A Basic Course in Real Analysis
Kumar, Ajit
A Basic Course in Real Analysis / Ajit Kumar - Boca Raton : Taylor & Francis, ©2014. - xix, 302 pages : illustrations ; 24 cm
Note continued: 5.4. Cauchy Product of Two Infinite Series --
6.1. Darboux Integrability --
6.2. Properties of the Integral --
6.3. Fundamental Theorems of Calculus --
6.4. Mean Value Theorems for Integrals --
6.5. Integral Form of the Remainder --
6.6. Riemann's Original Definition --
6.7. Sum of an Infinite Series as an Integral --
6.8. Logarithmic and Exponential Functions --
6.9. Improper Riemann Integrals --
7.1. Pointwise Convergence --
7.2. Uniform Convergence --
7.3. Consequences of Uniform Convergence --
7.4. Series of Functions --
7.5. Power Series --
7.6. Taylor Series of a Smooth Function --
7.7. Binomial Series --
7.8. Weierstrass Approximation Theorem --
D.1. Chapter 1 --
D.2. Chapter 2 --
D.3. Chapter 3 --
D.4. Chapter 4 --
D.5. Chapter 5 --
D.6. Chapter 6 --
D.7. Chapter 7.
Based on the authors' combined 35 years of experience in teaching, A Basic Course in Real Analysis introduces students to the aspects of real analysis in a friendly way. The authors offer insights into the way a typical mathematician works observing patterns, conducting experiments by means of looking at or creating examples, trying to understand the underlying principles, and coming up with guesses or conjectures and then proving them rigorously based on his or her explorations
9781498774789
Mathematics
Analysis
Functions of real variables --
Mathematical analysis --
Numbers, Real -
Mathematical analysis.
Power Series
515.8 KUM
A Basic Course in Real Analysis / Ajit Kumar - Boca Raton : Taylor & Francis, ©2014. - xix, 302 pages : illustrations ; 24 cm
Note continued: 5.4. Cauchy Product of Two Infinite Series --
6.1. Darboux Integrability --
6.2. Properties of the Integral --
6.3. Fundamental Theorems of Calculus --
6.4. Mean Value Theorems for Integrals --
6.5. Integral Form of the Remainder --
6.6. Riemann's Original Definition --
6.7. Sum of an Infinite Series as an Integral --
6.8. Logarithmic and Exponential Functions --
6.9. Improper Riemann Integrals --
7.1. Pointwise Convergence --
7.2. Uniform Convergence --
7.3. Consequences of Uniform Convergence --
7.4. Series of Functions --
7.5. Power Series --
7.6. Taylor Series of a Smooth Function --
7.7. Binomial Series --
7.8. Weierstrass Approximation Theorem --
D.1. Chapter 1 --
D.2. Chapter 2 --
D.3. Chapter 3 --
D.4. Chapter 4 --
D.5. Chapter 5 --
D.6. Chapter 6 --
D.7. Chapter 7.
Based on the authors' combined 35 years of experience in teaching, A Basic Course in Real Analysis introduces students to the aspects of real analysis in a friendly way. The authors offer insights into the way a typical mathematician works observing patterns, conducting experiments by means of looking at or creating examples, trying to understand the underlying principles, and coming up with guesses or conjectures and then proving them rigorously based on his or her explorations
9781498774789
Mathematics
Analysis
Functions of real variables --
Mathematical analysis --
Numbers, Real -
Mathematical analysis.
Power Series
515.8 KUM
