This is a brief bibliography. Some of the books listed here provide the necessary background. Others are suggested as collateral and further reading.

Analysis

Several generations of mathematics students have learnt their analysis from the classic

W. Rudin, Principles of Mathematical Analysis, McGraw Hill, first published in 1953, 3rd ed., 1976.

Chapters 1–8 of Rudin provide adequate preparation for reading most of this book. For some of the sections more advanced facts about integration are needed. These may be found in Chapter 10 of Rudin, and in greater detail in Part 1 of another famous text:

H. L. Royden, Real Analysis, MacMillan, 3rd ed., 1988.

Elementary facts about differential equations that we have used in this book are generally taught as applications of the Calculus. These may be found, for example, in

R. Courant, Differential and Integral Calculus, 2 volumes, Wiley Classics Library Edition, 1988.

or, in

W. Kaplan, Advanced Calculus, Pearson Addison-Wesley, 5th ed., 2002.

For a more detailed study of differential equations the reader may see

W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 7th ed., Wiley Text Books, 2002.

Chapter 10 of this book, titled “Partial differential equations and Fourier Series,” contains topics close to the ones we have studied in the early sections.

We have used elementary properties of complex numbers and functions in this book. At places we have pointed out connections with deeper facts in Complex Analysis.