Measure theory, integration, weak differentiation of functions, and basic introduction to functional analysis are topics studied by virtually all graduate students in mathematics and applied sciences.

Analysis: Foundations and Applications covers the core mathematical topics of the subject, and will particularly attract the reader with a more applied view. The focus of this modern text is to prepare the potential researcher to a way of thinking in applied mathematics and partial differential equations. The exposition is hands-on and accommodating to this group with little or no unnecessary abstractions

This text covers the core mathematical topics of analysis and will attract the reader with a more applied view. The focus is to prepare the potential researcher to a "way of thinking" in applied mathematics and partial differential equations. The exposition is hands-on and accommodating to this group with little or no unnecessary abstractions. May be used in an introductory graduate course in analysis and measure theory, or as a preparatory text for students and researchers expecting to work in analysis, PDEs, and applied mathematics. It is a solid building block for approximation theory and probability, and it provides an excellent background for PDEs and the calculus of variations.