**Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability, Second Edition by Tom M. Apostol, ISBN-13: 978-0471000075**

[PDF eBook eTextbook]

- Publisher: Wiley; 2nd edition (January 16, 1991)
- Language: English
- 673 pages
- ISBN-10: 0471000078
- ISBN-13: 978-0471000075

An 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

*, an interesting historical introduction precedes each important new concept.*

**first edition****Table of Contents:**

Linear Analysis.

Linear Spaces.

Linear Transformations and Matrices.

Determinants.

Eigenvalues and Eigenvectors.

Eigenvalues of Operators Acting on Euclidean Spaces.

Linear **Differential Equations**.

Systems of Differential Equations.

Nonlinear Analysis.

Differential Calculus of Scalar and Vector Fields.

Applications of the Differential Calculus.

Line Integrals.

Special Topics.

Set Functions and Elementary **Probability**.

Calculus of Probabilities.

Introduction to Numerical Analysis.

* TOM M. APOSTOL, *Emeritus Professor at the

*is the author of several highly regarded texts on calculus, analysis, and number theory, and is Director of Project*

**California Institute of Technology,****MATHEMATICS**!, a series of computer-animated mathematics videotapes.

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