556 pages, 10x7 inches
Nov 2001 Hardcover
ISBN 1-58949-019-3
US$88

 
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This is a book on basic analysis and related topics. It presents the most important theorems in measure and integration, an introduction to functional analysis, the big advanced calculus theorems about the Frechet derivative including the implicit function theorem, and other topics including fixed point theorems and applications, the Brouwer degree, and an introduction to the generalized Riemann integral. Although there are some abstract topics, the emphasis is on analysis which takes place in the context of n dimensional Euclidean space.

The book is directed to advanced undergraduates and beginning graduate students in math and physical science who are interested in analysis and is self contained for this audience. It could be used as a textbook for a two semester course.

 

 Preface
1. Basic set theory
 2. Linear algebra
 3. General topology
 4. Spaces of continuous functions
 5. Abstract measure and integration
 6. The construction of measures
 7. Lebesgue measure
 8. Product measure
 9. Fourier series
 10. The Frechet derivative		 11. Change of variables for C^1 maps
12. The L^p spaces
13. Fourier transforms
14. Banach spaces
15. Hilbert spaces
16. Brouwer degree
17. Differential forms
18. Representation theorems
19. Weak derivatives
20. Fundamental theorem of calculus
 App. A The Hausdorff maximal theorem
 App. B The generalized Riemann integral 


 

Kenneth Kuttler received his Ph.D from the University of Texas at Austin in 1981. He is a professor of mathematics at Brigham Young University. Previous to being at Brigham Young University he was an associate professor in the Math Science department at Michigan Tech. University for  roughly 15 years. His research interest is in abstract methods for  nonlinear partial differential equations and variational inequalities. Professor Kuttler has been teaching various math courses. His publications include many research papers in his specialty and a graduate textbook, Modern Analysis (1996, CRC Press).