Mathematical Method B.Sc. 2nd Year 3rd Sem Vandana

This comprehensive book on Mathematical Methods is an essential resource for students of B.Sc. 2nd Year, 3rd Semester. Authored by renowned scholars Dr. Vikash Rana, Dr. A.K. Singh, Dr. A.K. Srivastava, Dr. C.S. Singh, and Dr. Vidya Sagar Chaube, the book delves into critical mathematical concepts necessary for higher education. Published by Vandana Publication Gorakhpur, the book is structured into four key units, each addressing fundamental topics in mathematics. From limits and continuity to the calculus of variations, each unit is meticulously crafted to enhance the learning experience.

Contents:

• Unit 1:
  1. Limits and Continuity (Functions of Two Variables) (Pages 1-16)
  2. Differentiability and Taylor’s Series Expansion (Pages 17-37)
  3. Maxima and Minima (Pages 38-62)
  4. Exponential Functions and Logarithm of Complex Quantities (Pages 63-104)
• Unit 2: 5. The Laplace Transform (Pages 105-144) 6. The Inverse Laplace Transform (Pages 145-166) 7. Application of Laplace Transform to Differential and Integral Equations (Pages 167-196)
• Unit 3: 8. Integral Transform (Fourier Transform and Fourier Series) (Pages 197-246)
• Unit 4: 9. Calculus of Variations (Pages 247-295)
• Subject: Mathematics (Compulsory)
  Class: B.Sc. 2nd Year, 3rd Semester
  Authors: Dr. Vikash Rana, Dr. A.K. Singh, Dr. A.K. Srivastava, Dr. C.S. Singh, Dr. Vidya Sagar Chaube
  Pages: 295
  Publication: Vandana Publication Gorakhpur
• Contents:
  • Unit 1:
    1. Limits and Continuity (Functions of Two Variables) (Pages 1-16)
       • Explores the foundational concepts of limits and continuity for functions of two variables, essential for understanding more complex mathematical functions.
    2. Differentiability and Taylor’s Series Expansion (Pages 17-37)
       • Covers the principles of differentiability and introduces Taylor’s Series, a crucial tool for approximating functions.
    3. Maxima and Minima (Pages 38-62)
       • Discusses techniques for finding the maximum and minimum values of functions, which is fundamental in optimization problems.
    4. Exponential Functions and Logarithm of Complex Quantities (Pages 63-104)
       • Examines exponential functions and logarithms, extending these concepts to complex numbers.
  • Unit 2: 5. The Laplace Transform (Pages 105-144)
    • Introduces the Laplace transform, a powerful integral transform used to solve differential equations.
    6. The Inverse Laplace Transform (Pages 145-166)
       • Covers the methods for finding the inverse Laplace transform, critical for applying the Laplace transform to real-world problems.
    7. Application of Laplace Transform to Differential and Integral Equations (Pages 167-196)
       • Discusses practical applications of the Laplace transform in solving differential and integral equations.
  • Unit 3: 8. Integral Transform (Fourier Transform and Fourier Series) (Pages 197-246)
    • Explores the Fourier transform and Fourier series, key tools in analyzing periodic functions and solving partial differential equations.
  • Unit 4: 9. Calculus of Variations (Pages 247-295)
    • Introduces the calculus of variations, focusing on optimizing functionals, which has applications in physics, economics, and engineering.