Download Calculus On Manifolds Pdf Ebook Free

Calculus on Manifolds is a book written by mathematician Michael Spivak. The book was originally published in 2003 and offers a brief introduction to the theory of vector-valued functions of different variables. Manifolds of Euclidean space are the subject of the book. A book is a modern approach to most topics of Calculus that are normally explained with conventional methods in other books.

Calculus on Manifolds Pdf Review:

In the book, Spivak tries to explain vector calculus in a modern way, just the way it is used in today’s time. Similarly, multivariable is explained in a way that modern mathematicians use it and look at it. The book is suitable for a university student. One needs to have prior knowledge of math and especially Calculus in order to understand the terminologies and the concepts explained in the book. The book is suitable for those students who have previously only studied one variable calculus and now need to go to the advanced level of study at university level.

Calculus On Manifolds Pdf

Calculus on Manifolds Pdf Features:

  • The cover of the book is quite interesting as it has snippets of a legendary letter.
  • This was the letter sent by Lord Kelvin to Sir George Stokes in which Lord has disclosed the theorem that later became knows as Kelvin-Stokes theorem.

Table of Contents:

  1. Functions on Euclidean Space
    1. Norm and inner Product
    2. Subsets of Euclidean Space
    3. Functions and Continuity
  2. Differentiation
    1. Basic Definitions
    2. Basic Theorems
    3. Partial Derivatives
    4. Inverse Functions
    5. Implicit Functions
    6. Notation
  3. Integration
    1. Basic Definitions
    2. Measure Zero and Content Zero
    3. Integrable Functions
    4. Fubini’s Theorem
    5. Partitions of Unity
    6. Change of Variable
  4. Integration of Chains
    1. Algebraic Preliminaries
    2. Fields and Forms
    3. Geometric Preliminaries
    4. The Fundamental Theorem of Calculus
  5. Integration of Manifolds
    1. Manifolds
    2. Fields and Forms on Manifolds
    3. Stokes’ Theorem on Manifolds
    4. The Volume Element
    5. The Classical Theorems

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