Analysis 1

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Title: Analysis 1
Author: Khalagai, Jairus M.

Part 1 consists of three units:

Unit 1 - Analysis on the real line

In this unit we start by decomposing the set of real numbers into its subsets. We then define the so called standard metric on to be able to study its structure which consists of concepts like open and closed intervals, neighbourhoods, interior and limit points leading to examples of open and closed subsets of . Countability of such subsets and numerical sequences are also essential in the structure of as a metric space. We also study functions defined on sets of real numbers with respect to concepts of continuity differentiability and integrability.

Unit 2 – Vector Analysis

This unit deals with mainly vector calculus and its applications. Thus we specifically consider concepts like gradient, divergence and curl. This leads to well known theorems like Green’s stokes divergence theorems and other related results. The curvilinear coordinates system is also given a treat in this unit.

Unit 3 – Complex Analysis

The main objective in the study of this unit is to define a function of a complex variable and then look at its degree of smoothness such as existence of limit, continuity and differentiability along the lines of calculus of functions of a real variable. Also a look at integration and power series involving a function of a complex variable will complete this unit.

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Date: 2010-11-17

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Files Size Format View Description 1.082Mb QuickTime video View/Open Introduction (QuickTime) 2.944Mb QuickTime video View/Open Overview (QuickTime)
Analysis 1.doc 1.539Mb Microsoft Word View/Open Part 1 (doc)
Analysis 1.pdf 773.5Kb PDF View/Open Part 1 (pdf)

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