A Course in Real Analysis

A Course in Real Analysis Test Bank provides a rigorous treatment of the foundations of differential and integral calculus at the advanced undergraduate level. The content of this test bank has been extensively tested in the author’s two-semester undergraduate course on real analysis at The George Washington University.

The first part of the test bank covers the calculus of functions of one variable, including traditional topics such as sequences, continuity, differentiability, Riemann integrability, numerical series, and convergence of sequences and series of functions. Optional sections on Stirling’s formula, functions of bounded variation, Riemann–Stieltjes integration, and other topics are also included.

The second part focuses on functions of multiple variables, introducing topological concepts necessary to describe analytical properties of multivariable functions. It also discusses differentiability and integrability of multivariable functions and develops the theory of differential forms on surfaces in Rn.

The third part includes appendices on set theory and linear algebra, as well as solutions to some of the exercises. A complete solutions manual offers full solutions to all exercises for qualifying instructors.

With clear proofs, detailed examples, and numerous exercises, this test bank offers a comprehensive treatment of the subject. It progresses from single-variable to multivariable functions, providing a logical progression of material that will prepare students for more advanced research-based courses.

FAQs

What is included in this A Course in Real Analysis Test Bank?

This test bank includes a rigorous treatment of differential and integral calculus, covering topics such as sequences, continuity, differentiability, integrability, and multivariable functions.

Are solutions provided for the exercises in this test bank?

Yes, a complete solutions manual is included, offering full solutions to all exercises for instructors.

Is this test bank suitable for advanced undergraduate courses?

Yes, this test bank is designed for advanced undergraduate courses and provides a thorough preparation for more advanced research-based courses.

Conclusion

The A Course in Real Analysis Test Bank offers a comprehensive and rigorous treatment of calculus at the advanced undergraduate level. With detailed examples, clear proofs, and a solutions manual for exercises, this test bank is an essential resource for instructors teaching real analysis courses.