Cover
Half-title page
Series page
Title page
Copyright page
Dedication
Contents
Preface
1 Infinite Sequences
1.1 Introduction to Sequences
1.2 Notation
1.3 Example Sequences
1.4 Limits and Convergence
1.5 Examples
2 Infinite Series
2.1 Introduction to Series
2.2 Convergence and the Sequence of Partial Sums
2.3 Testing Infinite Series for Convergence
2.4 Alternating Series
2.5 Conditionally Convergent Series
2.6 Examples
3 Power Series
3.1 Interval of Convergence
3.2 Properties of Power Series
3.3 Power Series Expansions of Functions
3.4 Other Methods for Constructing Power Series Expansions
3.5 Accuracy of Series Approximations
3.6 Asymptotic Series Expansions
3.7 Examples
4 Complex Infinite Series
4.1 Complex Numbers
4.2 Complex Infinite Series
4.3 Determining the Disk of Convergence
4.4 Functions of Complex Variables
4.5 Laurent Series
4.6 Examples
5 Series Solutions for Differential Equations
5.1 Introduction
5.2 Series Solutions for Differential Equations
5.3 Generalized Series Solutions and the Method of Frobenius
5.4 Introduction to Special Functions: Bessel, Hermite, and Legendre
5.5 Examples
6 Fourier, Legendre, and Fourier-Bessel Series
6.1 Introduction
6.2 Fourier Series
6.3 Legendre Series
6.4 Fourier-Bessel Series
6.5 Examples
References
Index