Calculus Volume I  (English, Paperback, Apostol Tom M.)

Calculus Volume I by Tom M. Apostol provides students with a practical account of the equations and proofs in calculus and explains their origins, meaning, and applications.

Summary Of The Book

For a book that talks about equations and proofs, Calculus Volume I is highly compelling, thanks to Tom M. Apostol’s explanation of the concepts in calculus by relating it to simpler mathematical ideas empowering students with real practical knowledge.

Rightly regarded as a classic in mathematics, the book focusses on the words that explain the equations, detailing how the equations are derived, what they mean, and how they can be applied in real life. 

Apostol’s approach is at once, practical and formal, as he explains to students certain concepts that are rarely discussed in calculus due perceived difficulties in explanation. Apostol sweeps these aside as he explains difficult concepts like Lebesgue integrals in terms of set theory rather than using the measure-theory approach as is usually the case.

The book starts by introducing readers to the history of calculus and some basic concepts of set theory before explaining complicated ideas like summation notation and mathematical induction, continuous functions, differential calculus, relation between integration and differentiation, polynomial approximations to functions, and vector algebra.

Tom M. Apostol also talks about complex numbers, sequences, infinite series, improper integrals, applications of vector algebra to analytic geometry, vector-valued functions, and linear transformations and matrices. Apt for those wishing to advance their knowledge of calculus, Calculus Volume I not only clarifies but also tests their knowledge by featuring exercises and their solutions.

Calculus Volume I was first published in the year 1967 and is an influential college-level textbook. The book has become popular in the recent years as an alternative to those textbooks that focus on exercises or over-simplification resulting in sparseness of real knowledge. Calculus Volume 2 was published in the year 1969 and is intended for the second year of the course.

About Tom M. Apostol

Born in the year 1923 in Utah, Tom M. Apostol is an analytic number theorist and university professor.

Some of this other popular works include Mathematical Analysis: A Modern Approach to Advanced Calculus, Introduction to Analytic Number Theory, Calculus, Volume 2, Multi-variable Calculus And Linear Algebra With Applications To Differential Equations And Probability, and The Mechanical Universe: Mechanics and Heat, Advanced Edition.

Apostol is the creator and project director for Project MATHEMATICS! that produces videos to aid the teaching of mathematics to high school students. He has also worked with Mamikon Mnatsakanian in popularising visual calculus.

Apostol received his PhD in mathematics from the University of California, Berkeley, in 1948. He has since been a faculty member at his alma mater, Massachusetts Institute of Technology, and California Institute of Technology. In 2001, he was elected to the Academy of Athens. He became a fellow of the American Mathematical Society in 2012.