MATH 425b - Analysis II
MATH 425b was taught by Prof. Trevor Leslie in Spring 2023. As 425a gives us a solid foundation in analysis of metric spaces, this course, besides usual multivariable calculus, also acts as an introduction to functional analysis and Fourier series. The main reference of the course is Professor Leslie's lecture notes, which is available below. We also (occasionally) referred to W. Rudin. Principles of Mathematical Analysis, 3rd ed. and C. Pugh. Real Mathematical Analysis, 2nd ed.
This course was only more difficult than 425a. I wrote three times more pages of LaTeX homework than 425a, and I had to sweat quite a bit before finals after a 77/100 on midterm 2. But it is certainly worth the hard work as the content was really fun. I also did a final project to finish up the proof of pointwise convergence of Fourier series, which did not get covered in class due to lack of lecture time.
Class resources: syllabus | lecture notes | final project
This semester, I actually made my own lecture notes, available above. Again, I was also asked to not publicly release my homework solutions.
*Background from Spy X Family