What to read after ADVANCED CALCULUS & PARTIAL DIFFERENTIAL EQUATIONS?

Unit-I

0. Historical Background .... i-iii

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 .... 1-33

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 .... 34-80

Unit-II

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

term series .... 81-146

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

convergence of Series of real Terms .... 147-163

5. Uniform Continuity .... 164-185

6. Chain Rule of Differentiability .... 186-202

7. Mean Value Theorems and Their Geometrical Interpretations .... 203-228

Unit-III

8. Limit and continuity of functions of two variables .... 229-256

9. Change of Variables .... 257-280

10. Euler’s Theorem on Homogeneous Functions .... 281-294

11. Taylor’s Theorem For functions of two Variables .... 295-307

12. Jacobians .... 308-337

13. Maxima and Minima of Functions of Two Variables .... 338-354

14. Lagrange’s Multipliers Method .... 355-367

15. Beta and Gamma Functions .... 368-395

Unit-IV

16. Partial Differential Equations of The first order .... 396-415

17. Lagrange’s Solution .... 416-440

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

by methods other than the general method .... 441-462

19. Charpit’s General Method .... 463-474

20. Partial Differential Equation of Second and Higher Order .... 475-485

Unit-V

21. Classification of Partial Differential Equations of Second Order .... 486-494

22. Homogeneous and Non-homogeneous Partial Differential

Equations of Constant coefficients .... 495-541

23. Partial Differential Equations Reducible to Equtions with

Constant Coefficients .... 542-551