Description
Book SynopsisAn 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.
Table of ContentsI. 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
1. The Concepts of Integral Calculus
2. Some Applications of Integration
3. Continuous Functions
4. Differential Calculus
5. The Relation Between Integration and Differentiation
6. The Logarithm,the Exponential,and the Inverse Trigonmetric Functions
7. Polynomial Approximations to Functions
8. Introduction to Differential Equations
9. Complex Numbers
10. Sequences, Infinite Series, Improper Integrals
11. Sequences and Series of functions
12. Vector algebra
13. Applications of Vector Algebra to Analytic Geometry
14. Calculus of Vector Valued Functions
15. Linear Spaces
16. Linear Transformations and Matrices
Answers to exercises 617
Index 657
