I'm a physics major (undergrad) who wants to learn real and complex analysis, but don't have the time to do the courses in my programme. Can anyone recommend a good textbook for learning the subjects on your own?
Real analysis is a branch of mathematics that deals with the study of real numbers and their properties. It is concerned with the rigorous examination of mathematical concepts and their applications in calculus, geometry, and other areas of mathematics.
A real analysis textbook typically covers topics such as real number systems, sequences and series, continuity, differentiation, integration, and metric spaces.
Real analysis has various applications in fields such as physics, engineering, economics, and computer science. It is used to study and analyze complex systems and phenomena by providing a rigorous mathematical framework.
A strong foundation in calculus, linear algebra, and mathematical proofs is necessary to understand a real analysis textbook. Familiarity with mathematical notation and logical reasoning is also important.
Some recommended real analysis textbooks for beginners include "Principles of Mathematical Analysis" by Walter Rudin, "Real Analysis: A First Course" by Russell Gordon, and "Understanding Analysis" by Stephen Abbott. It is important to choose a textbook that is suitable for one's level of mathematical background and offers clear explanations and examples.