Book:Tom M. Apostol/Calculus Volume 1
Tom M. Apostol: Calculus Volume 1
Published $\text {1967}$, John Wiley & Sons, Inc.
Subject Matter
Contents
1. Introduction
- Part 1: Historical Introduction
- Part 2: Some Basic Concepts of the Theory of Sets
- Part 3: A Set of Axioms for the Real-Number System
- Part 4: Mathematical Induction, Summation Notation, and Related Topics
$\S 1$ The Concepts of Integral Calculus
$\S 2$ Some Applications of Integration
$\S 3$ Continuous Functions
$\S 4$ Differential Calculus
$\S 5$ The Relation between Integration and Differentiation
$\S 6$ The Logarithm, the Exponential, and the Inverse Trigonometrical Functions
$\S 7$ Polynomial Approximations to Functions
$\S 8$ Introduction to Differential Equations
$\S 9$ Complex Numbers
$\S 10$ Sequences, Infinite Series, and Improper Integrals
$\S 11$ Sequences and Series of Functions
$\S 12$ Vector Algebra
$\S 13$ Applications of Vector Algebra to Analytic Geometry
$\S 14$ Calculus of Vector-Valued Functions
$\S 15$ Linear Spaces
$\S 16$ Linear Transformations and Matrices