Engineering Mathematics, Volume III

Table of contents

1. Cover
2. Title Page
3. Contents
4. About the Authors
5. Dedication
6. Preface
7. Chapter 1. Special Functions
   1. 1.1 - Introduction
   2. 1.2 - Gamma Function
   3. 1.3 - Recurrence Relation or Reduction Formula
   4. 1.4 - Various Integral Forms of Gamma Function
   5. Exercise 1.1
   6. 1.5 - Beta Function
   7. 1.6 - Various Integral Forms of Beta Function
   8. 1.7 - Relation Between Beta and Gamma Functions
   9. 1.8 - Multiplication Formula
   10. 1.9 - Legendre's Duplication Formula
   11. Exercise 1.2
   12. 1.10 - Legendre Functions
   13. Exercise 1.3
   14. 1.11 - Bessel Functions
   15. Exercise 1.4
8. Chapter 2. Functions of a Complex Variable
   1. 2.1 - Introduction
   2. 2.2 - Complex Numbers—Complex Plane
   3. Exercise 2.1
   4. Exercise 2.2
   5. 2.3 - Laplace's Equation: Harmonic and Conjugate Harmonic Functions
   6. Exercise 2.3
9. Chapter 3. Elementary Functions
   1. 3.1 - Introduction
   2. 3.2 - Elementary Functions of a Complex Variable
   3. Exercise 3.1
10. Chapter 4. Complex Integration
    1. 4.1 - Introduction
    2. 4.2 - Basic Concepts
    3. 4.3 - Complex Line Integral
    4. 4.4 - Cauchy–Goursat Theorem
    5. 4.5 - Cauchy's Theorem for Multiply-Connected Domain Theorem
    6. 4.6 - Cauchy's Integral Formula (C.I.F.) or Cauchy's Formula Theorem
    7. 4.7 - Morera's Theorem (Converse of Cauchy's Theorem)
    8. 4.8 - Cauchy's Inequality
    9. Exercise 4.1
11. Chapter 5. Complex Power Series
    1. 5.1 - Introduction
    2. 5.2 - Sequences and Series
    3. 5.3 - Power Series
    4. 5.4 - Series of Complex Functions
    5. 5.5 - Uniform Convergence of a Series of Functions
    6. 5.6 - Weierstrass's M-Test
    7. 5.7 - Taylor's Theorem (Taylor Series)
    8. 5.8 - Laurent Series
    9. Exercise 5.1
12. Chapter 6. Calculus of Residues
    1. 6.1 - Evaluation of Real Integrals
    2. Exercise 6.1
    3. Exercise 6.2
    4. Exercise 6.3
13. Chapter 7. Argument Principle and Rouche's Theorem
    1. 7.1 - Introduction
    2. 7.2 - Meromorphic Function
    3. 7.3 - Argument Principle (Repeated Single Pole/Zero)
    4. 7.4 - Generalised Argument Theorem
    5. 7.5 - Rouche's Theorem
    6. 7.6 - Liouville Theorem
    7. 7.7 - Fundamental Theorem of Algebra
    8. 7.8 - Maximum Modulus Theorem for Analytic Functions
    9. Exercise 7.1
14. Chapter 8. Conformal Mapping
    1. 8.1 - Introduction
    2. 8.2 - Conformal Mapping: Conditions for Conformality
    3. 8.3 - Conformal Mapping by Elementary Functions
    4. 8.4 - Some Special Transformations
    5. 8.5 - Bilinear or Mobius or Linear Fractional Transformations
    6. 8.6 - Fixed Points of the Transformation w = (az+b)/(cz+d)
    7. Exercise 8.1
15. Question Bank
    1. Multiple Choice Questions
    2. Fill in the Blanks
    3. Match the Following
    4. True or False Statements
16. Question Papers
17. Notes
    1. Chapter 1
    2. Chapter 2
    3. Chapter 4
    4. Chapter 5
    5. Chapter 7
    6. Chapter 8
18. Bibliography
19. Acknowledgement
20. Copyright