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Engineering Mathematics, Volume III

Book Description

Mathematics lays the basic foundation for engineering students to pursue their core subjects. In Engineering Mathematics-III, the topics have been dealt with in a style that is lucid and easy to understand, supported by illustrations that enable the student to assimilate the concepts effortlessly. Each chapter is replete with exercises to help the student gain a deep insight into the subject. The nuances of the subject have been brought out through more than 300 well-chosen, worked-out examples interspersed across the book.

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