Computational Functional Analysis 2nd Edition by Ramon E Moore 1904275249 9781904275244

Computational Functional Analysis 2nd Edition by Ramon E. Moore, Michael J. Cloud – Ebook PDF Instant Download/Delivery: 1904275249, 9781904275244

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ISBN 10 : 1904275249
ISBN 13 : 9781904275244
Author: Ramon E. Moore, Michael J. Cloud

This course text fills a gap for first-year graduate-level students reading applied functional analysis or advanced engineering analysis and modern control theory. Containing 100 problem-exercises, answers, and tutorial hints, the first edition is often cited as a standard reference. Making a unique contribution to numerical analysis for operator equations, it introduces interval analysis into the mainstream of computational functional analysis, and discusses the elegant techniques for reproducing Kernel Hilbert spaces. There is discussion of a successful ‘‘hybrid’’ method for difficult real-life problems, with a balance between coverage of linear and non-linear operator equations. The authors successful teaching philosophy: ‘‘We learn by doing’’ is reflected throughout the book.

Computational Functional Analysis 2nd Edition Table of contents:

1 Introduction
2 Linear spaces
Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7
Exercise 8
Exercise 9
3 Topological spaces
Exercise 10
Exercise 11
Exercise 12
4 Metric spaces
Exercise 13
Exercise 14
Exercise 15
Exercise 16
Exercise 17
Exercise 18
Exercise 19
Exercise 20
Exercise 21
5 Normed linear spaces and Banach spaces
Exercise 22
Exercise 23
Exercise 24
Exercise 25
Exercise 26
Exercise 27
Exercise 28
6 Inner product spaces and Hilbert spaces
Exercise 29
Exercise 30
Exercise 31
Exercise 32
Exercise 33
Exercise 34
Exercise 35
Exercise 36
Exercise 37
Exercise 38
Exercise 39
7 Linear functionals
Exercise 40
Exercise 41
Exercise 42
Exercise 43
Exercise 44
Exercise 45
8 Types of convergence in function spaces
Exercise 46
Exercise 47
Exercise 48
Exercise 49
Exercise 50
Exercise 51
Exercise 52
9 Reproducing kernel Hilbert spaces
Exercise 53
Exercise 54
Exercise 55
Exercise 56
Exercise 57
10 Order relations in function spaces
Exercise 58
Exercise 59
Exercise 60
Exercise 61
Exercise 62
Exercise 63
11 Operators in function spaces
Exercise 64
Exercise 65
Exercise 66
Exercise 67
Exercise 68
Exercise 69
Exercise 70
Exercise 71
Exercise 72
Exercise 73
Exercise 74
12 Completely continuous (compact) operators
Exercise 75
Exercise 76
Exercise 77
Exercise 78
Exercise 79
Exercise 80
13 Approximation methods for linear operator equations
Exercise 81
Exercise 82
Exercise 83
1. Galerkin’s method in Hilbert spaces
Exercise 84
2. Collocation methods
Exercise 85
Exercise 86
3. Finite difference methods
Exercise 87
14 Interval methods for operator equations
Exercise 88
Exercise 89
15 Contraction mappings and iterative methods for operator equations in fixed point form
Exercise 90
Exercise 91
Exercise 92
Exercise 93
Exercise 94
Exercise 95
Exercise 96
16 Fréchet derivatives
Exercise 97
Exercise 98
Exercise 99
Exercise 100
Exercise 101
17 Newton’s method in Banach spaces
Exercise 102
18 Variants of Newton’s method
Exercise 103
19 Homotopy and continuation methods
Davidenko’s method
Computational aspects
20 A hybrid method for a free boundary problem
Hints for selected exercises
Further reading

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