Name: Mathematical Physics 8 Edition
Brand: Amit Book Depot
Price: 850 INR
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Product: Mathematical Physics (8th Edition)

Authors: H. K. Dass & Dr Rama Verma

Publisher: S. Chand Publishing

Overview

The 8th Edition of Mathematical Physics by H. K. Dass and Dr Rama Verma, published by S. Chand Publishing, is a comprehensive, examination-oriented book designed for undergraduate and postgraduate students of physics, engineering, and applied mathematics. This edition consolidates classical and modern mathematical methods essential for solving real-world physical problems. The book systematically bridges the gap between abstract mathematics and its physical applications, serving as a core mathematical methods resource.

Key Features & Syllabus Coverage

This volume is structured into four distinct units covering over 49 chapters of rigors content. It is an ideal physics reference book for courses on vector calculus, differential equations, complex variables, and linear algebra.

Unit I: Vector Calculus & Core Tools: Begins with a thorough review of vector algebra, progressing to differentiation and integration of vectors. Students master gradient, divergence, and curl with physical interpretations. This section includes orthogonal curvilinear coordinates, multiple integrals (double and triple) with applications to area, centre of gravity, mass, and volume, plus Gamma and Beta functions, theory of errors, and Fourier series.

Unit II: Differential Equations & Variational Methods: Focuses on solving first-order and linear second-order differential equations, covering Cauchy-Euler equations and the method of variation of parameters. It uniquely addresses coupled differential equations and calculus of variation, including maxima and minima of two-variable functions. Physics applications are integrated throughout, making it a strong applied mathematics text.

Unit III: Complex Variables & Special Functions: Delivers a complete course on functions of a complex variable, analytic functions, conformal transformation, and complex integration (Cauchy’s integral theorem and formula). Taylor’s and Laurent’s series lead to the calculus of residues for integration. The unit culminates in series solutions and detailed treatments of Legendre’s, Bessel’s, Hermite's, and Laguerre's functions—essential special functions for quantum mechanics and electromagnetism.

Unit IV: Linear Algebra, PDEs, Transforms & Tensors: It covers abstract vector spaces, linear transformations, null space, row space and column space, inner product spaces, determinants, matrix algebra, rank of a matrix, consistency of linear systems, and eigenvalues/eigenvectors, including the Cayley-Hamilton theorem and diagonalisation. Shifts to partial differential equations (first and second order, constant coefficients), integral transforms (Laplace and inverse Laplace for solving differential equations), the Dirac-delta function, and an introduction to tensor analysis.

Pedagogy & Audience

With numerous solved examples, practice exercises, and a clear step-by-step approach, this engineering mathematics book is suitable for B.Sc. (Physics & Maths), B.E./B.Tech, and M.Sc. Physics students. The 8th edition maintains the clarity of previous editions while updating problem sets. It works equally well for self-study or as a classroom text, helping students develop problem-solving skills in mathematical physics for quantum mechanics, electrodynamics, and fluid dynamics.

Conclusion

Mathematical Physics, 8th Edition, by S. Chand Publishing, remains a trusted, detailed, and affordable choice for mastering the mathematics underlying physical laws. Whether you need vector analysis, differential equation solutions, or complex integration, this book provides a systematic and rigors foundation.

Have Doubts Regarding This Product ? Ask Your Question

Q1

Does this book cover Cauchy’s integral theorem in detail?

A1

Yes. Unit III includes complex integration with Cauchy’s integral theorem, Cauchy’s integral formula, and derivatives of analytic functions for problem-solving.
Q2

Are orthogonal curvilinear coordinates discussed?

A2

Yes. Chapter 4 covers orthogonal curvilinear coordinates, essential for understanding gradient, divergence, and curl in non-Cartesian systems like spherical and cylindrical coordinates.
Q3

Which special functions are included?

A3

Chapter 28-31 cover Legendre’s, Bessel’s, Hermite, and Laguerre functions with series solutions of second-order differential equations.
Q4

Does it teach Laplace transforms for differential equations?

A4

Yes. Chapters 46-47 cover Laplace and inverse Laplace transforms explicitly for solving differential equations, including the Dirac-Delta function.
Q5

Is linear algebra fully covered?

A5

Yes. Unit IV covers abstract vector spaces, linear transformations, null space, row space, column space, inner products, eigenvalues, and Cayley-Hamilton theorem.
Q6

Does it have calculus of variations?

A6

Yes. Chapter 18 covers calculus of variation, including maxima/minima of two-variable functions, important for Lagrangian mechanics.
Q7

Are multiple integrals with physical applications included?

A7

Yes. Chapters 5-8 cover double and triple integrals applied to area, center of gravity, mass, and volume calculation.
Q8

Does it cover series solutions of ODEs?

A8

Yes. Chapter 27 details series solutions of second-order differential equations as a foundation for Legendre and Bessel functions.
Q9

Are partial differential equations with constant coefficients included?

A9

Yes. Chapter 43 covers linear and non-linear PDEs with constant coefficients of 2nd order, plus applications in Chapter 44.
Q10

Does it cover conformal transformation?

A10

Yes. Chapter 23 explains conformal transformation as part of complex variable theory, useful for electrostatics and fluid flow.

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UNIT - I

1. Review of Vector Algebra

2. Differentiation of Vectors

- (Point Function, Gradient, Divergence and Curl of a Vector and Their Physical Interpretations)

3. Integration of Vectors

4. Orthogonal Curvilinear Coordinates

5. Double Integrals

6. Application of the Double Integrals

- Area, Centre of Gravity, Mass, Volume)

7. Triple Integration

8. Application of Triple Integration

9. Gamma and Beta Functions

10. Theory of Errors

11. Fourier Series

UNIT II

12. Differential Equations of First Order

13. Linear Differential Equations of Second Order

14. Cauchy - Euler Equations, Method of Variation of Parameters

15. Differential Equations of Other Types

16. Coupled Differential Equations

17. Applications to Differential Equations

18. Calculus of Variation

19. Maxima and Minima of Functions (two variables)

UNIT III

20. Complex Numbers

21. Expansion of Trigonometric Functions

22. Functions of Complex Variable, Analytic Function

23. Conformal Transformation

24. Complex Integration

- (Cauchy’s Integral Theorem, Cauchy’s Integral Formula for Derivatives of Analytic Functions)

25. Taylor’s and Laurent’s Series

26. The Calculus of Residues (Integration)

27. Series Solutions of Second-Order Differential Equations

28. Legendre’s Functions

29. Bessel’s Functions

30. Hermite Function

31. Laguerre's Functions

UNIT IV

32. Abstract Vector Spaces

33. Vectors in Rⁿ

34. Linear Transformations

35. Basis of Null Space, Row Space and Column Space

36. Real Inner Product Spaces

37. Determinants

38. Algebra of Matrices

39. Rank of Matrix

40. Consistency of Linear System of Equations and their Solution (Linear Dependence)

41. Eigen Values, Eigen Vector, Cayley Hamilton Theorem, Diagonalisation (Complex and Unitary Matrices)

42. First Order Lagrange’s Linear and Non-Linear Partial Differential Equations

43. Linear and Non-linear Partial Differential Equations with Constant Coefficients of 2nd Order

44. Applications of Partial Differential Equations

45. Integral Transforms

46. Laplace Transform

47. Inverse Laplace Transforms (Solutions of differential equations)

48. Dirac-Delta Function

49. Tensor Analysis