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Mathematics for B.Sc. Students: Ring Theory and Linear Algebra-I, Multivariate Calculus, Semester V (NEP 2020 Bihar)

Mathematics for B.Sc. Students: Ring Theory and Linear Algebra-I, Multivariate Calculus, Semester V (NEP 2020 Bihar)

Author : H K Dass, Rajnish Verma & Rama Verma

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  • ISBN : 9789369583201
  • Pages : 608
  • Binding : Paperback
  • Language : English
  • Imprint : S Chand Publishing
  • © year : 2026
  • Size : 6.50*9.25

Price : 675.00 540.00

Quantity : - +

This textbook has been designed to meet the needs of B.Sc. Fifth Semester students of Mathematics as per Common Minimum Syllabus prescribed for Patna University and other Universities and Colleges under the recommended National Education Policy 2020 in Bihar. The book comprehensively covers two important mathematical areas—Ring Theory and Linear Algebra-I and Multivariate Calculus.

The first part introduces the fundamentals of Ring Theory, including concepts like rings, ideals, homomorphisms and isomorphisms and extends into the core topics of Linear Algebra such as Vector Spaces, Linear Transformations, Eigenvalues, Eigenvectors and the CayleyHamilton Theorem. The second part of the book focuses on Multivariate Calculus, offering an in-depth treatment of Functions of Several Variables, Partial and Total Derivatives, Multiple Integrals, Vector Fields and advanced theorems such as Green's, Stokes' and Gauss' Divergence Theorems.

  • Exhaustive and structured coverage of theory with stepwise explanations
  • Numerous solved examples and illustrative diagrams for conceptual clarity
  • Review exercises and problems for practice at the end of each unit
  • Includes recent university examination questions for effective preparation
  • Written in clear and student-friendly language

This book is an ideal companion for students aiming to build a strong foundation in abstract algebra and advanced calculus, equipping them with essential tools for further studies, research and competitive examinations.

Ring Theory and Linear Algebra-I 

UNIT 1

1. Rings, Field and Properties

UNIT 2

2. Ring Homomorphism and Isomorphism

UNIT 3 

3. Vector Spaces
4. Subspaces
5. Linearly Independent and Dependent Sets
6. Bases and Dimension

UNIT 4

7. Linear Transformations
8. Eigen Values and Eigen Vectors
9. Cayley-Hamilton Theorem

UNIT 5

10. Isomorphisms for Vector Spaces


MULTIVARIATE CALCULUS

UNIT 1

11. Functions of Several Variables - Limit and Continuity
12. Partial Derivatives
13. Total Differential and Differentiability

UNIT 2

14. Gradient and Directional Derivative
15. Tangent Planes and Normal Lines
16. Extrema of Functions of Two Variables
17. Method of Lagrange Multipliers

UNIT 3

18. Double Integrals in Cartesian and Polar Co-ordinates
19. Area and Surface Area using Double Integrals
20. Triple Integrals
21. Volume by Triple Integrals
22. Triple Integration in Cylindrical and Spherical Coordinates
23. Change of Variables in Double and Triple Integrals

UNIT 4

24. Line Integrals and Applications
25. Divergence and Curl
26. Green's, Stoke's and Gauss Divergence Theorems

Latest Questions Papers

 

This textbook has been designed to meet the needs of B.Sc. Fifth Semester students of Mathematics as per Common Minimum Syllabus prescribed for Patna University and other Universities and Colleges under the recommended National Education Policy 2020 in Bihar.

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