An Introduction to Analysis (Mathematics)

✍ Scribed by James R. Kirkwood

• Publisher: PWS Pub. Co.
• Year: 1994
• Tongue: English
• Leaves: 285
• Edition: 2 Sub
• Category: Library

✦ Synopsis

Provides introduction to analysis of real-valued functions of one variable. This text is for a student's first abstract mathematics course. Writing style is less formal and material presented in a way such that the student can develop an intuition for the subject and acquire some experience in constructing proofs. The slower pace of the subject and the attention given to examples are meant to ease the student's transition from computational to theoretical mathematics.

✦ Table of Contents

Title page......Page 1
Contents......Page 3
Preface......Page 5
Introduction......Page 8
1-1 Sets and Functions......Page 11
1-2 Properties of the Real Numbers as an Ordered Field......Page 21
1-3 The Completeness Axiom......Page 32
2-1 Sequences of Real Numbers......Page 43
2-2 Subsequences......Page 55
2-3 The Bolzano-Weierstrass Theorem......Page 59
3-1 Topology of the Real Numbers......Page 67
4-1 Limits and Continuity......Page 80
4-2 Monotone and Inverse Functions......Page 99
5-1 The Derivative of a Function......Page 111
5-2 Some Mean Value Theorems......Page 122
6-1 The Riemann Integral......Page 139
6-2 Some Properties and Applications of the Riemann Integral......Page 153
6-3 The Riemann-Stieltjes Integral (Optional)......Page 168
7-1 Tests for Convergence of Series......Page 181
7-2 Operations Involving Series......Page 191
8-1 Sequences of Functions......Page 207
8-2 Series of Functions......Page 222
8-3 Taylor Series......Page 234
9-1 Fourier Coefficients......Page 245
9-2 Representation by Fourier Series......Page 252
Bibliography......Page 273
Appendix: Hints and Answers for Selected Exercises......Page 274
Index......Page 282