Linear Algebra

Developed from the author's successful two-volume Calculus text this book presents Linear Algebra without emphasis on abstraction or formalization. To accommodate a variety of backgrounds, the text begins with a review of prerequisites divided into precalculus and calculus prerequisites. It continues to cover vector algebra, analytic geometry, linear spaces, determinants, linear differential equations and more.Dieses für einen breiten Leserkreis verständlich geschriebene Buch richtet sich besonders an Interessenten, die sich lange nicht mit Mathematik beschäftigt haben und nun eine grundlegende Einführung in die lineare Algebra ohne Überbetonung von Abstraktion und Formalismen suchen. Mit vielen Beispielen für die Anwendung auf Differentialgleichungen.

0. REVIEW OF PREREQUISITES

Part 1. Pre-Calculus Prerequisites 1

Part 2.Calculus Prerequisites 14

1. Vector Algebra 25

2. Applications of Vector Algebra to Analytic Geometry 51

3. Linear Spaces 91

4. Linear Transformations and Matrices 119

5. Determinants 161

6. Eigenvalues and Eigenvectors 187

7. Eigenvalues of Operators Acting on Euclidean Spaces 217

8. Applications to Linear Differential Equations 247

9. Applications to Systems of Differential Equations 273

10. The Method of Successive Approximations 303

Answers to Exercises 321

Index 343

Aus dem Inhalt:
Review of Prerequisites;
Vector Algebra;
Applications of Vector Algebra to Analytic Geometry;
Linear Spaces;
Linear Transformations and Matrices;
Determinants;
Eigenvalues and Eigenvectors;
Eigenvalues of Operators Acting on Euclidean Spaces;
Calculus Prerequisites;
Applications to Linear Differential Equations;
Applications to Systems of Differential Equations;
The Method of Successive Approximations. TOM M. APOSTOL, Emeritus Professor at the California Institute of Technology, is the author of several highly regarded texts on calculus, analysis, and number theory, and is Director of Project MATHEMATICS!, a series of computer-animated mathematics videotapes. A first course with applications to differential equations

This text provides ample coverage of major topics traditionally taught in a first course on linear algebra: linear spaces, independence, orthogonality, linear transformations, matrices, eigenvalues, and quadratic forms. The last three chapters describe applications to differential equations. Although much of the material has been extracted from the author's two-volume Calculus, the present text is designed to be independent of the Calculus volumes. Some topics have been revised or rearranged, and some new material has been added (for example, the triangularization theorem and the Jordan normal form). A review chapter contains pre-calculus prerequisites needed for the material on linear algebra in Chapters 1 through 7 and calculus prerequisites needed for the applications to differential equations in Chapters 8 through 10.

Special features

• Clarity of exposition that has characterized four decades of the author's writings
• Well-chosen examples and classroom-tested exercises that increase understanding of the concepts
• An arrangement of material that accommodates a variety of backgrounds and interests
• Early chapters on vectors and geometry that motivate abstract concepts in later chapters
• The exponential matrix explored through an interplay between linear algebra and matrix calculus