A Course in Modern Analysis and its Applications

Designed for one-semester courses at the senior undergraduate level, this 2003 book will appeal to mathematics undergraduates, to mathematics teachers, and to others who need to learn some mathematical analysis for use in other areas such as engineering, physics, biology or finance. Topics such as completeness and compactness are approached initially through convergence of sequences in metric space, and the emphasis remains on this approach. However, the alternative topological approach is described in a separate chapter. This gives the book more flexibility, making it especially useful as an introduction to more advanced areas such as functional analysis. Nominal divisions of pure and applied mathematics have been merged, leaving enough for students of either inclination to have a feeling for what further developments might look like. Applications have been included from such fields as differential and integral equations, systems of linear algebraic equations, approximation theory, numerical analysis and quantum mechanics.

• Painstakingly written approach through convergence of sequences, but gives space to topological view, so providing flexibility of use
• Applications in many areas of mathematics and science makes it pertinent to new quantitative approaches to engineering, physics and finance
• Begins with a comprehensive summary of notions of real analysis, then proceeds to an easy introduction to more advanced notions of functional analysis