Mathematics For B.Sc. Students Semester III: MJ-4 & MJ-5 | Ordinary Differential Equations-I | Abstract Algebra I - NEP 2020 Jharkhand

ORDINARY DIFFERENTIAL EQUATIONS
Unit I: First Order Differential Equations

1. Basic Concepts, Genesis of Ordinary Differential Equations, Order and Degree
2. Variable Separable Equations
3. Homogeneous Differential Equations of First Order and First Degree
4. Linear Differential Equations of First Order and First Degree
5. Exact Differential Equation and Integrating Factors
6. First Order Higher Degree Equations
7. Picard's Theorem for Existence and Uniqueness

Unit II: Second Order Linear Differential Equations

8. Linear Differential Equations of Second Order with Variable Coefficients
9. Linear Differential Equations of Second and Higher Order with Constant Coefficients
10. Transformation by Changing Dependent/Independent Variable
11. Method of Variation of Parameters
12. Method of Undetermined Coefficients

Unit III: Higher Order Linear Differential Equations

13. Wronskian and Properties
14. Euler-Cauchy Equations
15. Methods of Variation of Parameters and Undetermined Coefficients

Unit IV: Applications

16. Orthogonal Trajectories
17. Modeling

ABSTRACT ALGEBRA

Unit I: Groups and Subgroups

18. Group and Permutation
19. Dihedral and Quaternion Groups

Unit II: Subgroups and Cyclic Groups

20. Subgroup and Cyclic Group
21. Euler Theorem and Little Theorem

Unit III: Normal Subgroups and Permutation Groups

22. Normal Subgroups
23. Classification of Subgroups of Cyclic Groups
24. Permutations and Properties

Unit IV: Group Homomorphisms

25. Homomorphism and Isomorphism

Questions from Examination Papers