Problems and Solutions This page records my personalsolutions to the textbook problems.As a mathematician, I strongly recommend any reader should 'DO' theseexercises 'In Your Way' before read other guys' answers!!After solving the exercises,I also discuss on the connection between exercises and other knowntheorems or perspectives, for example, Exercise 5.16 in Evans' PDEs orChapter 6 of Folland's Real Analysis. I believe this will bring more funand communications between us.Corrections, Comments and improvements are welcome!!!Partial Differential Equations. Chapter 3. Chapter 4. Chapter 5 (Completed!).
Chapter 6 (Completed!). Chapter 7 (97% Completed!). Chapter 8. Chapter 9Last Modified: 2018. 05. Chapter 2 (Incomplete).
Harmonic function: Harmonic function, mathematical function of two variables having the property that its value at any point is equal to the average of its values along any circle around that point, provided the function is defined within the circle. Harmonic Functions. And their Riemann Sheets. Section 3.3 Harmonic Functions and their Riemann sheets. Let be a continuous real-valued function of the two real variables that is defined on a domain. (Recall from Section 1.6 that a domain is an connected and open set of points in the complex plane.) The partial differential equation.
Chapter 3 (Incomplete). Chapter 4 (Incomplete). Chapter 6 (Incomplete). Chapter 7 (Incomplete). Chapter 8 (Incomplete)Last Modified: 2019. 06Analysis.
Chapter 3 (60% Completed). Chapter 4 (Incomplete). Chapter 5 (16.08.25).
Chapter 6; (Incomplete)Last Modified: 2017. 13. Chapter 2. Chapter 3.
Chapter 4. Chapter 5. Chapter 6. Chapter 7 (Incomplete).
Chapter 8 (Incomplete)Almost Completed: 2018. 13.
Chapter 1 Measure Theory. Chapter 2 (In Progress).
Chapter 3 Differentiation and Integration. Chapter 4 (In Progress).
Chapter 5 (In Progress). Chapter 6 Abstract Measure and Integration Theory. Chapter 7 Hausdorff Measures and FractalsLast Modified: 2017.
07. Chapter 2 Positive Borel Measures. Chapter 3 (70% Completed, 16.08.25).
Chapter 4 (70% Completed, 16.08.25). Chapter 5 (Incomplete, 18.06.11).
Chapter 6 (Completed!). Chapter 7. Chapter 8 Integration on Product Spaces. Chapter 9 Fourier Transforms. Chapter 10 Elementary Properties of Holomorphic Functions.
Chapter 11. Chapter 12 The Maximum Modulus PrincipleLast Modified: 2018. 11. Chapter 1-6. Chapter 7-9.
Chapter 10-12. Chapter 13-15Last Modified: 2019. 18. (Incomplete). Chapter 4 Topics on Fourier SeriesLast Modified: 2018.