Unit-I

0. Historical Background ....

1. Field Structure and Ordered Structure of R, Intervals, Bounded

and unbounded sets, Supremum and infimum, Completeness

in R, Absolute value of a real Number ....

2. Sequence of Real Numbers, Limit of a Sequence, Bounded 

and Monotonic Sequences, Cauchy’s General Principle of

Convergence, Algebra of Sequence and Some Important

Theorems ....

Unit-II

3. Series of non-negative terms, Convergence of positive

term series ....

4. Alternating Series and Leibrintr’s test, Absolute and conditional

convergence of Series of real Terms ....

5. Uniform Continuity ....

6. Chain Rule of Differentiability ....

7. Mean Value Theorems and Their Geometrical Interpretations ....

Unit-III

8. Limit and continuity of functions of two variables ....

9. Change of Variables ....

10. Euler’s Theorem on Homogeneous Functions ....

11. Taylor’s Theorem For functions of two Variables ....

12. Jacobians ....

13. Maxima and Minima of Functions of Two Variables ....

14. Lagrange’s Multipliers Method ....

15. Beta and Gamma Functions ....

Unit-IV

16. Partial Differential Equations of The first order ....

17. Lagrange’s Solution ....

18. Some Special types of equations which can be solved easily

by methods other than the general method ....

19. Charpit’s General Method ....

20. Partial Differential Equation of Second and Higher Order ....

Unit-V

21. Classification of Partial Differential Equations of Second Order ....

22. Homogeneous and Non-homogeneous Partial Differential

Equations of Constant coefficients ....

23. Partial Differential Equations Reducible to Equtions with

Constant Coefficients ....