Is a math book about calculus which is written by Tom Apostle. This book gives an introduction to calculus which is also integrated with an introduction to linear algebra. The relationship between algebra and calculus is explained in the book too.

**Calculus, Volume 1: One-Variable Calculus with an Introduction to Linear Algebra PDF ****Review:**

In the book, the author has talked about algebra and calculus. It is a book for students and teachers, for students to learn about Calculus and for the teacher to teach the students about it. The author has explained theorems of calculus in the book and after that, he has also given an explanation about the theorems. The proofs of these theorems are also given in the book for the information and understanding of the readers. Rules of integration and differentiation are mentioned in the book and there are easy exercises following the chapters for the reader to test their skills and knowledge.

**Calculus Pdf Features:**

- The book is made interesting by the help of historical references. The author has talked of a historical aspect before he explains every new concept.
- The answers to each exercise in the book are also given at the end so that the reader can see if they solved the problems correctly.

**Table of Contents:**

Historical Introduction.

Some Basic Concepts of the Theory of Sets.

A Set of Axioms for the Real Number System.

Mathematical Induction, Summation Notation, and Related Topics.

The Concepts of the Integral Calculus.

Some Applications of Differentiation.

Continuous Functions.

Differential Calculus.

The Relation between Integration and Differentiation.

The Logarithm, the Exponential, and the Inverse Trigonometric Functions.

Polynomial Approximations to Functions.

Introduction to Differential Equations.

Complex Numbers.

Sequences, Infinite Series, Improper Integrals.

Sequences and Series of Functions.

Vector Algebra.

Applications of Vector Algebra to Analytic Geometry.

Calculus of Vector-Valued Functions.

Linear Spaces.

Linear Transformations and Matrices.

Exercises.

Answers to Exercises.

Index.

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