Mathematical Methods

PrefaceChapter One. Algebraic Theory of 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 Applications 13. Algebraic Theory of Tensors BibliographyChapter 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 BibliographyChapter Three. The Lebesgue Integral and Related Topics 1. 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 BibliographySubject and Author IndexIndex of Notation