Author : H K Dass, Rajnish Verma & Rama Verma
Price : 775.00 620.00
This textbook has been designed to meet the needs of the B.Sc. Fifth Semester students of Mathematics as per the Common Minimum Syllabus prescribed for Ranchi University and other Universities and Colleges under the recommended National Education Policy 2020 in Jharkhand. The book is divided into three major parts, and it offers an in-depth exploration of foundational and advanced mathematical concepts:
Enriched with clear definitions, detailed theorems, illustrative examples, and exercises, this volume is ideal for building both theoretical understanding and practical problem-solving skills. It is an essential companion for students preparing for university examinations as well as competitive tests.
MJ9: REAL ANALYSIS-II
Unit-I: Limit and Continuity
1 Limit
2. Continuity
Unit-II: Differentiability
3. Differentiability
4. Mean Value Theorems
Unit III: Riemann Integration
5. Riemann Integrals
Unit IV: Improper Integrals
6. Improper Integral
7. Beta and Gamma Functions
8. Change of Order of Integration
9. Change of Variables of Integration
MJ10: LINEAR ALGEBRA & HYDROSTATICS
Unit-I: Vector Spaces
10. Vector Spaces
11. Subspaces
12. Linearly Independent and Dependent Sets
13. Bases and Dimension
Unit-II: Linear Transformations
14. Linear Transformations
Unit III: Further Properties of Linear Transformations
15. Isomorphism and Dual of Vector Spaces
16. Eigen Vectors and Eigen Values and Diagonalisation of Linear Transformation
17. Cayley-Hamilton Theorem and Inverse
Unit-IV: Hydrostatics
18. Cayley-Hamilton Theorem and Inverse
MJ 11: PARTIAL DIFFERENTIAL EQUATIONS & CALCULUS OF VARIATIONS
Unit I: First Order Partial Differential Equations
19. First Order Partial Differential Equations
20. Equations Solved by Methods Other than General Method
Unit-II: Second Order Partial Differential Equations with Constant Coefficients
21. Second Order Partial Differential Equations with Constant Coefficients
Unit-III: Second Order Partial Differential Equations with Variable Coefficients
22. Partial Differential Equations Reducible to Equations with Constant Coefficient
23. Second Order Partial Differential Equations with Variable Coefficients
Unit IV: Calculus of Variations-Variational Problems with Fixed Boundaries
24. Calculus of Variations
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