A Course in Mathematical Analysis Volume 1: Derivatives and Differentials; Definite Integrals; Expansion in Series; Applications to Geometry (Dover Books on Mathematics)

Édouard 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 first of the three volumes, include derivatives and differentials; implicit functions; functional determinants; change of variable; Taylor's series; maxima and minima; definite and indefinite integrals; double and multiple integrals; integration of total differentials; infinite series; power series; trigonometric series; plane and skew curves; and surfaces. Volume 2 addresses functions of a complex variable and differential equations; and Volume 3 explores variations of solutions, partial differential equations of the second order, integral equations, and calculus of variations.