Mathematical Methods of Engineering Analysis

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Sets and Functions
This introductory chapter is devoted to general notions regarding sets, functions, sequences, and series. The aim is to introduce and review the basic notation, terminology,conventions, and elementary facts
Metric Spaces Basic questions of analysis on the real line are tied to the notions of closeness and distances between points. The same issue of closeness comes up in more complicated settings, for instance, like when we try to approximate a function by a simpler function.Our aim is to introduce the idea of distance in general, so that we can talk of the distancebetween two functions with the same conceptual ease as when we talk of the distance between two points in the plane. After that, we discuss the main issues: convergence,continuity, approximations. All along, there will be examples of different spaces and different ways of measuring distances
Functions on Metric Spaces
Differential and Integral Equations
Convex Analysis
Measure and Integration

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