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IIT Palakkad
IIT Palakkad Logo

Real Analysis II 
offered by IIT Palakkad

  • A+ NAAC accredited
  • Public/Government Institute
  • Estd. 2015

Real Analysis II
 at 
IIT Palakkad 
Overview

Advanced Real Analysis: Delve deeper into mathematical rigor with Real Analysis II, exploring complex functions, sequences, and series intricacies.

Duration

12 weeks

Mode of learning

Online

Official Website

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Credential

Certificate

Real Analysis II
 at 
IIT Palakkad 
Highlights

  • Industry Support
  • Earn a Paid Certification
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Real Analysis II
 at 
IIT Palakkad 
Course details

Who should do this course?
  • Anyone Interested Learners
More about this course
  • This is the follow-up course to Real Analysis I. This time we deal with differentiation and integration of functions of several variables. First, we set the stage by studying metric spaces with special emphasis on normed vector spaces.
  • Even here we will encounter several deep theorems like the existence of the completion of metric space, the Arzela—Ascolli theorem as well as the famous Stone—Weierstrass theorem.
  • We will then study the derivative as a linear map and prove the famous implicit and inverse function theorems. These theorems will naturally lead on to the definition of a manifold.

Real Analysis II
 at 
IIT Palakkad 
Curriculum

Week 1:

Metric spaces and normed linear spaces

Week 2:

Compactness and completeness in metric spaces

Week 3:

The Arzelà–Ascoli and Stone--Weierstrass theorems

Week 4:

The derivative in several variables as a linear map I

Week 5:

The derivative in several variables as a linear map II

Week 6:

The inverse and implicit function theorems

Week 7:

Manifolds, Tangent spaces and Lagrange multipliers

Week 8:

A precis of curves and surfaces

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Real Analysis II
 at 
IIT Palakkad 
Faculty details

Prof. Jaikrishnan J

Real Analysis II
 at 
IIT Palakkad 
Entry Requirements

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Real Analysis II
 at 
IIT Palakkad 

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