Calculus Vol. 2 by Tom M. Apostol.The Art of Calc

Calculus Vol. 2
Multi-Variable Calculus and Linear Algebra with Applications
By
Tom M. Apostol

An introduction to the calculus, with an excellent balance between theory and technique. Integration is treated before differentiation--this is a departure from most modern texts, but it is historically correct, and it is the best way to establish the true connection between the integral and the derivative. Proofs of all the important theorems are given, generally preceded by geometric or intuitive discussion. This Second Edition introduces the mean-value theorems and their applications earlier in the text, incorporates a treatment of linear algebra, and contains many new and easier exercises.