I am currently an undergraduate and I am particularly interested in mathematical analysis and pde and I hope to do some simple undergraduate research in mathematical analysis and pde in two years later.Here is the booklist I searched online and I have compiled all of them. Do I still lack of anything that required me to start to do research in mathematical analysis and pde? Do I need to add-on stochastic analysis in this booklist?
1) Larry Smith Linear Algebra
2) Apostol Calculus Volume 1 & 2
3) Differential Equation with Boundary-Value Problem
4) Elias M.Stein Fourier Analysis
5) Rudin Principle of Mathematical Analysis
6) Evans Partial Differential Equation
7) Munkres Topology
8) Rudin Complex and Real Analysis
9) A First Course in Abstract Algebra Fraleigh
10) Rudin Functional Analysis
11) Elias M.Stein Harmonic Analysis
12) Hormander " An introduction to Complex Analysis in Several Variables"
13) doCarmo, Differential Geometry of Curve and Surfaces
14) Hirsch, Differential topology
I would appreciate it if you can give me any suggestions. Thank you.
As you are interested in pde, I would add Brezis book (give special attention to chapters 8 and 9, which complement chapters 5 and 6 of Evans).