In the present edition we have made changes in Chapter 1, mainly as a result of comments by Professor A. S. Besicovitch. Some theorems are stated more explicitly, a few proofs are added, and some are shortened. We are indebted to him for an elementary proof of the theorem of bounded convergence for Riemann integrals, which appears in the notes. In Chapter 6 the proof of Poisson's equation has been improved.

Preface

Chapter 1.The Real Variable

 2.Scalars and Vectors

 3.Tensors

 4.Matrices

 5.Multiple Integrals

 6.Potential Theory

 7.Operational Methods

 8.Physical Applications of the Operational Method

 9.Numerical Methods

 10.Caloulns of Variations

 11.Functions of a Complex Variable

 12.Contour Integration and Bromwich‘s Integral

 13.Conformal Representation

 14.Fourier‘s Theorem

 15.The Factorial and Related Functions

 16.Solution of Linear Differential Equations of the Second Order

 17.Asymptotic Expansions

 18.The Equations of Potential， Waves， and Heat Conduction

 19.Waves in One Dimension and Waves with Spherical Symmetry

 20.Conduction of Heat in One and Three Dimensions

 21.Bessel Functions

 22.Applications of Bessel Functions

 23.The Conflutent Hypergeomtrio Function

 24.Legendre Functions and Associated Functions

 25.Elliptic Functions

Notes

Appendix on Notatin

Index