Bashirov, Agamirza E. creator author. text bibliography Electronic books. Electronic books. ne 2014 1st ed. monographic eng

electronic resource

1 online resource. The author's goal is a rigorous presentation of the fundamentals of analysis, starting from elementary level and moving to the advanced coursework. The curriculum of all mathematics (pure or applied) and physics programs include a compulsory course in mathematical analysis. This book will serve as can serve a main textbook of such (one semester) courses. The book can also serve as additional reading for such courses as real analysis, functional analysis, harmonic analysis etc. For non-math major students requiring math beyond calculus, this is a more friendly approach than many math-centric options. Friendly and well-rounded presentation of pre-analysis topics such as sets, proof techniques and systems of numbers. Deeper discussion of the basic concept of convergence for the system of real numbers, pointing out its specific features, and for metric spaces Presentation of Riemann integration and its place in the whole integration theory for single variable, including the Kurzweil-Henstock integration Elements of multiplicative calculus aiming to demonstrate the non-absoluteness of Newtonian calculus. 1. Sets and proofs -- 2. Numbers -- 3. Convergence -- 4. Point set theory -- 5. Continuity -- 6. Space C(E, E') -- 7. Differentiation -- 8. Bounded variation -- 9. Riemann integration -- 10. Generalizations of Riemann integration -- 11. Transcendental functions -- 12. Fourier series and integrals. A.E. Bashirov. Includes bibliographical references. Mathematical analysis MATHEMATICS Calculus MATHEMATICS Mathematical Analysis Mathematical analysis Analysis QA300 515 Bashirov, Agamirza E. (OCoLC)870424847 9780128010501 0128010509 2014931794 http://www.sciencedirect.com/science/book/9780128010013 http://www.sciencedirect.com/science/book/9780128010013 N$T 140403 20190328114807.0 ocn875558741 eng