# Real Analysis Study Materials 2020 – Download B.Sc, M.Sc Mathematics E-Books

Download Real Analysis Study Materials 2020. In this article, we are going to provide Study Notes for the School of Sciences. These study books will be more useful to Mathematics Students. The basic topics in this subject are Real Numbers, Functions, Sequence, Series, Integrability, Limit and Continuity, etc. Download Unit PDF files, Important Questions, Chapters & Topics by the links provided below on our Exams Time.Â

## Real Analysis Study Materials

 Name of the Subject Real AnalysisÂ Category School of Sciences Useful for B.Sc, M.Sc (Mathematics) Course Type Under Graduation and Post Graduation Courses Article on Study Materials 2020 Study Material Format PDF Download Other Study Materials Click Here

## Chapters & Topics

Real Numbers and Functions

• Real Functions
• Topology of the Real Line
• Structure of Real Numbers
• Sets and Numbers

Sequences and Series

• General Series
• Positive Term Series
• Sequences

Limit and Continuity

• Properties of Continuous Functions
• Continuity
• Limit of a Function
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Differentiability

• Higher-Order Derivatives
• Mean-Value Theorems
• Derivatives

Integrability

• Sequences and Series of Functions
• Integrability and Differentiability
• The Riemann Integration

## Subject in the Universities

This subject will be useful to the students who are pursuing a Bachelor of Science. The following university students can also download Real AnalysisÂ study materials :

• IGNOU
• Uttarakhand Open University
• University of Calicut
• Pondicherry University

### Subject in the Semesters

Real Analysis subject will be studied by the students in the following semesters of their respective courses :

• B.Sc Mathematics VI Semester
• M.Sc Mathematics I Year

### Important Topics

We have mentioned some of the important topics of Real Analysis subject :

• Algebraic Functions
• Algebraic Combinations of Functions
• Notion of an Algebraic Function
• Polynomial Functions
• Rational Functions
• Irrational Functions
• Modulus of a Real Number
• Open Sets
• Closed Sets
• Order Relations in’Real Numbers
• Sets and Functions
• The Complex Numbers
• Mathematical Induction
• Leibnitz’s Series
• Absolute and conditional Convergence
• Riemann Integrability
• Riemann Integrable Functions ‘
• Algebra of Integrable Functions
• Computing an Integral
• Fundamental Theorem of Calculus
• Mean Value Theorems
• First Mean Value Theorem
• Second Mean Value Theorem
• Sequences of Functions
• Taylor’s Theorem
• Rolle’s Theorem
• Mean Value’Theorem
• Lagrange’s Meal] Value Theorem
• Cauchy’s Mean Value Theorem
• Generalized Mean Value Theorem
• Intermediate Value Theorem for Derivatives
• Darboux Theorem
• Continuous Functions
• Algebra of Continuous Functions
• Non-continuous Functions
• Finite Limits
• Infinite Limits
• Sequential Limits
• Algebra of Limits
• Infinite Series
• Series of Positive Terms
• General Tests of Convergence
• D’Alembert’s Ratio Test
• Cauchy’s Root Test
• Cauchy’s Integral Test
• Raabe’s Test
• Ciauss’s Test
• Real Sequences
• Bounded Sequences
• Monotonic Sequences
• Convergent Sequences
• Criteria for the Convergence of Sequences
• Cauchy Sequences
• Algebra of Convergent Sequences

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