Contents

Chapter 6:- Differentiation
6.1 The Derivative
6.2 The Mean Value Teorem
6.3 L'Hospital's Rules
6.4 Taylor's Theorem

Chapter 7:- The Riemann Integral
7.1 Rieman Integral
7.2 Riemann Integable Functions
7.3 The Fundamental Theorem
7.4 The Darboux Integral
7.5 Approximate Integration
Chapter 8:- Sequences of Functions
8.1 Pointwise and Uniform Convergence
8.2 Interchange of Limits
8.3 The Exponential and Logarithmic Functions
8.4 The Trignometric Functions

Chapter 9:- Infinite Series
9.1 Absolute Convergence
9.2 Tests in absolute Convergence
9.3 Tests for Non-absolute Convergence
9.4 Series of Functions

Chapter 10:- The Generalized Rieman Integral
10.1 Difinition and Main Properties
10.2 Improper and Lebesgue Integrals
10.3 Infinite Integrals
10.4 Convergence Theorems

Chapter 11:- A Glimpse Into Topology
11.1 Open and Close Set of R
11.2 Compact Sets
11.3 Continuous Functions
11.4 Metric Spaces

Appendix A:- Logic and Proofs
Appendix B:- Finite and Countable Sets
Appendix C:- The Rieman and Lebesgue Criteria
Appendix D:- Approximate Integration
Appendix E:- Two Examples
References
Photo Credits
Hints for Selected Exercises

Index