
30.05.2024 13:10-16:00	志希070221	Week 15 - Self-study (Thursday): no class
06.06.2024 13:10-16:00	志希070221	Week 16 - Lecture (Thursday): Fourier transform and convolution for distributions [Return Homework 9 and Homework 10]
13.06.2024 13:10-16:00	志希070221	Week 17 - Final exam (Thursday)
20.06.2024 14:30-16:00	志希070221	Week 18 - Lecture (Thursday): Return all exercises and exams after 14:30. There is a colloquium entitled "由歐拉到黎曼" from 12:40--14:30.

Completion

• The course can be taken for credit by attending the lectures, returning written solutions (60%) and taking taking midterm and final exams (each 20%).