|C o o r d i n a t e s (4,8,0)|
Student: Joe Erickson (firstname.lastname@example.org)
May 03, 2015 - Chapter 11 will be in the spirit of Chapter 3 of Spivak's Calculus on Manifolds. Chapter 12 on differential forms will be a basic treatment of 1-forms and 2-forms on the plane and in space, which is all that is needed most of the time in classical branches of analysis dealing with, say, functions of a single complex variable and harmonic functions. The main source will be the corresponding chapter in Buck's Advanced Calculus, and also section 2.6 in Fleming's Functions of Several Variables.
January 01, 2015 - The Implicit Function Theorem and its proof is done.
December 28, 2014 - The Inverse Function Theorem and its proof is now done.
December 13, 2014 - Work on Chapter 10 begins in earnest, with primary reference being Chapter 9 of Rudin's Principles of Mathematical Analysis.
November 29, 2014 - I've reshuffled the chapters some, and thrown three chapters out. In particular I've removed a chapter on differential forms, since that is better done in a book on manifolds. The current line-up of chapters is similar to that in Rudin's "Principles of Mathematical Analysis."
May 13, 2013 - A textbook on the subject of introductory mathematical analysis (otherwise known as advanced calculus) will be under development here. All document links except for Chapter 7 are currently nonfunctional. Regarding Chapter 6, it is very much under construction, with some references to theorems or definitions in the Calculus Notes still present, and some proofs still needing updating to bring them into conformity with the more "grown up" definition of limit used in analysis.
Elementary Analysis 08/31/15 - 72
1. The Real & Complex Number Systems
2. Basic Topology
3. Sequences & Series of Numbers
6. Riemann Integration 05/15/13 - 22
7. The Riemann-Stieltjes Integral
8. Sequences & Series of Functions
9. Power Series & Special Functions
10. Differentiation in Euclidean Space 08/31/15 - 50
11. Integration in Euclidean Space
12. Differential Forms