One-variable calculus, with an introduction to linear algebra

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.