Mathematical Analysis Fundamentals

Mathematical Analysis Fundamentals is designed to serve as a transition from calculus to rigorous analysis. Ideal for instructors who require a condensed mathematical analysis book, as well as for anyone looking to gain expertise in that area.

Agamirza Bashirov (Author)

9780128102695

Paperback, published 19 August 2016

362 pages
22.9 x 15.1 x 2.3 cm, 0.45 kg

"... the book does have numerous good exercises that test the student’s grasp and cover some advanced topics, and it does give thorough coverage of much of classical analysis…" --MAA Reviews, 2014

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.

1. Sets and Proofs 2. Numbers 3. Convergence 4. Point Set Topology 5. Continuity 6. The Space 7. Differentiation8. Bounded Variation 9. Reimann Integration10. Generalizations of Reimann Integration 11. Transcendental Functions 12. Fourier Series and Integers

Subject Areas: Real analysis, real variables [PBKB]