Front Cover; Linear Algebra / Normed Spaces / Distributions / Integration; Copyright Page; PREFACE; Table of Contents; CHAPTER ONE. ALGEBRAIC THEORYOF VECTOR SPACES; 1. VECTOR SPACES; 2. GENERATING SETS, LINEARLY INDEPENDENT SETS, AND BASES; 3. DIMENSION OF A VECTOR SPACE; 4. LINEAR TRANSFORMATIONS; 5. LINEAR FUNCTIONALS; 6. RECTANGULAR MATRICES; 7. SQUARE MATRICES; 8. DETERMINANTS; 9. SYSTEMS OF LINEAR EQUATIONS; 10. EIGENVALUE PROBLEMS; 11. USE OF EIGENVECTORS AND GENERALIZED EIGENVECTORS IN THE REPRESENTATION OF LINEAR OPERATORS.

12. further representation theorems for linear operators and applications13. algebraic theory of tensors; bibliography; chapter two. introduction to functional analysis. distributions; 1. various kinds of convergence; 2. metric spaces; 3. normed vector spaces; 4. completeness and completion; 5. the banach spaces l, lp, and c; 6. continuous linear functionals; 7. distributions or generalized functions (part 1); 8. distributions or generalized functions (part 2); 9. delta sequences and convergence and approximation; 10. spanning sets and schauder bases; bibliography.

Chapter three. the lebesgue integral and related topics1. definition of the lebesgue integral; 2. approximation of integrable functions and applications; 3. integration of sequences and series; 4. lebesgue measure; 5. functions of bounded variation and the stieltjes integral; 6. rules based on the use of indefinite integrals; 7. multiple integrals; 8. curves and line integrals; 9. holomorphic functions and integrals in the complex plane; bibliography; subject and author index; index of notation.