A Course in Mathematical Analysis Volume 2: Functions of a Complex Variable; Differential Equations (Dover Books on Mathematics)

Edouard Goursat's three-volume A Course in Mathematical Analysis remains a classic study and a thorough treatment of the fundamentals of calculus. As an advanced text for students with one year of calculus, it offers an exceptionally lucid exposition.
Subjects in this, the second of the three volumes, begin with functions of a complex variable and elements of the theory; the general theory of analytic functions according to Cauchy; single-valued analytic functions; analytic extension; and analytic functions of several variables. The second part of this volume covers differential equations, including elementary methods of integration; existence theorems; linear and non-linear differential equations; and partial differential equations of the first order.
The preceding volume in this series addresses applications to geometry, expansion in series, definite integrals, and derivatives and differentials; the succeeding volume explores variations of solutions, partial differential equations of the second order, integral equations, and calculus of variations.