Rev. ed. of: Real analysis with real applications.

Includes bibliographical references (p. 505-506) and index.

1. Review -- 2. The real numbers -- 3. Series -- 4. Typology of Rn -- 5. Functions -- 6. Differentiation and integration -- 7. Norms and inner products -- 8. Limits of functions -- 9. Metric spaces -- 10. Approximation by polynomials -- 11. Discrete dynamical systems -- 12. Differential equations -- 13. Fourier series and physics -- 14. Fourier series and approximation -- 15. Wavelets -- 16. Convexity and optimization.

This new approach to real analysis stresses the use of the subject in applications, showing how the principles and theory of real analysis can be applied in various settings. Applications cover approximation by polynomials, discrete dynamical systems, differential equations, Fourier series and physics, Fourier series and approximation, wavelets, and convexity and optimization. Each chapter has many useful exercises. The treatment of the basic theory covers the real numbers, functions, and calculus, while emphasizing the role of normed vector spaces, and particularly of Rn. The applied chapters are mostly independent, giving the reader a choice of topics. This book is appropriate for students with a prior knowledge of both calculus and linear algebra who want a careful development of both analysis and its use in applications.