A Course in Mathematical Analysis [Hardcover]

The third volume of three providing a full and detailed account of undergraduate mathematical analysis.This is the third of three volumes that provide a full and detailed account of all those elements of real and complex analysis the undergraduate mathematics student can expect to encounter in their first two or three years of study. Numerous exercises, examples and applications are included.This is the third of three volumes that provide a full and detailed account of all those elements of real and complex analysis the undergraduate mathematics student can expect to encounter in their first two or three years of study. Numerous exercises, examples and applications are included.The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and teachers. Volume I focuses on the analysis of real-valued functions of a real variable. Volume II goes on to consider metric and topological spaces. This third volume covers complex analysis and the theory of measure and integration.Introduction; Part I. Complex Analysis: 1. Holomorphic functions and analytic functions; 2. The topology of the complex plane; 3. Complex integration; 4. Zeros and singularities; 5. The calculus of residues; 6. Conformal transformations; 7. Applications; Part II. Measure and Integration: 8. Lebesgue measure on R; 9. Measurable spaces and measurable functions; 10. Integration; 11. Constructing measures; 12. Signed measures and complex measures; 13. Measures on metric spaces; 14. Differentiation; 15. Applications; Index.