Calculus, Vol. 1: One-Variable Calculus, With an Introduction to Linear Algebra

Description

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. As in the first edition, an interesting historical introduction precedes each important new concept.

MR0214705

The book is written for those who wish to have some knowledge of calculus and analytic geometry. The presentation differs considerably from what is usually found in standard books of the same nature. Each important new concept is preceded by a historical introduction and, whenever possible, is explained geometrically. Each chapter begins with an introduction and is followed by unsolved examples, some of which are illuminating while others are routine. Also, there are several worked examples to illustrate new concepts. Chapters 1–11 deal with integral calculus, continuous and differentiable functions, elementary differential equations, complex numbers, sequences and series. Chapters 12–14 contain vector algebra and the calculus of vector-valued functions, and the last two chapters give discussions on linear spaces, linear transformations and matrices. Reviewed by B. K. Lahiri