ADVANCED CALCULUS & PARTIAL DIFFERENTIAL EQUATIONS (IN HINDI)
α’αααΈααααα βα’αα‘α·α ααααΌαα·αααα
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, BoundedΒ
and Monotonic Sequences, Cauchyβs 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 Leibrintrβs 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. Eulerβs Theorem on Homogeneous Functions ....
11. Taylorβs Theorem For functions of two Variables ....
12. Jacobians ....
13. Maxima and Minima of Functions of Two Variables ....
14. Lagrangeβs Multipliers Method ....
15. Beta and Gamma Functions ....
Unit-IV
16. Partial Differential Equations of The first order ....
17. Lagrangeβs Solution ....
18. Some Special types of equations which can be solved easily
by methods other than the general method ....
19. Charpitβs 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 ....
