Lecture Notes

User Tools

Site Tools

You are here: Course Notes » Math 104: Introduction to Real Analysis (2021 Fall)
math104-f21:start

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision 		Previous revision
Last revision Both sides next revision
math104-f21:start [2021/11/12 01:09]
pzhou [Textbooks] 		math104-f21:start [2022/01/11 08:36]
pzhou ↷ Links adapted because of a move operation
Line 59: Line 59:
   * Sep 17: Finish Cauchy sequence is convergent. Limit points and subsequence.    * Sep 17: Finish Cauchy sequence is convergent. Limit points and subsequence. 
   * [[HW4]] Due next Tuesday 6pm   * [[HW4]] Due next Tuesday 6pm
-  * [[math104:midterm1-review|]]+  * [[math104-f21:midterm1-review]]
  
 ==== Week 5 ==== ==== Week 5 ====
Line 82: Line 82:
   * Oct 11 Closure and Interior. Open covers and Compact sets   * Oct 11 Closure and Interior. Open covers and Compact sets
   * Oct 13 Compact sets are closed. Closed subset of compact set is compact. Compactness is absolute notion. (Rudin 2.30, 2.33, 2.34, 2.35)   * Oct 13 Compact sets are closed. Closed subset of compact set is compact. Compactness is absolute notion. (Rudin 2.30, 2.33, 2.34, 2.35)
-  * Oct 15 Towards Thm 2.41. Finishing compactness. (will not talk about perfect set). [[math104:compactness|sequential compactness and compactness]] +  * Oct 15 Towards Thm 2.41. Finishing compactness. (will not talk about perfect set). [[math104-f21:compactness|sequential compactness and compactness]] 
   * [[HW8]] Due next Thursday 6pm.    * [[HW8]] Due next Thursday 6pm. 
  
Line 117: Line 117:
   * Nov 8: Pointwise convergence and Uniform Convergence.   * Nov 8: Pointwise convergence and Uniform Convergence.
   * Nov 10: [[Midterm 2]] policy about cheat sheet is the same as midterm 1   * Nov 10: [[Midterm 2]] policy about cheat sheet is the same as midterm 1
-  * Nov 12: Uniform convergence preserves continuity. Examples. +  * Nov 12: Uniform convergence preserves continuity. Examples. 
 +  * No HW this week 
  
 ==== Week 13 ==== ==== Week 13 ====
-  * Nov 15 +Rudin Ch 5, Differentiation.  
-  * Nov 17 +One can also see notes from 2021 spring [[math104-2021sp:start|previous version]] 
-  * Nov 19+ 
 +  * Nov 15: definition. examples. Chain rule.  
 +  * Nov 17: mean value theorem.  
 +  * Nov 19: L'hopital rule. Smooth Functions. Taylor theorem.  
 +  * [[HW13]]. Due Nov 29 Monday. 
  
 ==== Week 14 ==== ==== Week 14 ====
-  * Nov 22 +Rudin Ch6 
-  * Nov 24 + 
-  * Nov 26 Thanksgiving. No class+  * Nov 22 A brief encounter with Lebesbue measure theory and integration (optional). The definition of Riemann integrable functions.  
 +  * Nov 24 No class.  
 +  * Nov 26 No class
  
 ==== Week 15 ==== ==== Week 15 ====
-  * Nov 29 +  * Office hour of GSI changed this week:  3pm - 6pm Tuesday and 9am-4pm Wednesday. 
-  * Dec 1 +  * Videos from [[math104-2021sp:start|past semester]] are available on bcourse media gallery. You can use them for review. 
-  * Dec 3+ 
 +  * Nov 29: Continuous function and Monotone functions are Riemann integrable.  
 +  * Dec 1: Riemann Stieltjes integral 
 +  * Dec 3: Fundamental Theorem of Calculus  
 +  * [[HW15]], this is only for practice, not due. 
 + 
 +==== Week 16 ==== 
 +Review week. No class. We have daily office hours 12-1pm, at [[https://berkeley.zoom.us/j/97935304012|zoom link]], from Monday-Thursday. If you plan to come, please arrive by 12:10.  
 + 
 +  * Tuesday office hour will be held in-person only. 12:10noon-1pm.  
 + 
 + 
 +==== Final ==== 
 + 
 +{{ math104-f21:math_104-final.pdf |final exam and solution}}, [[math104-f21:final-mistakes]], [[final-grades]]
  
  
  
  
math104-f21/start.txt · Last modified: 2022/01/11 10:57 by pzhou

Page Tools

Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
CC Attribution-Share Alike 4.0 International Donate Powered by PHP Valid HTML5 Valid CSS Driven by DokuWiki